Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2010"

Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

Abstract: Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of number of modified theories, including traditional $F(R)$ and Hořava-Lifshitz $F(R)$ gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, non-minimally coupled models, and power-counting renormalizable covariant gravity are discussed. Different representations and relations between such theories are investigated. It is shown that some versions of above theories may be consistent with local tests and may provide qualitatively reasonable unified description of inflation with dark energy epoch. The cosmological reconstruction of different modified gravities is made in great detail. It is demonstrated that eventually any given universe evolution may be reconstructed for the theories under consideration: the explicit reconstruction is applied to accelerating spatially-flat FRW universe. Special attention is paid to Lagrange multiplier constrained and conventional $F(R)$ gravities, for last theory the effective $\Lambda$CDM era and phantom-divide crossing acceleration are obtained. The occurrence of Big Rip and other finite-time future singularities in modified gravity is reviewed as well as its curing via the addition of higher-derivative gravitational invariants.

Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0

Abstract: In this paper, instead of invoking Dark Energy, we try and fit various cosmological observations with a large Gpc scale under-dense region (Void) which is modeled by a Lema?tre-Tolman-Bondi metric that at large distances becomes a homogeneous FLRW metric. We improve on previous analyses by allowing for nonzero overall curvature, accurately computing the distance to the last-scattering surface and the observed scale of the Baryon Acoustic peaks, and investigating important effects that could arise from having nontrivial Void density profiles. We mainly focus on the WMAP 7-yr data (TT and TE), Supernova data (SDSS SN), Hubble constant measurements (HST) and Baryon Acoustic Oscillation data (SDSS and LRG). We find that the inclusion of a nonzero overall curvature drastically improves the goodness of fit of the Void model, bringing it very close to that of a homogeneous universe containing Dark Energy, while by varying the profile one can increase the value of the local Hubble parameter which has been a challenge for these models. We also try to gauge how well our model can fit the large-scale-structure data, but a comprehensive analysis will require the knowledge of perturbations on LTB metrics. The model is consistent with the CMB dipole if the observer is about 15 Mpc off the centre of the Void. Remarkably, such an off-center position may be able to account for the recent anomalous measurements of a large bulk flow from kSZ data. Finally we provide several analytical approximations in different regimes for the LTB metric, and a numerical module for cosmomc, thus allowing for a MCMC exploration of the full parameter space.

On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity

Abstract: The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.

Modified F(R) Horava-Lifshitz gravity: a way to accelerating FRW cosmology

Abstract: We propose a general approach for the construction of modified gravity which is invariant under foliation-preserving diffeomorphisms. Special attention is paid to the formulation of modified $F(R)$ Hořava-Lifshitz gravity (FRHL), whose Hamiltonian structure is studied. It is demonstrated that the spatially-flat FRW equations of FRHL are consistent with the constraint equations. The analysis of de Sitter solutions for several versions of FRHL indicates that the unification of the early-time inflation with the late-time acceleration is possible. It is shown that a special choice of parameters for FRHL leads to the same spatially-flat FRW equations as in the case of traditional $F(R)$-gravity. Finally, an essentially most general modified Hořava-Lifshitz gravity is proposed, motivated by its fully diffeomorphism-invariant counterpart, with the restriction that the action does not contain derivatives higher than the second order with respect to the time coordinate.

Manifestly gauge-invariant general relativistic perturbation theory: I. Foundations

Abstract: Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided eg by cosmic microwave anisotropy probes A key issue in that theory is to extract the gauge-invariant degrees of freedom which allow unambiguous comparison between theory and experiment When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to nth order in terms of quantities that are gauge-invariant up to terms of higher orders becomes highly non-trivial and cumbersome This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature In this series of papers we circumvent these difficulties by passing to a manifestly gauge-invariant framework In other words, we only perturb gauge-invariant, ie measurable quantities, rather than gauge variant ones Thus, gauge invariance is preserved non-perturbatively while we construct the perturbation theory for the equations of motion for the gauge-invariant observables to all orders In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchař as well as the relational formalism due to Rovelli In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge-invariant generalization to higher orders This will also allow us to settle the stability issue in a future publication

Thermodynamics of apparent horizon and modified Friedmann equations

Abstract: Starting from the first law of thermodynamics, dE=T h dS h +W dV, at the apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a quantum-corrected relation, $S=\frac{A}{4G}-\alpha \ln \frac{A}{4G}+\beta \frac{4G}{A}$ , we derive modified Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy including the quantum-corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon. Our study shows that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.

