Posts Tagged planck length

Recent Postings from planck length

Spacetime-symmetry violations: motivations, phenomenology, and tests

An important open question in fundamental physics concerns the nature of spacetime at distance scales associated with the Planck length. The widespread belief that probing such distances necessitates Planck-energy particles has impeded phenomenological and experimental research in this context. However, it has been realized that various theoretical approaches to underlying physics can accommodate Planck-scale violations of spacetime symmetries. This talk surveys the motivations for spacetime-symmetry research, the SME test framework, and experimental efforts in this field.

Cosmological Constant from the Emergent Gravity Perspective

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $\Lambda$, with the dimensionless parameter $\Lambda L_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value $4 \pi$, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

Cosmological Constant from the Emergent Gravity Perspective [Cross-Listing]

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $\Lambda$, with the dimensionless parameter $\Lambda L_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value $4 \pi$, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

Cosmological Constant from the Emergent Gravity Perspective [Cross-Listing]

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $\Lambda$, with the dimensionless parameter $\Lambda L_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value $4 \pi$, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

$\lambda\phi^{4}$ Kink and sine-Gordon Soliton in the GUP Framework

We consider $\lambda\phi^{4}$ kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to $p^4$ and the generalized Schr\"odinger equation is expressed as a forth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with 1-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter so that the effects of the minimal length have the dominant role.

$\lambda\phi^{4}$ Kink and sine-Gordon Soliton in the GUP Framework [Replacement]

We consider $\lambda\phi^{4}$ kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to $p^4$ and the generalized Schr\"odinger equation is expressed as a forth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with 1-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter so that the effects of the minimal length have the dominant role.

Why the length of a quantum string cannot be Lorentz contracted [Cross-Listing]

We propose a quantum gravity-extended form of the classical length contraction law obtained in Special Relativity. More specifically, the framework of our discussion is the UV self-complete theory of quantum gravity. Against this background, we show how our results are consistent with, i) the generalised form of the Uncertainty Principle (GUP), ii) the so called hoop-conjecture which we interpret, presently, as the saturation of a Lorentz boost by the formation of a black hole in a two-body scattering, and iii) the intriguing notion of "classicalization" of trans-Planckian physics. Pushing these ideas to their logical conclusion, we argue that there is a physical limit to the Lorentz contraction rule in the form of some minimal universal length determined by quantum gravity, say the Planck Length, or any of its current embodiments such as the string length, or the TeV quantum gravity length scale. In the latter case, we determine the \emph{critical boost} that separates the ordinary "particle phase," characterized by the Compton wavelength, from the "black hole phase", characterized by the effective Schwarzschild radius of the colliding system. Finally, with the "classicalization" of quantum gravity in mind, we comment on the remarkable identity, to our knowledge never noticed before, between three seemingly independent universal quantities, namely, a) the "string tension", b) the "linear energy density," or \emph{tension} that exists at the core of all Schwarzschild black holes, and c) the "superforce" i.e., the Planckian limit of the static electro-gravitational force and, presumably, the unification point of all fundamental forces.

Planck's uncertainty principle and the saturation of Lorentz boosts by Planckian black holes

A basic inconsistency arises when the Theory of Special Relativity meets with quantum phenomena at the Planck scale. Specifically, the Planck length is Lorentz invariant and should not be affected by a Lorentz boost. We argue that Planckian relativity must necessarily involve the effect of black hole formation. Recent proposals for resolving the noted inconsistency seem unsatisfactory in that they ignore the crucial role of gravity in the saturation of Lorentz boosts. Furthermore, an invariant length at he Planck scale amounts to a universal quantum of resolution in the fabric of spacetime. We argue, therefore, that the universal Planck length requires an extension of the Uncertainty Principle as well. Thus, the noted inconsistency lies at the core of Quantum Gravity. In this essay we reflect on a possible resolution of these outstanding problems.

