Friedmann Robertson Walker Spacetime Research Articles

Cosmological dynamics in higher-dimensional Einstein–Gauss–Bonnet gravity

In this paper we perform a systematic classification of the regimes of cosmological dynamics in Einstein–Gauss–Bonnet gravity with generic values of the coupling constants. We consider a manifold which is a warped product of a four dimensional Friedmann–Robertson–Walker space-time with a $$D$$ -dimensional Euclidean compact constant curvature space with two independent scale factors. A numerical analysis of the time evolution as function of the coupling constants and of the curvatures of the spatial section and of the extra dimension is performed. We describe the distribution of the regimes over the initial conditions space and the coupling constants. The analysis is performed for two values of the number of extra dimensions ( $$D\geqslant 6$$ both) which allows us to describe the effect of the number of the extra dimensions as well.

On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.

The propagator W(t0,t1)(g,h) for the wave equation in a given space-time takes initial data (g(x),h(x)) on a Cauchy surface {(t,x) : t=t0} and evaluates the solution (u(t1,x),∂ tu(t1,x)) at other times t1. The Friedmann-Robertson-Walker space-times are defined for t0,t1>0, whereas for t0→0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K=0 and K=-1 given by S.Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0<t0<t the limit, [Formula: see text] exists, it is independent of h(x), and for all reasonable initial data g(x), it gives rise to a well-defined solution for all t>0 emanating from the space-time singularity at t=0. Under reflection t→-t, the Friedmann-Robertson-Walker metric gives a space-time metric for t<0 with a singular future at t=0, and the same solution formulae hold. We thus have constructed solutions u(t,x) of the wave equation in Friedmann-Robertson-Walker space-times which exist for all [Formula: see text] and [Formula: see text], where in conformally regularized coordinates, these solutions are continuous through the singularity t=0 of space-time, taking on specified data u(0,⋅)=g(⋅) at the singular time.

Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann–Robertson–Walker space–time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components are described by Chevallier–Polarski–Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch.

FRW universe in the laboratory

We consider an expanding relativistic fluid with spherical symmetry as a model for an analog Friedmann-Robertson-Walker (FRW) spacetime. In the framework of relativistic acoustic geometry we demonstrate how to mimic an arbitrary FRW spacetime with positive, zero, or negative spatial curvature. In the Lagrangian description we show that a particular FRW spacetime is obtained by choosing the appropriate potential. We discuss several examples and in particular the analog de Sitter spacetime in the coordinate representation with positive and negative spatial curvature.

Nonsingular Promises from Born-Infeld Gravity

Born-Infeld determinantal gravity formulated in Weitzenböck spacetime is discussed in the context of Friedmann-Robertson-Walker (FRW) cosmologies. It is shown how the standard model big bang singularity is absent in certain spatially flat FRW spacetimes, where the high energy regime is characterized by a de Sitter inflationary stage of geometrical character, i.e., without the presence of the inflaton field. This taming of the initial singularity is also achieved for some spatially curved FRW manifolds where the singularity is replaced by a de Sitter stage or a big bounce of the scale factor depending on certain combinations of free parameters appearing in the action. Unlike other Born-Infeld-like theories in vogue, the one here presented is also capable of deforming vacuum general relativistic solutions.

INFLATION AS AN ATTRACTOR IN SCALAR COSMOLOGY

We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann–Robertson–Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton–Jacobi equation solving the field equations. The equation relates a solution "generating function" with the scalar potential. We analyze its stability and find a later time attractor which describes a Universe approaching to an eternal-de Sitter inflation driven by the potential energy, V0&gt;0. The attractor exists when the potential is regular and does not have a linear and quadratic terms of the field. When the potential has a mass term, the attractor exists if the scalar field is in a symmetric phase and is weakly coupled, λ&lt;9V0/16. We also find that the attractor property is intact under small modifications of the potential. If the scalar field has a positive mass-squared or is strongly coupled, there exists a quasi-attractor. However, the quasi-attractor property disappears if the potential is modified. On the whole, the appearance of the eternal inflation is not rare in scalar cosmology in the presence of an attractor.

Type II hidden symmetries for the homogeneous heat equation in some general classes of Riemannian spaces

We study the reduction of the heat equation in Riemannian spaces which admit a gradient Killing vector, a gradient homothetic vector and in Petrov Type D, N, II and Type III space–times. In each reduction we identify the source of the Type II hidden symmetries. More specifically we find that (a) if we reduce the heat equation by the symmetries generated by the gradient KV the reduced equation is a linear heat equation in the nondecomposable space. (b) If we reduce the heat equation via the symmetries generated by the gradient HV the reduced equation is a Laplace equation for an appropriate metric. In this case the Type II hidden symmetries are generated from the proper CKVs. (c) In the Petrov space–times the reduction of the heat equation by the symmetry generated from the nongradient HV gives PDEs which inherit the Lie symmetries hence no Type II hidden symmetries appear. We apply the general results to cases in which the initial metric is specified. We consider the case that the irreducible part of the decomposed space is a space of constant nonvanishing curvature and the case of the spatially flat Friedmann–Robertson–Walker space–time used in Cosmology. In each case we give explicitly the Type II hidden symmetries provided they exist.