Background independent quantization and the uncertainty principle

Abstract: It is shown that polymer quantization leads to a modified uncertainty principle similar to that motivated by string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to the uncertainty principle acquire a metric dependence. For Friedmann–Robertson–Walker cosmology this translates to a scale factor dependence which gives a large effect in the early Universe.

Applicability of the linearly perturbed FRW metric and Newtonian cosmology

Abstract: It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of nonlinear density perturbations. We discuss why the arguments based on the linear theory are not valid. We emphasize the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.

Modified F(R) Hořava–Lifshitz gravity: a way to accelerating FRW cosmology

Abstract: We propose a general approach for the construction of modified gravity which is invariant under foliation-preserving diffeomorphisms. Special attention is paid to the formulation of a modified F(R) Hořava–Lifshitz gravity (FRHL), whose Hamiltonian structure is studied. It is demonstrated that the spatially flat FRW equations of FRHL are consistent with the constraint equations. The analysis of de Sitter solutions for several versions of FRHL indicates that the unification of the early-time inflation with the late-time acceleration is possible. It is shown that a special choice of parameters for FRHL leads to the same spatially flat FRW equations as in the case of the traditional F(R)-gravity. Finally, an essentially most general modified Hořava–Lifshitz gravity is proposed, motivated by its fully diffeomorphism-invariant counterpart, with the restriction that the action does not contain derivatives higher than the second order with respect to the time coordinate.

Generalized second law of thermodynamics for FRW cosmology with logarithmic correction

Abstract: In the previous analyses in the literature about the generalized second law (GSL) in an accelerated expanding universe the usual relation for the entropy, i.e. , was used for the cosmological horizon entropy. But this entropy relation may be modified due to thermal and quantum fluctuations or corrections motivated by loop quantum gravity giving rise to S=A/4+πα ln(A/4)+γ, where α and γ are some constants whose the values are still in debate in the literature. Our aim is to study the constraints that GSL puts on these parameters. Besides, we investigate the conditions that the presence of such modified terms in the entropy puts on other physical parameters the system such as the temperature of dark energy via requiring the validity of GSL. In our study we consider a spatially flat Friedman-Robertson-Walker universe and assume that it is composed of several interacting components (including dark energy). The model is investigated in the context of thermal equilibrium and non-equilibrium situations. We show that in a (super) accelerated universe the GSL is valid whenever α ( 0 leading to a (negative) positive contribution from logarithmic correction to the entropy. In the case of super acceleration the temperature of the dark energy is obtained to be less than or equal to the Hawking temperature.

Unifying inflation with dark energy in modified F(R) Horava-Lifshitz gravity

Abstract: We study FRW cosmology for a non-linear modified F(R) Horava-Lifshitz gravity which has a viable convenient counterpart. A unified description of early-time inflation and late-time acceleration is possible in this theory, but the cosmological dynamic details are generically different from the ones of the convenient viable F(R) model. Remarkably, for some specific choice of parameters they do coincide. The emergence of finite-time future singularities is investigated in detail. It is shown that these singularities can be cured by adding an extra, higher-derivative term, which turns out to be qualitatively different when compared with the corresponding one of the convenient F(R) theory.

A test of Hořava gravity: the dark energy

Abstract: Recently Ho?ava proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I consider a non-trivial test of the new gravity theory in FRW universe by considering an IR modification which breaks ``softly'' the detailed balance condition in the original Ho?ava model. I separate the dark energy parts from the usual Einstein gravity parts in the Friedman equations and obtain the formula of the equations of state parameter. The IR modified Ho?ava gravity seems to be consistent with the current observational data but we need some more refined data sets to see whether the theory is really consistent with our universe. From the consistency of our theory, I obtain some constraints on the allowed values of w0 and wa in the Chevallier, Polarski, and Linder's parametrization and this may be tested in the near future, by sharpening the data sets.

