Flat Robertson-Walker Spacetime Research Articles

Focusing conditions for extended teleparallel gravity theories

In the context of extended theories of teleparallel gravity f(T) we derive the focusing conditions for a one-parameter dependent congruence of timelike auto-parallels of the Levi-Civita connection. We also consider the f(T) field equations for a general metric tensor before moving on to consider a spatially flat Robertson-Walker space-time. Following this, we study the expansion rate for a one-parameter dependent congruence of timelike auto-parallel curves of the Levi-Civita connection. Given the fact that test particles follow auto-parallels of the Levi-Civita connection, the torsion-free Raychaudhuri equation is used in order to determine the desired focusing conditions. Finally we study the obtained focusing conditions for three f(T) paradigmatic cosmological models and discuss the satisfaction or violation of these conditions. Through this, we find f(T) models that allow for the weak and strong focusing conditions to be satisfied or violated. It is mentioned that this behaviour can also be found in the so-called f(R) and f(Q) theories.

A massless scalar field in Robertson-Walker spacetimes: Adiabatic regularization and Green’s function * * Supported by NSFC (11421303, 11675165, 11633001, 11961131007), B. Wang is supported by CPSF (2019M662168)

We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker (RW) spacetimes. For the conformal coupling, the 2nd-order regularized power spectrum and 4th-order regularized stress tensor are zero, and no trace anomaly exists in general RW spacetimes. This is a new result that exceeds those found in de Sitter space. For the minimal coupling, the regularized spectra are also zero in the radiation-dominant and matter-dominant stages, as well as in de Sitter space. The vanishing of these adiabatically regularized spectra is further confirmed by direct regularization of the Green's function. For a general coupling and general RW spacetimes, the regularized spectra can be negative under the conventional prescription. At a higher order of regularization, the spectra will generally become positive, but will also acquire IR divergence, which is inevitable for a massless field. To avoid the IR divergence, the inside-horizon regularization is applied. Through these procedures, nonnegative UV- and IR-convergent power spectrum and spectral energy density will eventually be achieved.

Cosmological effective Hamiltonian from full loop quantum gravity dynamics

The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes. We apply the same idea of its derivation in LQC to the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson–Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian.

Quantum thermodynamics and quantum entanglement entropies in an expanding universe

We investigate an asymptotically spatially flat Robertson–Walker space–time from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in space–time. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying space–time. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the parameters of space–time.

Entanglement of self-interacting scalar fields in an expanding spacetime

We evaluate self-interaction effects on the quantum correlations of field modes of opposite momenta for scalar theory in a two-dimensional asymptotically flat Robertson-Walker spacetime. Such correlations are encoded both in the von Neumann entropy defined through the reduced density matrix in one of the modes and in the covariance expressed in terms of the expectation value of the number operators for each mode in the evolved state. The entanglement between field modes carries information about the underlying spacetime evolution.

Nonlocality and Multipartite Entanglement in Asymptotically Flat Space-Times

We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson–Walker space-time. For two qubit case, we show that the Bell's inequality always is violated as measured by the accelerated observers which are in the causally connected regions. On the other hand, for those observers in the causally disconnected regions inequality is not violated for any values of acceleration. The generated three qubit state from two qubit state due to acceleration of one parties has a zero 3-tangle. For a three qubit state, the inequality violated for measurements done by both causally connected and disconnected observers. Initially GHZ state with non zero 3-tangle, in accelerated frame, transformed to a four qubit state with vanishing 4-tangle value. On the other hand, for a W-state with zero 3-tangle, in non inertial frame, transformed to a four qubit state with a non-zero 4-tangle acceleration dependent. In an expanding space-time with asymptotically flat regions, for an initially maximally entangled state, the maximum value of violation of Bell's inequality in the far past decreased in the far future due to cosmological particle creation. For some initially maximally entangled states, the generated four qubit state due to expansion of space-time, has non vanishing 4-tangle.

Two-point function for the Maxwell field in flat Robertson-Walker spacetimes

We obtain an explicit two-point function for the Maxwell field in flat Roberson-Walker spaces, thanks to a new gauge condition which takes the scale factor into account and assume a simple form. The two-point function is found to have the short distance Hadamard behavior.

The Spatially Homogeneous Relativistic Boltzmann Equation with a Hard Potential

In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in spatially flat Robertson-Walker spacetimes.

Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson–Walker spacetime

In this paper, we study the relativistic Boltzmann equation in the spatially flat Robertson–Walker spacetime. For a certain class of scattering kernels, global existence of classical solutions is proved. We use the standard method of Illner and Shinbrot for the global existence and apply the splitting technique of Guo and Strain for the regularity of solutions. The main interest of this paper is to study the evolution of matter distribution, rather than the evolution of spacetime. We obtain the asymptotic behaviour of solutions and will understand how the expansion of the universe affects the evolution of matter distribution.