Cosmological model with local symmetry of very special relativity and constraints on it from supernovae

Based on Cohen \& Glashow's very special relativity [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. {\bf 97} (2006) 021601], we propose an anisotropic modification to the Friedmann-Robertson-Walker (FRW) line element. An arbitrarily oriented 1-form is introduced and the FRW spacetime becomes of the Randers-Finsler type. The 1-form picks out a privileged axis in the universe. Thus, the cosmological redshift as well as the Hubble diagram of the type Ia supernovae (SNe Ia) becomes anisotropic. By directly analyzing the Union2 compilation, we obtain the privileged axis pointing to \((l,b)=({304^\circ}\pm{43^\circ},{-27^\circ}\pm{13^\circ})\) (\(68\%~\rm{C.L.}\)). This privileged axis is close to those obtained by comparing the best-fit Hubble diagrams in pairs of hemispheres. It should be noticed that the result is consistent with isotropy at the \(1\sigma\) level since the anisotropic magnitude is \(D=0.03\pm 0.03\).

Scalar tensor teleparallel dark gravity via Noether symmetry

In this paper, in the framework of teleparallel gravity we consider scalar tensor theories of gravity in which scalar field is non-minimal coupled to torsion scalar. Noether symmetry of the Lagrangian of such a theory for the Friedmann–Robertson–Walker space-time is used to determine the explicit forms for the coupling function and for the potential, and it is shown that both must be power-law forms as a functions of the scalar field. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. It is shown that the equation of state parameter in the present model can cross the phantom divide line for a special case with the coupling function $F(\phi) = \frac{3}{16} \phi^{2}$ and for the potential V(ϕ)=λϕ 2.

DARK ENERGY IN SOME INTEGRABLE AND NONINTEGRABLE FRW COSMOLOGICAL MODELS

One of the greatest challenges in today's cosmology to determine the nature of dark energy, the sourse of the observed present acceleration of the universe. Besides the vacuum energy, various dark energy models have been suggested. The Friedmann–Robertson–Walker (FRW) spacetime plays an important role in modern cosmology. In particular, the most popular models of dark energy work in the FRW spacetime. In this work, a new class of integrable FRW cosmological models is presented. These models induced by the well-known Painlevé equations. Some nonintegrable FRW models are also considered. These last models are constructed with the help of Pinney, Schrödinger and hypergeometric equations. Scalar field description and two-dimensional generalizations of some cosmological models are presented. Finally some integrable and nonintegrable F(R) and F(G) gravity models are constructed.

Hubble’s law and faster than light expansion speeds

Naively applying Hubble’s law to a sufficiently distant object gives a receding velocity larger than the speed of light. We discuss a similar situation in special relativity and argue that Hubble’s law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects. We clarify the meaning of Hubble’s receding speed v by showing that in a Friedmann–Robertson–Walker spacetime, if the four-velocity vector of a comoving object is parallel transported along the straight line in flat comoving coordinates to the position of a second comoving object, v/c becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one.

Approximate KMS States for Scalar and Spinor Fields in Friedmann–Robertson–Walker Spacetimes

We construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large class of spatially flat Friedmann–Robertson–Walker spacetimes characterised by an initial phase either of exponential or of power-law expansion. The states we obtain can be interpreted as being in thermal equilibrium at the time when the scale factor a has a specific value a = a 0. In the case a 0 = 0, these states fulfil a strict KMS condition on the boundary of the spacetime, which is either a cosmological horizon or a Big Bang hypersurface. Furthermore, in the conformally invariant case, they are conformal KMS states on the full spacetime. However, they provide a natural notion of an approximate KMS state also in the remaining cases, especially for massive fields. On the technical side, our results are based on a bulk-to-boundary reconstruction technique already successfully applied in the scalar case and here proven to be suitable also for spinor fields. The potential applications of the states we find range over a broad spectrum, but they appear to be suited to discuss in particular thermal phenomena such as the cosmic neutrino background or the quantum state of dark matter.