Distribution of Entropy of Bardeen Regular Black Hole with Corrected State Density

We consider corrections to all orders in the Planck length on the quantum state density, and calculate the statistical entropy of the scalar field on the background of the Bardeen regular black hole numerically. We obtain the distribution of entropy which is inside the horizon of black hole and the contribution of the vicinity of horizon takes a great part of the whole entropy.

Notes on several phenomenological laws of quantum gravity [Cross-Listing]

Phenomenological approaches to quantum gravity try to infer model-independent laws by analyzing thought experiments and combining both quantum, relativistic, and gravitational ingredients. We first review these ingredients -three basic inequalities- and discuss their relationships with the nature of fundamental constants. In particular, we argue for a covariant mass bound conjecture: in a spacetime free of horizon, the mass inside a surface $A$ cannot exceed $16 \pi G^2 m^2< A $, while the reverse holds in a spacetime with horizons. This is given a precise definition using the formalism of light-sheets. We show that $\hbar/c$ may be also given a geometrical interpretation, namely $4 \pi \hbar^2/m^2< A$. We then combine these inequalities and find/review the following: (1) Any system must have a size greater than the Planck length, in the sense that there exists a minimal area (2) We comment on the Minimal Length Scenarios and the fate of Lorentz symmetry near the Planck scale (3) Quanta with transplanckian frequencies are allowed in a large enough boxes (4) There exists a mass-dependent maximal acceleration given by $m c^3/\hbar$ if $m<m_p$ and by $c^4/G m$ if $m>m_p$ (5) There exists a mass dependent maximal force and power (6) There exists a maximal energy density and pressure (7) Physical systems must obey the Holographic Principle (8) Holographic bounds can only be saturated by systems with $m>m_p$; systems lying on the “Compton line” $l \sim 1/m$ are fundamental objects without substructures (9) We speculate on a new bound from above for the action. In passing, we note that the maximal acceleration is of the order of Milgrom’s acceleration $a_0$ for ultra-light particles ($m\sim H_0)$ that could be associated to the Dark Energy fluid. This suggests designing toy-models in which modified gravity in galaxies is driven by the DE field, via the maximal acceleration principle.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Quantum astrometric observables II: time delay in linearized quantum gravity [Replacement]

A clock synchronization thought experiment is modeled by a diffeomorphism invariant "time delay" observable. In a sense, this observable probes the causal structure of the ambient Lorentzian spacetime. Thus, upon quantization, it is sensitive to the long expected smearing of the light cone by vacuum fluctuations in quantum gravity. After perturbative linearization, its mean and variance are computed in the Minkowski Fock vacuum of linearized gravity. The na\"ive divergence of the variance is meaningfully regularized by a length scale $\mu$, the physical detector resolution. This is the first time vacuum fluctuations have been fully taken into account in a similar calculation. Despite some drawbacks this calculation provides a useful template for the study of a large class of similar observables in quantum gravity. Due to their large volume, intermediate calculations were performed using computer algebra software. The resulting variance scales like $(s \ell_p/\mu)^2$, where $\ell_p$ is the Planck length and $s$ is the distance scale separating the ("lab" and "probe") clocks. Additionally, the variance depends on the relative velocity of the lab and the probe, diverging for low velocities. This puzzling behavior may be due to an oversimplified detector resolution model or a neglected second order term in the time delay.

Bimetric Gravity, Variable Speed of Light Cosmology and Planck2013 [Cross-Listing]

A bimetric gravity model with a variable speed of light is shown to be in agreement with the results reported from the Planck satellite in 2013. The predicted scalar mode spectral index is $n_s\approx 0.96$ and its running is $\alpha_s\approx 8\times 10^{-4}$ when the fundamental length scale $\ell_0$ in the model is fixed to be $\ell_0\approx 10^5\ell_P$, where $\ell_P$ is the Planck length $\ell_P=1.62\times 10^{-33}\,{\rm cm}$, giving the observed CMB fluctuations: $\delta_H\approx 10^{-5}$. The enlarged lightcone ensures that horizon and flatness problems are solved. The model is free from many of the fine-tuning problems of the inflationary models and the fluctuations that form the seeds of structure formation do not lead to a chaotic inhomogeneous universe and the need for a multiverse.

