Effects Of Gravitational Back Reaction Research Articles

Gravitational backreaction on piecewise linear cosmic string loops

We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational back reaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, back reaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" (maximally symmetric) loop evaporates without changing shape, but for all other loops in this class, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, it will evaporate before its kinks are significantly changed, if it is far from square, the opening out of the kinks is much faster than evaporation of the loop.

Gravitational backreaction effects on the holographic phase transition

We study radion stabilization in the compact Randall-Sundrum model by introducing a bulk scalar field, as in the Goldberger and Wise mechanism, but (partially) taking into account the backreactions from the scalar field on the metric. Our generalization reconciles the radion potential found by Goldberger and Wise with the radion mass obtained with the so-called superpotential method where backreaction is fully considered. Moreover we study the holographic phase transition and its gravitational wave signals in this model. The improved control over backreactions opens up a large region in parameter space and leads, compared to former analysis, to weaker constraints on the rank N of the dual gauge theory. We conclude that, in the regime where the 1/N expansion is justified, the gravitational wave signal is detectable by LISA.

Can the universe exit from phantom inflation due to gravitational back reaction?

The effects of the gravitational back reaction of cosmological perturbations are investigatedin a phantom inflation model. The effective energy–momentum tensor of thegravitational back reaction of cosmological perturbations whose wavelengths arelarger than the Hubble radius is calculated. Our results show that the effectsof gravitational back reaction will counteract that of the phantom energy. It isdemonstrated in a chaotic phantom inflation model that if the phantom field at the end ofinflation is larger than a critical value determined by the necessary e-folds, thephantom inflation phase might be terminated by the gravitational back reaction.

Effects of gravitational backreaction on cosmological perturbations

Because of the nonlinearity of the Einstein equations, the cosmological fluctuations which are generated during inflation on a wide range of wavelengths do not evolve independently. In particular, to second order in perturbation theory, the first order fluctuations back-react both on the background geometry and on the perturbations themselves. In this paper, the gravitational backreaction of long-wavelength (super-Hubble) scalar metric fluctuations on the perturbations themselves is investigated for a large class of inflationary models. Specifically, the equations describing the evolution of long-wavelength cosmological metric and matter perturbations in an inflationary universe are solved to second order in both the amplitude of the perturbations and in the slow-roll expansion parameter. Assuming that the linear fluctuations have random phases, we show that the fractional correction to the power spectrum due to the leading infrared backreaction terms does not change the shape of the spectrum. The amplitude of the effect is suppressed by the product of the inflationary slow-roll parameter and the amplitude of the linear power spectrum. The nongaussianity of the spectrum induced by backreaction is commented upon.

Cosmological parameter dependence in local string theories of structure formation

We perform a new and accurate study of the dependence on cosmological parameters of structure formation with local cosmic strings. The crucial new ingredients are the inclusion of the effects of gravitational back reaction on the evolution of the network, and the accurate evolution of the network through the radiation to matter transition. Our work re-iterates the fact that expanding universe numerical simulations only probe a transient regime, and we incorporate our results into the unequal time correlators recently measured. We then compute the CMB and CDM fluctuations' power spectra for various values of the Hubble constant ${H}_{0}$ and baryon fraction ${\ensuremath{\Omega}}_{b}.$ We find that, whereas the dependence on ${\ensuremath{\Omega}}_{b}$ is negligible, there is still a strong dependence on ${H}_{0}.$

Unitary and nonunitary evolution in quantum cosmology

We analyse when and why unitarity violations might occur in quantum cosmology restricted to minisuperspace. To this end we discuss in detail backscattering transitions between expanding and contracting solutions of the Wheeler-DeWitt equation. We first show that upon neglecting only backscattering, one obtains an intermediate regime in which matter evolves unitarily but which does not correspond to any Schr\"odinger equation in a given geometry since gravitational backreaction effects are taken into account at the quantum level. We then show that backscattering amplitudes are exponentially smaller than matter transition amplitudes. Both results follow from an adiabatic treatment valid for macroscopic universes. To understand how backscattering and the intermediate regime should be interpreted, we review the problem of electronic transitions induced by nuclear motion since it is mathematically very similar. In this problem, transition amplitudes are obtained from the conserved current. The same applies to quantum cosmology and shows that the unique consistent interpretation is based on the current when backscattering is neglected. We then review why, in a relativistic context, backscattering is interpreted as pair production whereas it is not in the non relativistic case. In each example the correct interpretation is obtained by coupling the system to an external quantum device. From the absence of such external systems in cosmology, we conclude that backscattering does not have a unique consistent interpretation in quantum cosmology.

Closed-form expression for the momentum radiated from cosmic string loops.

We modify the recent analytic formula given by Allen and Casper for the rate at which piecewise linear cosmic string loops lose energy to gravitational radiation to yield the analogous analytic formula for the rate at which loops radiate momentum. The resulting formula (which is exact when the effects of gravitational back-reaction are neglected) is a sum of O(N^4) polynomial and log terms where, N is the total number of segments on the piecewise linear string loop. As illustration, we write the formula explicitly for a simple one-parameter family of loops with N=5. For most loops the large number of terms makes evaluation ``by hand" impractical, but, a computer or symbolic manipulator may by used to yield accurate results. The formula has been used to correct numerical results given in the existing literature. To assist future work in this area, a small catalog of results for a number of simple string loops is provided.

Closed-form expression for the gravitational radiation rate from cosmic strings.

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.

Evolution of cosmic string configurations.

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance, or extension, of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: \ensuremath{\xi}, related to the overall string density, \ensuremath{\xi}\ifmmode\bar\else\textasciimacron\fi{}, the persistance length along the string, and \ensuremath{\zeta}, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study that if gravitational radiation and small-scale structure effects are neglected the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while \ensuremath{\xi} and \ensuremath{\xi}\ifmmode\bar\else\textasciimacron\fi{} grow, \ensuremath{\zeta} initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back reaction.

Effects of gravitational back reaction on small-scale structure of cosmic strings.

Effects of gravitational back reaction on small-scale structure of cosmic strings.