Interacting entropy-corrected new agegraphic tachyon, K-essence and dilaton scalar field models of dark energy in non-flat universe

Abstract: We present the new agegraphic dark energy model by introducing the quantum corrections to the entropy-area relation in the setup of loop quantum gravity. Employing this new form of dark energy, we investigate the model of interacting dark energy and derive its equation of state. We study the correspondence between the tachyon, K-essence and dilaton scalar field models with the interacting entropy-corrected new agegraphic dark energy model in the non-flat FRW universe. Moreover, we reconstruct the corresponding scalar potentials which describe the dynamics of the scalar field models.

The generalized second law of gravitational thermodynamics on the apparent and event horizons in FRW cosmology

Abstract: We investigate the validity of the generalized second law (GSL) of gravitational thermodynamics on the apparent and event horizons in a non-flat Friedmann?Robertson?Walker (FRW) universe containing dark energy interacting with dark matter. We show that for the dynamical apparent horizon, the GSL is always satisfied throughout the history of the universe for any spatial curvature and it is independent of the equation of state parameter of the interacting dark energy model. On the other hand, for the cosmological event horizon, the validity of the GSL depends on the equation of state parameter of the model.

Effects of cosmological model assumptions on galaxy redshift survey measurements

Abstract: The clustering of galaxies observed in future redshift surveys will provide a wealth of cosmological information. Matching the signal at different redshifts constrains the dark energy driving the acceleration of the expansion of the Universe. In tandem with these geometrical constraints, redshift-space distortions depend on the build up of large-scale structure. As pointed out by many authors, measurements of these effects are intrinsically coupled. We investigate this link and argue that it strongly depends on the cosmological assumptions adopted when analysing data. Using representative assumptions for the parameters of the Euclid survey in order to provide a baseline future experiment, we show how the derived constraints change due to different model assumptions. We argue that even the assumption of a Friedman–Robertson–Walker space–time is sufficient to reduce the importance of the coupling to a significant degree. Taking this idea further, we consider how the data would actually be analysed and argue that we should not expect to be able to simultaneously constrain multiple deviations from the standard Λ cold dark matter (ΛCDM) model. We therefore consider different possible ways in which the Universe could deviate from the ΛCDM model, and show how the coupling between geometrical constraints and structure growth affects the measurement of such deviations.

Thermodynamics of interacting entropy-corrected holographic dark energy in a non-flat frw universe

Abstract: An entropy-corrected holographic dark energy (ECHDE) was recently proposed to explain the dark energy-dominated universe with the help of quantum corrections to the entropy–area relation in the setup of loop quantum cosmology. Using this new definition, we investigate its thermodynamical features including entropy and energy conservation. We describe the thermodynamical interpretation of the interaction between ECHDE and dark matter in a non-flat universe. We obtain a relation between the interaction term of the dark components and thermal fluctuation. Our study further generalizes the earlier works86, 87 in this direction.

Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter

Abstract: We study the late time evolution of flat and negatively curved Friedmann?Robertson?Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of f(R) theories nonminimally coupled to matter. Under mild assumptions on the potential V we prove that equilibria corresponding to the non-negative local minima for V are asymptotically stable, as well as horizontal asymptotes approached from above by V. We classify all cases of the flat model where one of the matter components eventually dominates. In particular for a nondegenerate minimum of the potential with zero critical value we prove in detail that if ?, the parameter of the equation of state, is larger than 1, then there is a transfer of energy from the fluid to the scalar field and the latter eventually dominates in a generic way.