Wave function of the Universe, preferred reference frame effects and metric signature transition [Replacement]

Non-minimally coupled Brans Dicke (BD) gravity with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter described in terms of the BD field as $~\phi^n.$ Aim of the paper is to seek cosmological models exhibiting metric signature transition. The problem is studied in both classical and quantum cosmological approach. Solutions of classical dynamical equations lead to nonsingular inflationary scale factor of space time as $R(t)=l_p\cosh(t/l_p)$ where $l_p$ denotes to Planck length. Corresponding Euclidean signature scale factor is obtained directly by changing $t\to it$ which describes re-collapsing universe. Dynamical vector field together with the BD scalar field treats as fluid with time dependent barotropic index $\gamma(t)$. At large scales of the space time we obtain $\gamma(t)\to -1$ corresponding to dark matter dominant of the fluid. Positive values of this parameter is obtained only at the Euclidean regime of the space time and whose values are changed from $-\infty$ to $+\infty$ on the metric signature transition hypersurface $t=0$ where metric is degenerated. Dust and radiation domains of the fluid stands on the Euclidean regime of the space time. Euclidean regime is also contained $\gamma(t)<0$ corresponding dark matter dominate for short times. In the quantum cosmological approach we solve corresponding Weeler De Witt (WD) wave equation with large values of BD parameter. Assuming a discreet non-zero ADM mass $M_j=2(2j+1)/l_p$ with $j=0,1,2,\cdots$, WD wave solution is described in terms of simple harmonic quantum Oscillator eigne functionals. WD wave solutions of the Lorentzian and Euclidean signature of the flat RW space time have same nonzero values on the metric signature transition hypersurface and whose maximum value is obtained at ground state $j=0$.

Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry [Replacement]

Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the analysis of some candidate indirect implications of spacetime quantization, such as a possible curvature of momentum space. Some recent proposals have raised hope that we might also gain direct experimental access to quantum properties of spacetime, by finding evidence of limitations to the measurability of the center-of-mass coordinates of some macroscopic bodies. However I here observe that the arguments that originally lead to speculating about spacetime quantization do not apply to the localization of the center of mass of a macroscopic body. And I also analyze some popular formalizations of the notion of quantum spacetime, finding that when the quantization of spacetime is Planckian for the constituent particles then for the composite macroscopic body the quantization of spacetime is much weaker than Planckian. These results show that finding evidence of spacetime quantization with studies of macroscopic bodies is extremely unlikely. And they also raise some conceptual challenges for theories of mechanics in quantum spacetime, in which for example free protons and free atoms should feel the effects of spacetime quantization differently.

Solution to the cosmological constant problem

The current, accelerated, phase of expansion of our universe can be modeled in terms of a cosmological constant. A key issue in theoretical physics is to explain the extremely small value of the dimensionless parameter \Lambda L_P^2 ~ 3.4 x 10^{-122}, where L_P is the Planck length. We show that this value can be understood in terms of a new dimensionless parameter N, which counts the number of modes inside a Hubble volume crossing the Hubble radius, from the end of inflation until the beginning of the accelerating phase. Theoretical considerations suggest that N = 4\pi. On the other hand, N is related to ln (\Lambda L_P^2) and two other parameters which will be determined by high energy particle physics: (a) the ratio between the number densities of photons and matter and (b) the energy scale of inflation. For realistic values of (n_\gamma / n_m) ~ 4.3 x 10^{10} and E_{inf} ~ 10^{15} GeV, our postulate N =4\pi leads to the observed value of the cosmological constant. This provides a unified picture of cosmic evolution relating the early inflationary phase to the late accelerating phase.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Replacement]

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination of the precise scale at which quantum fluctuations of space-time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Replacement]

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination of the precise scale at which quantum fluctuations of space-time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Replacement]

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination of the precise scale at which quantum fluctuations of space-time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Cross-Listing]

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination of the precise scale at which quantum fluctuations of space-time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime.

