Flat Robertson-Walker Research Articles

High Momentum Behavior of Geometric Bremsstrahlung in the Expanding Universe

We shall discuss various kinds of geometric bremsstrahlung processes in the spatially flat Robertson-Walker universe. Despite that the temperature of the universe is much higher than particle masses and the Hubble parameter, the transition probability of these processes do not vanish. It is also pointed out that explicit forms of the probability possess a new duality with respect to scale factor of background geometry.

Quantum-mechanical consequences of the Hubble expansion

Quantum-mechanical effects associated with a locally expanding space-time, described by a flat Robertson-Walker metric, are investigated. Specifically, we ask the following question: Can the local expansion rate of the Universe be detected by making precision measurements on atomic and molecular systems? A simple example involving a particle in an expanding box would seem to indicate that time-dependent fractional energy shifts may be detectable. Next, a careful perturbative analysis of realistic quantum-mechanical systems possessing quite generic smooth, continuous potentials is performed by employing an adiabatic approximation. It is found thatfor realistic systems the quantum effects due to a local spacetime expansion are too small to be detectable. Consequently, we also conclude that theactual physical size of an atomic or molecular system remains fairly constant, independent of the current rate of spatial expansion.

A class of cosmological solutions of Brans-Dicke theory with cosmological constant

We present a class of exact cosmological solutions of Brans-Dicke (B-D) equations with cosmological constant in flat Robertson-Walker metric. These solutions are based on the relation oRn= constant between the B-D field and the scale factor of the universe. This relation turns out to be consistent with the equation of statep =mρ for the cosmic matter, provided thatn andm are suitably related to each other. Several special cases and asymptotic solutions are derived and discussed.

Symmetry breaking in dynamical spacetimes

The behaviour of scalar electrodynamics under symmetry breaking by the Higgs mechanism is studied in a class of dynamical spacetimes—those having a Bianchi type I symmetry—which includes the spatially flat Robertson-Walker spacetimes. The Einstein equations are used to obtain the effective Lagrangian, from which it is shown thateither the gauge field does not become massive during symmetry breaking (in marked contrast with the case in which the background spacetime is static),or the symmetry breaking chooses not only a direction in the phase space of the Higgs field, but also a spatial direction in the spacetime sections.

Plasma electrodynamics in the expanding Universe.

The 3+1 formalism of Thorne and Macdonald is used to formulate the electrodynamic equations for a plasma in a spatially flat Robertson-Walker metric. The conformal flatness of this space-time ensures that these equations closely mirror those of flat space-time. The linearized Vlasov-Maxwell equations are solved for the case of an unmagnetized plasma of ultrarelativistic particles and antiparticles, and the results are compared with those of classical kinetic theory and quantum field theory in special relativity. The Vlasov-Maxwell equations for a plasma of nonrelativistic particles are not conformally invariant, so a fluid approximation is used to obtain the linear modes of oscillation, again for an unmagnetized plasma. The plasma modes redshift at rates which depend on the rate of expansion of the Universe, and whether the electromagnetic fields or the particles dominate the dynamics.

Exact superstring motivated cosmological models

We present a number of new, exact scalar field cosmologies where the potential consists of two or more exponential terms. Such potentials are motivated by supergravity or superstring models formulated in higher-dimensional spacetimes that have been compactified to 3+1 dimensions. We have found solutions in both curved and flat Robertson-Walker spacetimes. These models have a diverse range of properties and often possess several distinct phases, with a smooth transition between ordinary and inflationary expansion. While exponential potentials typically produce power-law inflation, we find models where the inflationary period contains eras of both power-law and exponential growth.

Cosmological solutions of the Einstein equations with a causal viscous fluid

We investigate the behaviour of the solutions to the Einstein equations with a causal viscous fluid source in the case of the spatially flat Robertson-Walker metric. In our model, the bulk viscosity coefficient is related to the energy density as zeta = alpha rho m, and the relaxation time is given by zeta / rho . We find the exact solutions when m = 1/2 , and we study analytically the asymptotic stability of the distinct families of solutions for arbitrary m. We find that the qualitative asymptotic behaviour in the far future is not altered by relaxation processes, but they change the behaviour in the past, either excluding deflationary evolutions or making the Universe bounce due to the violation of the energy conditions.

