Flat Robertson-Walker Background Research Articles

Accelerating universe with decreasing gravitational constant

We study the cosmology of dark energy in an extended theory of gravity in Lyra’s geometry. By analyzing a possible phenomenological interaction between the matter field with a constant equation-of-state parameter ωm (0≤ωm<1) and the geometric displacement field in Lyra’s geometry, we find that the displacement vector field engenders an effective time-dependent gravitational constant Geff constrained in the region 0<Geff(t)≤G. We show that the effective equation-of-state parameter ωeff(t) evolves in the same way as the effective time-dependent gravitational constant which, by decreasing with time, can give rise to the late-time cosmic acceleration with ω=-1 crossing in a flat Robertson-Walker background without adding dynamical ghost mode.

On the linear stability of a scalar-field with exponential potential in a flat Robertson-Walker background

We study covariant and gauge-invariant linear scalar perturbations of a scalar-field with positive exponential potential in a flat Robertson-Walker background. By applying a dynamical systems approach we investigate how the phase of the perturbations evolves, finding bounds on the wave-number in terms of the slope parameter, for which the perturbations decays when approaching the inflationary solution.

Scalar–vector–tensor gravity from preferred reference frame effects

Using some suitable combinations of a dynamical unit time-like four-velocity of a preferred reference frame, Ricci tensor and covariant derivatives of the Brans–Dicke (BD) scalar field, we propose a new scalar–vector–tensor gravity model in which an Euclidean Jordan–Brans–Dicke (JBD) action is reduced to its Lorentzian version with no used complex coordinates. Thus it should be play an important role in the process of metric signature transition of a suitable dynamical curved space-time. In this work we follow the ideas proposed by Barbero et al. As an application of the model, we study a classical perfect fluid cosmological universe described in a flat Robertson–Walker background metric. Mathematical derivations of the equations predict a non-singular scale factor for the space-time in the both of dust and radiation dominated states where value of the Brans–Dicke parameter \({\omega}\) is fixed, but there is still an arbitrary parameter which should be determined by the boundary values of the cosmological system. Furthermore its classical cosmological vacuum solutions is obtained as a non-singular model with a fixed Brans–Dicke parameter. Although there is obtained a singular perfect fluid cosmological solution which may not be suitable, because in this case the Brans–Dicke parameter is not still fixed.

Perturbative quantum gravity and Newton's law on a flat Robertson-Walker background

We derive the Feynman rules for gravity in the presence of a flat Robertson-Walker background and give explicit expressions for the propagator in the physically interesting cases of inflation, radiation domination, and matter domination. The aforementioned background is generated by a scalar field source which should be taken to be dynamical. As an elementary application, we compute the corrections to the Newtonian gravitational force in the present matter dominated era and conclude — as expected — that they are negligible except for the largest scales.

Relation between Einstein and quantum field equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.

Remarks on squeezed states of a harmonic oscillator in spatially flat Robertson-Walker space-time

We have investigated the time evolution of a non-relativistic harmonic oscillator in a spatially flat Robertson-Walker background space-time. It is found that the time evolution operator of the system is a product of a squeeze operator and a rotation operator, and thus the initial cohrent state evolves into a squeezed state at a later time. In other words, the time evolution of the non-relativistic oscillator in a spatially flat Robertson-Walker background spacetime is a «squeezing» process. The squeezing effect is induced by the continuous scale dilation in expanding space-time, and depends on the specific model for an expanding universe. For instance, there is no squeezing in the de Sitter model, whereas squeezing does occur in the spatially flat Friedmann model.

Self-consistent solution to the back-reaction problem for vector fields in two dimensions

We describe vector fields propagating in a two-dimensional spatially flat Robertson-Walker background using a curved space-time generalization of the Stueckelberg formalism. We prove that the energy-momentum tensor expectation value in the vacuum defined through energy minimization is renormalizable and yields the usual anomalous trace in the massless limit of vector mesons. Further on we study the back-reaction problem using the semiclassical Einstein equations. In the massive case we found that the physical solution requires the cosmological constant to vanish but not necessarily with a vanishing curvature. However, for certain initial conditions of the scale factor, the de Sitter metric is a consistent solution with the cosmological constant depending on powers of the curvature scalar greater than one. In addition, matter is continuously being created at a steady state.