Minimum-length deformed QM/QFT, issues and problems [Replacement]

Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the framework of a minisuperspace approximation, is uniquely tied to the fact that this sort of quantum mechanics implies the reduced Hilbert space of state-vectors consisting of the functions nonlocalizable beneath the Planck length. (Corrections to the Hamiltonian do not provide such an universal mechanism for avoiding singularities.) Following this discussion, as a next step we take a critical view of the meaning of wave-function in such a quantum theory. For this reason we focus on the construction of current vector and the subsequent continuity equation. Some issues gained in the framework of this discussion are then considered in the context of field theory. Finally, we discuss the classical limit of the minimum-length deformed quantum mechanics and its dramatic consequences.

Minimum-length deformed QM/QFT, issues and problems [Replacement]

Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the framework of a minisuperspace approximation, is uniquely tied to the fact that this sort of quantum mechanics implies the reduced Hilbert space of state-vectors consisting of the functions nonlocalizable beneath the Planck length. (Corrections to the Hamiltonian do not provide such an universal mechanism for avoiding singularities.) Following this discussion, as a next step we take a critical view of the meaning of wave-function in such a quantum theory. For this reason we focus on the construction of current vector and the subsequent continuity equation. Some issues gained in the framework of this discussion are then considered in the context of field theory. Finally, we discuss the classical limit of the minimum-length deformed quantum mechanics and its dramatic consequences.

Trans-Planckian Issues for Inflationary Cosmology

The accelerated expansion of space during the period of cosmological inflation leads to trans-Planckian issues which need to be addressed. Most importantly, the physical wavelength of fluctuations which are studied at the present time by means of cosmological observations may well originate with a wavelength smaller than the Planck length at the beginning of the inflationary phase. Thus, questions arise as to whether the usual predictions of inflationary cosmology are robust considering our ignorance of physics on trans-Planckian scales, and whether the imprints of Planck-scale physics are at the present time observable. These and other related questions are reviewed in this article.

Is a tabletop search for Planck scale signals feasible [Cross-Listing]

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon’s degree of freedom with one of a macroscopic probe to test Wheeler’s conception of "spacetime foam", the assertion that on length scales of the order Planck’s, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

Is a tabletop search for Planck scale signals feasible? [Replacement]

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon’s degree of freedom with one of a macroscopic probe to test Wheeler’s conception of "quantum foam", the assertion that on length scales of the order Planck’s, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

The Physical Principle that determines the Value of the Cosmological Constant [Cross-Listing]

Observations indicate that the evolution of our universe can be divided into three epochs consisting of early time inflation, radiation (and matter) domination and the late time acceleration. One can associate with each of these epochs a number N which is the phase space volume of the modes which cross the Hubble radius during the corresponding epoch. This number turns out to be (approximately) the same for the cosmologically relevant ranges of the three epochs. When the initial de Sitter space is characterized by the Planck length, the natural value for N is 4\pi. This allows us to determine the cosmological constant which drives the late time acceleration, to be \Lambda L_P^2 = 3 \exp(-24\pi^2 \mu) where \mu\ is a number of order unity. This expression leads to the observed value of cosmological constant for \mu ~ 1.19. The implications are discussed.