Self-consistent solutions of the semi-classical Einstein equations with cosmological constant and perfect fluid

Exact solutions of the semi-classical Einstein equations with cosmological constant for conformally invariant free quantum fields in a spatially flat Robertson-Walker metric are found when a classical perfect fluid is present. The stability of the asymptotically Friedmann-de Sitter solutions is studied. The formers are found to be stable ifα < 0, while the stability of the latter depends of the signs ofα β, and A.

Effects of R□R Term in High Dimensional Inflation

In this paper the R□R term is introduced to a high dimensional spacetime. We obtain various inflations at large R and □R ~ Rm for all anisotropic Bianchi types except IX. If the dimension of spacetime is larger than 2 but less than 6, the inflation will be inflation of power-law in flat Robertson-Walker metric.

Dissipative Boltzmann-Robertson-Walker cosmologies.

The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically. The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted. The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models. It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications. For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero. The Eckart model also expands more rapidly than the Israel-Stewart models. These results suggest that "bulk-viscous" inflation may be an artifact of using a pathological fluid theory such as the Eckart theory.

Null charts and naked singularities in spherically symmetric, homothetic spacetimes

We give a unified derivation of a null chart for all spherically symmetric, homothetic spacetimes. These spacetimes contain an interesting class of naked singularities which we are also able to elucidate. Much use is made of graphical representation; in particular a chart of the spacetimes based on their homothetic group motions is introduced. Dust spacetimes, and two homogeneous examples with non-zero pressure (flat Robertson-Walker and a Kantowski-Sachs example) are studied in detail. We show the horizon structure in the null atlas, in comoving coordinates, in terms of the areal radius and comoving time, and in the homothetic diagrams. The critical delay between comoving observers for the onset of “nakedness” is interpreted in terms of a decreasing mass concentration in the spirit of Thorne's “hoop” conjecture. We also give a simple criterion for the existence of apparent horizons isolating the various singularities, and study in detail how this criterion is circumvented in the naked examples. We conclude that this type of naked singularity is a consequence of the imposed homothetic symmetry, by showing it to be generally present and timelike in the homothetic group chart even when it is not visible at comoving infinity (before the onset of criticality). It is the delayed final collapse of initially distant observers in inhomogeneous spacetimes that causes the initial singularity to become visible at comoving infinity. We conclude that these examples do not present an obstacle to the “Event Horizon Conjecture” as summarized by W. Israel (1984). That is, one can formulate criteria for the formation of apparent horizons that do not imply that all singularities are necessarily so enclosed. It is still possible that all singularities stronger than homothetic are isolated by an apparent horizon, in the spirit of Tipler's conjecture.

Shear-free spherically symmetric inhomogeneous cosmological model with heat flow and bulk viscosity.

An exact solution to the Einstein equations with a shear-free imperfect-fluid source is obtained. The solution approaches a locally flat Robertson-Walker one in the large-$t$ limit and thus serves as a viable candidate for a realistic cosmological model. The model built out of this solution is found to be free of horizon, entropy, and flatness problems.

Renormalizability of the functional schrödinger picture in Robertson-Walker space-time

We study free and self-interacting scalar quantum field theories in a flat Robertson-Walker metric in the functional Schrödinger picture. We discuss Schrödinger picture quantization, relating it to conventional Heisenberg picture quantization. For the interacting theory, we introduce the time-dependent Gaussian approximation to study time evolution of pure and mixed states and we establish renormalizability of the approximation. We also study the question of computing a finite, renormalized energy-momentum tensor for both the free and the interacting theory in the Gaussian approximation. Using the adiabatic expansion, we show that the entire subtraction necessary to make the energy-momentum tensor finite in the free theory can be written in terms of covariantly conserved tensors. We further show that the same subtraction is sufficient to make the energy-momentum tensor finite in the Gaussian approximation for the interacting theory provided that the mass and coupling constants are renormalized.

Massive symmetric tensor field in curved spacetime

Derives the condition on the background spacetime for the straightforward generalisation of the massive symmetric tensor field (MSTF) equation to be possible. The author studies the MSTF in spatially flat Robertson-Walker spacetimes in detail. The above-mentioned condition is verified in these spacetimes by calculating the Klein-Gordon inner products among the solutions of the field equation. The author also shows that the MSTF theory in some spacetimes has features which are probably undesirable even if this condition on the spacetime is satisfied.