Propagation of self-gravitating density waves in the deDonder gauge: the physical importance of gauge solutions and the problem of initial conditions

The propagation of perturbations on a spatially flat Robertson-Walker background is studied within linear perturbation theory in deDonder gauge and for comparison in synchronous gauge. The metric perturbations should be determined uniquely by the density/pressure perturbations, therefore only two initial conditions, namely for the density contrast and its time derivative, should be needed. Since the number of fundamental solutions for the density perturbations is higher than 2 in both gauges (6 resp. 3) an additional reduction of possible initial conditions, resp. a physically motivated exclusion of solutions, is needed. It is shown that the common treatment of excluding the so-called gauge solutions (solutions which can be gauged to zero in an already chosen gauge) leads to unphysical results. If gauge solutions are excluded the density perturbation solutions are the same in both gauges. But the correct Newtonian limit — which is present in deDonder gauge but not in synchronous gauge — is bound to the differences in the two gauges for large spatial scales of perturbations. Furthermore, compressional wave solutions should vanish for infinite spatial scales of perturbations (isotropy), but this is guaranteed in deDonder gauge by gauge solutions again. Gauge solutions should therefore not be taken as unphysical.

"Swiss cheese" models with pressure.

Local spherically symmetric inhomogeneities are matched to a spatially flat Robertson-Walker background with pressure. In the cases in which the background evolves to an Einstein--de Sitter dust universe, the interior metrics tend with time either to the vacuum Schwarzschild solution or to the spatially flat Tolman dust metrics. The whole construction may be interpreted as the history of the dust-filled ''Swiss cheese'' models.

Development of voids in the thin-wall approximation. II - Radiation-filled voids in a flat background

view Abstract Citations (14) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Development of Voids in the Thin-Wall Approximation. II. Radiation-filled Voids in a Flat Background Pim, R. ; Lake, K. Abstract The evolution of spherical radiation-filled voids in a spatially flat Robertson-Walker background is studied within the context of the general relativistic thin-wall approximation. This work extends previous discussions of vacuum voids. It is found that the inclusion of radiation within the void has significant quantitative and important qualitative effects on the evolution of the void. In particular, it is found that voids which do not collapse grow, at late times, like the particle horizon. Publication: The Astrophysical Journal Pub Date: May 1986 DOI: 10.1086/164145 Bibcode: 1986ApJ...304...75P Keywords: Astronomical Models; Black Body Radiation; Cosmology; Relativity; Voids; Numerical Integration; Photon Density; Space-Time Functions; Thin Walls; Physics (General); COSMOLOGY; RELATIVITY full text sources ADS | Related Materials (2) Part 1: 1985ApJ...298..439L Part 3: 1988ApJ...330..625P

Local inhomogeneities in a Robertson-Walker background. III - Elementary growth rates in a flat background with a relativistic equation of state

view Abstract Citations (4) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Local inhomogeneities in a Robertson-Walker background. III - Elementary growth rates in a flat background with a relativistic equation of state Helaby, C. ; Lake, K. Abstract An examination is undertaken of a class of inhomogeneities, embedded in a spatially flat Robertson-Walker background, which is restricted by the simplifying assumption that isotropic pressure equals local energy flux. Both a noninteracting mixture of blackbody photons and dust, and a baryon-conserving equilibrium mixture of blackbody photons and a neutral, two-component, relativistic Maxwell-Boltzmann gas, are used to describe the background. It is demonstrated through a comparison of the resultant mass of the inhomogeneities with the Jeans and particle horizon mass scales that varying the initial photon-to-baryon ratio in the background has a critical effect on all masses. Publication: The Astrophysical Journal Pub Date: December 1981 DOI: 10.1086/159480 Bibcode: 1981ApJ...251..429H Keywords: Background Radiation; Cosmology; Inhomogeneity; Relativity; Baryons; Black Body Radiation; Dust; Equations Of State; Photons; Astrophysics full text sources ADS |

Infrared divergences in a class of Robertson-Walker universes

We investigate infrared divergences of expectation values of products of field operators in a class of curved space-times. The massless minimally coupled scalar field and the linearized gravitational field, quantized on a subset of spatially flat Robertson-Walker background metrics, have such divergences for an apparently natural choice of state vectors. For those states which give a large infrared contribution to the energy-momentum tensor, we show that these metrics cannot be self-consistent solutions of Einstein's equations. Finally, we show that such divergences cannot evolve dynamically in these models from initial conditions which are free of them. These divergences provide one possible criterion for limiting the acceptable choices of state vectors in curved space-time.