A simple model of universe with a polytropic equation of state

We construct a simple model of universe with a generalized equation of state $p=(\alpha +k\rho^{1/n})\rho c^2$ having a linear component $p=\alpha\rho c^2$ and a polytropic component $p=k\rho^{1+1/n}c^2$. For $\alpha=1/3$, $n=1$ and $k=-4/(3\rho_P)$, where $\rho_P=5.16 10^{99} {\rm g/m}^3$ is the Planck density, this equation of state provides a model of the early universe without singularity describing the transition between the pre-radiation era and the radiation era. The universe starts from $t=-\infty$ but, when $t<0$, its size is less than the Planck length $l_P=1.62 10^{-35} {\rm m}$. The universe undergoes an inflationary expansion that brings it to a size $a_1=2.61 10^{-6} {\rm m}$ on a timescale of a few Planck times $t_P=5.39 10^{-44} {\rm s}$. When $t \gg t_P$, the universe decelerates and enters in the radiation era. For $\alpha=0$, $n=-1$ and $k=-\rho_{\Lambda}$, where $\rho_{\Lambda}=7.02 10^{-24} {\rm g/m}^3$ is the cosmological density, this equation of state describes the transition from a decelerating universe dominated by baryonic and dark matter to an accelerating universe dominated by dark energy (second inflation). The transition takes place at a size $a_2=8.95 10^{25} {\rm m}$ corresponding to a time of the order of the cosmological time $t_{\Lambda}=1.46 \times 10^{18} {\rm s}$. This polytropic model reveals a nice "symmetry" between the early and late evolution of the universe, the cosmological constant $\Lambda$ in the late universe playing a role similar to the Planck constant $\hbar$ in the early universe. We interpret the cosmological constant as a fundamental constant of nature describing the "cosmophysics" just like the Planck constant describes the microphysics. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by ${122}$ orders of magnitude. The cosmological constant "problem" may be a false problem.

Models of universe with a polytropic equation of state: I. The early universe

We construct models of universe with a generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider positive indices $n>0$. In that case, the polytropic component dominates in the early universe where the density is high. For $\alpha=1/3$, $n=1$ and $k=-4/(3\rho_P)$, we obtain a model of early universe describing the transition from a pre-radiation era to the radiation era. The universe exists at any time in the past and there is no singularity. However, for $t<0$, its size is less than the Planck length $l_P=1.62 10^{-35} {\rm m}$. In this model, the universe undergoes an inflationary expansion with the Planck density $\rho_P=5.16 10^{99} {\rm g/m}^3$ that brings it to a size $a_1=2.61 10^{-6} {\rm m}$ at $t_1=1.25 10^{-42} {\rm s}$ (about 20 Planck times $t_P$). For $\alpha=1/3$, $n=1$ and $k=4/(3\rho_P)$, we obtain a model of early universe with a new form of primordial singularity: The universe starts at t=0 with an infinite density and a finite radius $a=a_1$. Actually, this universe becomes physical at a time $t_i=8.32 10^{-45} {\rm s}$ from which the velocity of sound is less than the speed of light. When $a\gg a_1$, the universe evolves like in the standard model. We describe the transition from the pre-radiation era to the radiation era by analogy with a second order phase transition where the Planck constant $\hbar$ plays the role of finite size effects (the standard Big Bang theory is recovered for $\hbar=0$).

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe states of flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. It is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that accounts for properties of classical space-time in the macroscopic limit; to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. The model predicts directional fluctuations on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe quantum geometrical states of a flat, emergent space-time on large scales. It excludes all standard quantum degrees of freedom as well as gravity, but describes new quantum properties of position states of a distant massive body in the emergent geometry. The proposed algebra of position operators is manifestly covariant in the classical limit. In the non relativistic limit, it is identical to the standard quantum algebra of angular momentum, with a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The system is discrete and holographic, and agrees with thermodynamic derivations of gravity if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. The model displays quantum geometrical uncertainty in direction with variance given by $\langle \Delta \theta^2\rangle = l_P/\sqrt{4\pi}L$ at separation $L$, and directional fluctuations with this magnitude on timescale $\tau \approx L/c$. To approximate locality in the macroscopic limit, position states of multiple bodies must be entangled, and fluctuations of neighboring bodies must be correlated, simply by proximity. The model and its physical interpretation can be tested by correlating signals between appropriately configured interferometers.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe quantum geometrical states of a flat, emergent space-time on large scales. It excludes all standard quantum degrees of freedom as well as gravity, but describes new quantum properties of position states of a distant massive body in the emergent geometry. The proposed algebra of position operators is manifestly covariant in the classical limit. In the non relativistic limit, it is identical to the standard quantum algebra of angular momentum, with a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$. The system is discrete and holographic, and agrees with thermodynamic derivations of gravity if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. To approximate locality in the macroscopic limit, position states of multiple bodies must be entangled, and fluctuations of neighboring bodies must be correlated, simply by proximity. Coherent directional fluctuations occur on timescale $\tau \approx L/c$. The model and its physical interpretation can be tested by correlating signals between appropriately configured interferometers.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe states of flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. It is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that accounts for properties of classical space-time in the macroscopic limit; to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. The model predicts directional fluctuations on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers.