Effect of electromagnetic fields on the creation of scalar particles in a flat Robertson–Walker space-time

The influence of electromagnetic fields on the creation of scalar particles from vacuum in a flat Robertson–Walker space-time is studied. The Klein–Gordon equation with varying electric field and constant magnetic one is solved. The Bogoliubov transformation method is applied to calculate the pair creation probability and the number density of created particles. It is shown that the electric field amplifies the creation of scalar particles while the magnetic field minimizes it.

Schwinger Effect in a Robertson-Walker Space-Time

The problem of particle creation from vacuum in a flat Robertson-Walker space-time in the presence of a varying electric field is studied. The Klein Gordon equation is exactly solved when the scale factor is a(η)=A+Btanh(λη). The canonical method based on Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated. The particular case of radiation dominated universe is considered where the total probability is written as a Schwinger-like series. It is shown that the electric field amplifies gravitational particle creation.

ON THE CREATION OF SCALAR PARTICLES IN A FLAT ROBERTSON–WALKER SPACETIME

The problem of particle creation from vacuum in a flat Robertson–Walker spacetime is studied. Two sets of exact solutions for the Klein–Gordon equation are given when the scale factor is a2(η) = a+b tanh(λη)+c tanh2 (λη). Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.

A kinetic theory of diffusion in general relativity with cosmological scalar field

A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario.

DYNAMICAL BACKREACTION IN ROBERTSON–WALKER SPACETIME

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson–Walker spacetime. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the singularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson–Walker scale parameter a(t) coupled to the scalar field is finally derived for the case of conformal and also general coupling.

PARTICLE PRODUCTION IN COSMOLOGICAL SPACETIMES WITH ELECTROMAGNETIC FIELDS

We calculate the charged scalar particle creation in the presence of gravitational and electromagnetic fields in two models of spatially flat Robertson–Walker spacetimes: de Sitter space and asymptotically radiation dominated model. We used the Bogoliubov transformation to compute the rate of production of the particles. Possibility of creation of massless charged particles is also discussed.

Modification to the luminosity distance redshift relation in modified gravity theories

We derive an expression for the luminosity distance as a function of redshift for a flat Robertson-Walker spacetime perturbed by arbitrary scalar perturbations possibly produced by a modified gravity theory with two different scalar perturbation potentials. Measurements of the luminosity distance as function of redshift provide a constraint on a combination of the scalar potentials and so they can complement weak lensing and other measurements in trying to distinguish among the various alternative theories of gravity.

New counterterms induced by trans-Planckian physics in semiclassical gravity

We consider free and self-interacting quantum scalar fields satisfying modified dispersion relations in the framework of Einstein-Aether theory. Using adiabatic regularization, we study the renormalization of the equation for the mean value of the field in the self-interacting case, and the renormalization of the semiclassical Einstein-Aether equations for free fields. In both cases we consider Bianchi type I background spacetimes. Contrary to what happens for free fields in flat Robertson-Walker spacetimes, the self-interaction and/or the anisotropy produce nonpurely geometric terms in the adiabatic expansion, i.e. terms that involve both the metric g{sub {mu}}{sub {nu}} and the aether field u{sub {mu}}. We argue that, in a general spacetime, the renormalization of the theory would involve new counterterms constructed with g{sub {mu}}{sub {nu}} and u{sub {mu}}, generating a fine-tuning problem for the Einstein-Aether theory.

Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity

A spatially flat Robertson-Walker spacetime driven by a cosmological constant is nonconformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially isotropic perturbations of the metric and the quantum state. These results are independent of the free renormalization parameters.

Creation of Scalar and Dirac Particles in Asymptotically Flat Robertson-Walker Spacetimes

In the present article we obtain the exact solutions of the Klein-Gordon and Dirac equations for two models of Robertson-Walker spaces with asymptotically Minkowskian regions. Using the obtained exact solutions we calculate the density of scalar and Dirac particles created through Bogolubov transformations technique. For Dirac field it is shown that the creation rate of particles and anti particles are equal.

Variational approach to Robertson–Walker spacetimes with homogeneous scalar fields

Existence of solutions between prescribed configurations is proved for spatially flat Robertson–Walker spacetimes coupled with homogeneous scalar field sources, using a modified version of the Euler–Maupertuis least action variational principle. The solutions are obtained as limits of approximating variational problems, solved using the techniques originally introduced by Rabinowitz.