HAWKING-LIKE RADIATION AS TUNNELING FROM THE APPARENT HORIZON IN AN FRW UNIVERSE

We study Hawking-like radiation in a Friedmann–Robertson–Walker (FRW) universe using the quasi-classical WKB/tunneling method, which pictures this process as a "tunneling" of particles from behind the apparent horizon. The correct temperature of the Hawking-like radiation from the FRW space–time is obtained using a canonical invariant tunneling amplitude. In contrast to the usual quantum-mechanical WKB/tunneling problem, where the tunneling amplitude has only a spatial contribution, we find that the tunneling amplitude for FRW space–time (i.e. the imaginary part of the action) has both spatial and temporal contributions. In addition we study backreaction and energy conservation of the radiated particles and find that the tunneling probability and the change in entropy, [Formula: see text], are related by the relationship [Formula: see text], which differs from the standard result, [Formula: see text]. By regarding the whole FRW universe as an isolated adiabatic system, the change in the total entropy is zero. Then, splitting the entropy between the interior and exterior parts of the horizon [Formula: see text], we can explain the origin of the minus sign difference with the usual result: our [Formula: see text] is for the interior region, while the standard result from black hole physics is for the exterior region.

Cosmological particle creation in states of low energy

The recently proposed states of low energy provide a well-motivated class of reference states for the quantized linear scalar field on cosmological Friedmann–Robertson–Walker space-times. The low energy property of a state is localized close to some value of the cosmological time coordinate. We present calculations of the relative cosmological particle production between a state of low energy at early time and another such state at later time. In an exponentially expanding Universe, we find that the particle production shows oscillations in the spatial frequency modes. The basis of the method for calculating the relative particle production is completely rigorous. Approximations are only used at the level of numerical calculation.

Tachyonization of the ΛCDM cosmological model

In this work a tachyonization of the ΛCDM model for a spatially flat Friedmann–Robertson–Walker space–time is proposed. A tachyon field and a cosmological constant are considered as the sources of the gravitational field. Starting from a stability analysis and from the exact solutions for a standard tachyon field driven by a given potential, the search for a large set of cosmological models which contain the ΛCDM model is investigated. By the use of internal transformations two new kinds of tachyon fields are derived from the standard tachyon field, namely, a complementary and a phantom tachyon fields. Numerical solutions for the three kinds of tachyon fields are determined and it is shown that the standard and complementary tachyon fields reproduces the ΛCDM model as a limiting case. The standard tachyon field can also describe a transition from an accelerated to a decelerated regime, behaving as an inflationary field at early times and as a matter field at late times. The complementary tachyon field always behaves as a matter field. The phantom tachyon field is characterized by a rapid expansion where its energy density increases with time.

Thermodynamics of cosmological models with a variable matter equation of state

We consider cosmological models with a self-interacting scalar field and a perfect fluid with a variable equation of state in spatially flat Friedmann—Robertson—Walker space-times. The main purpose of the paper is a study of general thermodynamic properties of such models and their relationship with the dynamics of geometry.

C-field Cosmological Models with Variable G in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=Rn and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also discussed.

Fermions tunneling from apparent horizon of FRW universe

In the paper [R.-G. Cai, L.-M. Cao, Y.-P. Hu, arXiv: 0809.1554], the scalar particles' Hawking radiation from the apparent horizon of Friedmann–Robertson–Walker (FRW) universe was investigated by using the tunneling formalism. They obtained the Hawking temperature associated with the apparent horizon, which was extensively applied in investigating the relationship between the first law of thermodynamics and Friedmann equations. In this Letter, we calculate fermions' Hawking radiation from the apparent horizon of FRW universe via tunneling formalism. Applying WKB approximation to the general covariant Dirac equation in FRW spacetime background, the radiation spectrum and Hawking temperature of apparent horizon are correctly recovered, which supports the arguments presented in the paper [R.-G. Cai, L.-M. Cao, Y.-P. Hu, arXiv: 0809.1554].

Notes on an interacting holographic dark energy model in a closed universe

We consider an interacting holographic dark energy model in Friedmann–Robertson–Walkerspacetime with positive spatial curvature and investigate the behavior of the geometricparameter and dark energy density in an accelerated expanding epoch. We alsoderive some conditions needed to cross the phantom dividing line in this model.

Energy-momentum in the viscous Kasner-type universe in teleparallel gravity

Using the teleparallel gravity versions of the Einstein and Landau–Lifshitz’s energy and/or momentum complexes, I obtain the energy and momentum of the universe in viscous Kasner-type cosmological models. The energy and momentum components (due to matter plus field) are found to be zero and this agree with a previous work of Rosen and Johri et al., who investigated the problem of the energy in Friedmann–Robertson–Walker (FRW) universe. The result that the total energy and momentum components of the universe in these models is zero same as Bergmann–Thomson’s energy–momentum and props the viewpoint of Tryon. Rosen found that the energy of the FRW space–time is zero, which agrees with the studies of Tryon.