The Trans-Planckian Problem in the Healthy Extension of Horava-Lifshitz Gravity [Cross-Listing]

Planck scale physics may influence the evolution of cosmological fluctuations in the early stages of cosmological evolution. Because of the quasi-exponential redshifting, which occurs during an inflationary period, the physical wavelengths of comoving scales that correspond to the present large-scale structure of the Universe were smaller than the Planck length in the early stages of the inflationary period. This trans-Planckian effect was studied before using toy models. The Horava-Lifshitz (HL) theory offers the chance to study this problem in a candidate UV complete theory of gravity. In this paper we study the evolution of cosmological perturbations according to HL gravity assuming that matter gives rise to an inflationary background. As is usually done in inflationary cosmology, we assume that the fluctuations originate in their minimum energy state. In the trans-Planckian region the fluctuations obey a non-linear dispersion relation of Corley-Jacobson type. In the “healthy extension” of HL gravity there is an extra degree of freedom which plays an important role in the UV region but decouples in the IR, and which influences the cosmological perturbations. We find that in spite of these important changes compared to the usual description, the overall scale-invariance of the power spectrum of cosmological perturbations is recovered. However, we obtain oscillations in the spectrum as a function of wavenumber with a relative amplitude of order unity and with an effective frequency which scales nonlinearly with wavenumber. Taking the usual inflationary parameters we find that the frequency of the oscillations is so large as to render the effect difficult to observe.

The Trans-Planckian Problem in the Healthy Extension of Horava-Lifshitz Gravity [Replacement]

Planck scale physics may influence the evolution of cosmological fluctuations in the early stages of cosmological evolution. Because of the quasi-exponential redshifting, which occurs during an inflationary period, the physical wavelengths of comoving scales that correspond to the present large-scale structure of the Universe were smaller than the Planck length in the early stages of the inflationary period. This trans-Planckian effect was studied before using toy models. The Horava-Lifshitz (HL) theory offers the chance to study this problem in a candidate UV complete theory of gravity. In this paper we study the evolution of cosmological perturbations according to HL gravity assuming that matter gives rise to an inflationary background. As is usually done in inflationary cosmology, we assume that the fluctuations originate in their minimum energy state. In the trans-Planckian region the fluctuations obey a non-linear dispersion relation of Corley-Jacobson type. In the “healthy extension” of HL gravity there is an extra degree of freedom which plays an important role in the UV region but decouples in the IR, and which influences the cosmological perturbations. We find that in spite of these important changes compared to the usual description, the overall scale-invariance of the power spectrum of cosmological perturbations is recovered. However, we obtain oscillations in the spectrum as a function of wavenumber with a relative amplitude of order unity and with an effective frequency which scales nonlinearly with wavenumber. Taking the usual inflationary parameters we find that the frequency of the oscillations is so large as to render the effect difficult to observe.

The role of quantum expansion in cosmic evolution

A quantum expansion parameter, analogous to the Hubble parameter in cosmology, is defined for a free particle quantum wavefunction. By considering the universe as an initial single Gaussian quantum wavepacket whose mass is that of present-day observable universe and whose size is that of the Planck Length at the Planck Time, it is demonstrated that this quantum expansion parameter has a value at the present epoch of the same order as the value of the Hubble constant. The coincidence suggests examining the effect of including this type of quantum wave expansion in traditional general relativistic cosmology and a sample model illustrating this is presented here. Using standard Einstein-de Sitter cosmology ($\Omega$m = 1) it is found that cosmic acceleration (aka dark energy) arises naturally during cosmic history. The time at which the universe switched from deceleration to acceleration (observationally ~7 Gyr before the present epoch) yields a value for the mass of the wavepacket representing the universe at the Planck Time and its present age. This same mass may then be used to obtain a curve for the cosmic expansion rate versus z. This curve is well fit to observational data. The model is used also to obtain an estimate of the inflationary expansion factor.