Pair creation by a photon and the time-reversed process in a Robertson-Walker universe with time-assymetric expansion

We investigate pair creation by a photon and the time-reversed process in a spatially flat Robertson-Walker universe. The expansion law C( η) = C in + exp(2 bη) provides a time-asymmetric background gravitational field. The explicit evaluation of the total decay probabilities for electron-positron pairs which are non-relativistic at Compton time and soft photons yields a violation of CPT invariance such that the time-reversed (annihilation) process is the more effective one. This CPT non-invariance takes place even though the interaction term of the lagrangian density of quantum electrodynamics does not additionally break the conformal symmetry of the theory.

Pair creation by a photon and the time-reversed process in a Robertson-Walker universe with time-symmetric expansion

We investigate pair creation by a photon and the time-reversed process in a spatially flat Robertson-Walker universe. The time-dependent external gravitational field breaks time translation invariance and thus energy conservation. So the otherwise forbidden processes are expected to occur even as first-order processes of quantum electrodynamics. We evaluate the total decay probabilities for electron-positron pairs which are non-relativistic at Campton time and soft photons in a time-symmetrically expanding radiation-dominated Friedman universe. As a characteristic trait there appears an infrared divergence. Special attention is drawn to CPT non-invariance as a consequence of time evolution of the states. As is to be expected it does not occur in a totally time-symmetric situation.

Decreasing density perturbations and the isotropy of the cosmic microwave background

We compute the effect on the small-scale anisotropy of the cosmic background radiation induced by decreasing density fluctuations in a spatially flat Robertson-Walker universe.

Growth of scalar-field quantum fluctuations in Robertson-Walker universes.

We investigate the behavior of the quantum expectation value of ${\ensuremath{\varphi}}^{2}$ where \ensuremath{\varphi} is a massless, minimally coupled scalar field in a spatially flat Robertson-Walker universe. The scale factor is a(t)\ensuremath{\propto}${t}^{\ensuremath{\alpha}}$, where t is the comoving time. If \ensuremath{\alpha}\ensuremath{\gg}1, this metric is locally approximately de Sitter space. It is found that 〈${\ensuremath{\varphi}}^{2}$〉 grows linearly in time for a finite interval during which it is approximated by the de Sitter-space result: 〈${\ensuremath{\varphi}}^{2}$〉=${H}^{3}$t/(4${\ensuremath{\pi}}^{2}$). It subsequently approaches a constant value. If ${R}_{0}$ denotes the value of the scalar curvature at the time that growth begins, then the interval of growth lasts for a time of the order of \ensuremath{\Delta}t=\ensuremath{\alpha}(3/${R}_{0}$${)}^{1/2}$ and the asymptotic value of 〈${\ensuremath{\varphi}}^{2}$〉 is \ensuremath{\alpha}${R}_{0}$/(96${\ensuremath{\pi}}^{2}$).

Particle decay and violation of CPT invariance in expanding universes: the π0-2γ model

The author investigates the decay of one massive conformally coupled scalar particle into two photons and the time-reversed decay according to the pi 0-2 gamma -model interaction in a spatially flat Robertson-Walker universe. Besides a few conceptual remarks concerning decay processes in pair-creating external fields, special attention is drawn to the problem of CPT non-invariance. It is found that both decay processes are not CPT invariant if (i) the expansion of the universe provides a T-asymmetric background and (ii) the conditions for free-particle creation are fulfilled for at least one of the quantum fields participating in the interaction. The results are illustrated for particular scale factors of the universe.

A general, gauge-invariant analysis of the cosmic microwave anisotropy

view Abstract Citations (147) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A General, Gauge-invariant Analysis of the Cosmic Microwave Anisotropy Abbott, L. F. ; Schaefer, R. K. Abstract A general, gauge-invariant analysis of the large-scale anisotropies in the cosmic background radiation produced by arbitrary scalar, vector, or tensor perturbations in open, closed, or flat Robertson-Walker spacetimes (with no cosmological constant) is presented. The multipole moment predictions for the scale invariant spectrum and Omega = 1 universe predicted by inflationary cosmologies are contrasted with those for other spectra and for open and closed universes. Using the measured value of the dipole moment, limits are set on the expected value of the quadrupole moment as a function of Omega for various spectra. Publication: The Astrophysical Journal Pub Date: September 1986 DOI: 10.1086/164525 Bibcode: 1986ApJ...308..546A Keywords: Background Radiation; Cosmic Rays; Gauge Invariance; Radiation Distribution; Anisotropy; Big Bang Cosmology; Dipole Moments; Microwaves; Normal Density Functions; Space-Time Functions; Space Radiation; COSMIC BACKGROUND RADIATION full text sources ADS |