Cosmology Without Averaging

Abstract: We construct cosmological models consisting of large numbers of identical, regularly spaced masses. These models do not rely on any averaging procedures, or on the existence of a global Friedmann-Robertson-Walker (FRW) background. They are solutions of Einstein's equations up to higher order corrections in a perturbative expansion, and have large-scale dynamics that are well modelled by the Friedmann equation. We find that the existence of arbitrarily large density contrasts does not change either the magnitude or scale of the background expansion, at least when masses are regularly arranged, and up to the prescribed level of accuracy. We also find that while the local space-time geometry inside each cell can be described as linearly perturbed FRW, one could argue that a more natural description is that of perturbed Minkowski space (in which case the scalar perturbations are simply Newtonian potentials). We expect these models to be of use for understanding and testing ideas about averaging in cosmology, as well as clarifying the relationship between global cosmological dynamics and the static space-times associated with isolated masses.

Interplay between curvature and Planck-scale effects in astrophysics and cosmology

Abstract: Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inonu-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planck-scale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of ``quantum spacetime curvature'' within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant.

Reconstructing interacting new agegraphic polytropic gas model in non-flat FRW universe

Abstract: We study the correspondence between the interacting new agegraphic dark energy and the polytropic gas model of dark energy in the non-flat FRW universe. This correspondence allows us to reconstruct the potential and the dynamics for the scalar field of the polytropic model, which describe accelerated expansion of the universe.

Vector and tensor perturbations in Horava-Lifshitz cosmology

Abstract: We study cosmological vector and tensor perturbations in Horava-Lifshitz gravity, adopting the most general Sotiriou-Visser-Weinfurtner generalization without the detailed balance but with projectability condition. After deriving the general formulas in a flat Friedmann-Robertson-Walker (FRW) background, we find that the vector perturbations are identical to those given in general relativity. This is true also in the nonflat cases. For the tensor perturbations, high order derivatives of the curvatures produce effectively an anisotropic stress, which could have significant efforts on the high-frequency modes of gravitational waves, while for the low-frequency modes, the efforts are negligible. The power spectrum is scale-invariant in the UV regime, because of the particular dispersion relations. But, due to lower-order corrections, it will eventually reduce to that given in general relativity (GR) in the IR limit. Applying the general formulas to the de Sitter and power-law backgrounds, we calculate the power spectrum and index, using the uniform approximations, and obtain their analytical expressions in both cases.

Oscillating Flat FRW Dark Energy Dominated Cosmology from Periodic Functional Approach

Abstract: I discuss the modification of Einstein's Theory of General Relativity based on a periodic functional approach. In this new approach, a corrected periodic gravitational coupling constant arises and plays the role of periodic damping term acting on the theory. It is found that it is achievable to have an oscillating universe dominated by dark energy and expanding acceleratedly in time.

Manifestly gauge-invariant general relativistic perturbation theory: II. FRW background and first order

Abstract: In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically coupled observer. The evolution of those observables is governed by a physical Hamiltonian and we derived the corresponding equations of motion. Linear perturbation theory of those equations of motion around a general exact solution in terms of manifestly gauge-invariant perturbations was then developed. In this paper we specialize our previous results to an FRW background which is also a solution of our modified equations of motion. We then compare the resulting equations with those derived in standard cosmological perturbation theory (SCPT). We exhibit the precise relation between our manifestly gauge-invariant perturbations and the linearly gauge-invariant variables in SCPT. We find that our equations of motion can be cast into SCPT form plus corrections. These corrections are the trace that the dust leaves on the system in terms of a conserved energy–momentum current density. It turns out that these corrections decay; in fact, in the late universe they are negligible whatever the value of the conserved current. We conclude that the addition of dust which serves as a test observer medium, while implying modifications of Einstein's equations without dust, leads to acceptable agreement with known results, while having the advantage that one now talks about manifestly gauge-invariant, that is measurable, quantities, which can be used even in perturbation theory at higher orders.

Black Hole in the Expanding Universe with Arbitrary Power-Law Expansion

Abstract: We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordstroem (RN) black hole and the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the D-dimensional Einstein-Maxwell-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a (D-1)-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential n{sub T}, the U(1) charge Q, and the nonextremality {tau}. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.