A Four-Dimensional {\Lambda}CDM-Type Cosmological Model Induced from Higher Dimensions Using a Kinematical Constraint [Cross-Listing]

A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a 3-dimensional (physical, flat) external space metric and an n-dimensional (compact, flat) internal space metric. A simple kinematical constraint is postulated that correlates the expansion rates of the external and internal spaces in terms of a real parameter \lambda. A specific solution for which both the external and internal spaces expand at different rates is given analytically for n=3. Assuming that the internal dimensions were at Planck length scales at the beginning t=0, the external space starts with a Big Bang and the external and internal spaces both reach the same size after 10^{-176} Gyr. Then during the lifetime of the observed universe (13.7 Gyr), the external dimensions would expand 10^{59} times while the internal dimensions expand only 1.49 times. The effective four dimensional universe would exhibit a behavior consistent with our current understanding of the observed universe. It would start in a stiff fluid dominated phase and evolve through radiation dominated and pressureless matter dominated phases, eventually going into a de Sitter phase at late times.

A Four-Dimensional {\Lambda}CDM-Type Cosmological Model Induced from Higher Dimensions Using a Kinematical Constraint [Replacement]

A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a 3-dimensional (physical, flat) external space metric and an n-dimensional (compact, flat) internal space metric. A simple kinematical constraint is postulated that correlates the expansion rates of the external and internal spaces in terms of a real parameter {\lambda}. A specific solution for which both the external and internal spaces expand at different rates is given analytically for n=3. Assuming that the internal dimensions were at Planck length scales when the external space starts with a Big Bang (t=0), they expand only 1.49 times and stay at Planck length scales even in the present age of the universe (13.7 Gyr). The effective four dimensional universe would exhibit a behavior consistent with our current understanding of the observed universe. It would start in a stiff fluid dominated phase and evolve through radiation dominated and pressureless matter dominated phases, eventually going into a de Sitter phase at late times.

A four-dimensional {\Lambda}CDM-type cosmological model induced from higher dimensions using a kinematical constraint [Replacement]

A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a 3-dimensional (physical, flat) external space metric and an n-dimensional (compact, flat) internal space metric. A simple kinematical constraint is postulated that correlates the expansion rates of the external and internal spaces in terms of a real parameter {\lambda}. A specific solution for which both the external and internal spaces expand at different rates is given analytically for n=3. Assuming that the internal dimensions were at Planck length scales when the external space starts with a Big Bang (t=0), they expand only 1.49 times and stay at Planck length scales even in the present age of the universe (13.7 Gyr). The effective four dimensional universe would exhibit a behavior consistent with our current understanding of the observed universe. It would start in a stiff fluid dominated phase and evolve through radiation dominated and pressureless matter dominated phases, eventually going into a de Sitter phase at late times.

On Quantum Spacetime and the horizon problem [Replacement]

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with the work of Doplicher, Fredenhagen and Roberts (DFR), imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of DFR, since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations. We shall then describe the influence of this minimal length scale in a cosmological model, namely a simple universe filled with radiation, which is effectively described by a conformally coupled scalar field in a conformal KMS state. Solving the backreaction, a power law inflation scenario appears close to the initial singularity. Furthermore, the initial singularity becomes light like and thus the standard horizon problem is avoided in this simple model. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events, which point to a background dependence of the effective Planck length, through which a-causal effects may be transmitted.

Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology [Cross-Listing]

We study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology. The equations of motion include quantum geometry effects and therefore hold at all curvature scales so long as the wavelengths of the modes of interest remain larger than the Planck length. These equations are obtained by including holonomy corrections in an effective Hamiltonian constraint and then using the standard variational principle. The holonomy corrections do not introduce any anomalies in the nontrivial constraint algebra. We also make some comments regarding potential inverse triad corrections.

Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology [Replacement]

We study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology. The equations of motion include quantum geometry effects and hold at all curvature scales so long as the wavelengths of the inhomogeneous modes of interest remain larger than the Planck length. These equations are obtained by including holonomy corrections in an effective Hamiltonian and then using the standard variational principle. We show that the effective scalar and diffeomorphism constraints are preserved by the dynamics. We also make some comments regarding potential inverse triad corrections.

Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology [Replacement]

We study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology. The equations of motion include quantum geometry effects and hold at all curvature scales so long as the wavelengths of the inhomogeneous modes of interest remain larger than the Planck length. These equations are obtained by including holonomy corrections in an effective Hamiltonian and then using the standard variational principle. We show that the effective scalar and diffeomorphism constraints are preserved by the dynamics. We also make some comments regarding potential inverse triad corrections.

Using CMB data to constrain non-isotropic Planck-scale modifications to Electrodynamics

We develop a method to constrain non-isotropic features of Cosmic Microwave Background (CMB) polarization, of a type expected to arise in some models describing quantum gravity effects on light propagation. We describe the expected signatures of this kind of anomalous light propagation on CMB photons, showing that it will produce a non-isotropic birefringence effect, i.e. a rotation of the CMB polarization direction whose observed amount depends in a peculiar way on the observation direction. We also show that the sensitivity levels expected for CMB polarization studies by the \emph{Planck} satellite are sufficient for testing these effects if, as assumed in the quantum-gravity literature, their magnitude is set by the minute Planck length.

Do we live in the universe successively dominated by matter and antimatter? [Cross-Listing]

We wonder if a cyclic universe may be dominated alternatively by matter and antimatter. Such a scenario demands a mechanism for transformation of matter to antimatter (or antimatter to matter) during the final stage of a big crunch. By giving an example, we have shown that in principle such a mechanism is possible. Our mechanism is based on a hypothetical repulsion between matter and antimatter, existing at least deep inside the horizon of a black hole. When universe is reduced to a supermassive black hole of a small size, a very strong field of the conjectured force might create (through a Schwinger type mechanism) particle-antiparticle pairs from the quantum vacuum. The amount of antimatter created from the vacuum is equal to the decrease of mass of the black hole and violently repelled from it. When the size of the black hole is sufficiently small, the creation of antimatter may become so fast, that matter of our Universe might be transformed to antimatter in a fraction of second. Such a fast conversion of matter into antimatter may look as a Big Bang. Our mechanism prevents a singularity; a new cycle might start with an initial size more than 30 orders of magnitude greater than the Planck length, suggesting that there is no need for inflationary scenario in Cosmology. In addition, there is no need to invoke CP violation for explanation of matter-antimatter asymmetry. Simply, our present day Universe is dominated by matter, because the previous universe was dominated by antimatter.

Big bounce from spin and torsion [Replacement]

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density $\epsilon\propto gT^4$ was on the order of $n^2/m_\textrm{Pl}^2$ (in natural units), where $n\propto gT^3$ is the fermion number density and $g$ is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles ($g\approx 100$), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about $10^{32}$ times smaller than its present value, giving $\approx 50 \mum$. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.

Vacuum fluctuations in a supersymmetric model in FRW spacetime [Cross-Listing]

We study a noninteracting supersymmetric model in an expanding FRW spacetime. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density. A short distance cutoff of the order of Planck length provides a scale for the vacuum energy density comparable with the observed cosmological constant. Assuming the presence of a dark energy substance in addition to the vacuum fluctuations of the field an effective equation of state is derived in a selfconsistent approach. The effective equation of state is sensitive to the choice of the cut-off but no fine tuning is needed.

 

You need to log in to vote

The blog owner requires users to be logged in to be able to vote for this post.

Alternatively, if you do not have an account yet you can create one here.

Powered by Vote It Up

^ Return to the top of page ^