arXiv subjects

Richard Easther

Publications and source records attributed to Richard Easther.

126 records · Page 7Linked to original sources

arXiv2000

Gravity, Parametric Resonance and Chaotic Inflation

We investigate the possibility that nonlinear gravitational effects influence the preheating era after inflation. Our work is based on numerical solutions of the inhomogeneous Einstein field equations, and is free of perturbative approximations. The one restriction we impose is to limit the inhomogeneity to a single spatial direction. We compare our results to perturbative calculations and to solutions of the nonlinear field equations in a rigid (unperturbed) spacetime, in order to isolate gravitational phenomena. We consider two types of initial conditions: where only one mode of the field perturbation has a non-zero initial amplitude, and where all the modes begin with a non-zero amplitude. Here we focus on preheating following inflation driven by a scalar field with a quartic potential. We confirm the broad picture of preheating obtained from the nonlinear field equations in a rigid background, but gravitational effects have a measurable impact on the dynamics for both sets of initial data. The rigid spacetime results predict that the amplitude of a single initially excited mode drops rapidly after resonance ends, whereas in the relativistic case the amplitude is roughly constant. With all modes initially excited, the longest modes in the simulation grow much more rapidly in the relativistic calculation than with a rigid background. However, we see no evidence for the sort of gravitational collapse associated with the formation of primordial black holes. The numerical codes described here are easily extended to more complicated resonant models, which we will examine in the future.

hep-ph↗

arXiv1999

Fast Evaluation of Feynman Diagrams

We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based on based on the theory of generalized sinc ($\sin(x)/x$) functions, from which we derive an approximation to the propagator that is expressed as an infinite sum. When the propagators in the Feynman integrals are replaced with the approximate form all integrals over internal momenta and vertices are converted into Gaussians, which can be evaluated analytically. Performing the Gaussians yields a multi-dimensional infinite sum which approximates the corresponding Feynman integral. The difference between the exact result and this approximation is set by an adjustable parameter, and can be made arbitrarily small. We discuss the extraction of regularization independent quantities and demonstrate, both in theory and practice, that these sums can be evaluated quickly, even for third or fourth order diagrams. Lastly, we survey strategies for numerically evaluating the multi-dimensional sums. We illustrate the method with specific examples, including the the second order sunset diagram from quartic scalar field theory, and several higher-order diagrams. In this initial paper we focus upon scalar field theories in Euclidean spacetime, but expect that this approach can be generalized to fields with spin.

hep-ph↗

arXiv1999

The Sinc Function Representation and Three-Loop Master Diagrams

We test the Sinc function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc function representation converges rapidly, and it is straightforward to obtain accuracies of 1 part in 10^6 for these diagrams and with longer runs we found results better than 1 part in 10^{12}. Finally, this paper extends the Sinc function representation to diagrams containing massless propagators.

hep-ph↗

arXiv1999

Preheating, Parametric Resonance and the Einstein Field Equations

We consider the interaction between perturbations in the inflaton and in the metric during the preheating phase in simple inflationary models. By numerically integrating the Einstein field equations we are able to gauge the impact of non-linear gravitational effects on preheating for the first time. In the lambda phi^4 model we find a large increase in the amplitude of sub-Hubble metric modes, beyond that due to gravitational collapse alone. There is significant mode-mode coupling and the amplification is eventually terminated by back reaction effects. We suggest that such enhancement of inhomogeneity will change the behaviour of the post-inflationary universe.

hep-ph↗

arXiv1999

On the Interaction of Monopoles and Domain Walls

We study the interaction between monopoles and embedded domain walls in a O(3) linear sigma model. We discover that there is an attractive force between the monopole and the wall. We provide evidence that after the monopole and domain wall collide, the monopole unwinds on the wall, and that the winding number spreads out on the surface. These results support the suggestion by Dvali et al. (hep-ph/9710301) that the monopole problem can be solved by monopole-domain wall interactions.

hep-ph↗

arXiv1999

Holography, Cosmology and the Second Law of Thermodynamics

We propose that in time dependent backgrounds the holographic principle should be replaced by the generalized second law of thermodynamics. For isotropic open and flat universes with a fixed equation of state, the generalized second law agrees with the cosmological holographic principle proposed by Fischler and Susskind. However, in more complicated spacetimes the two proposals disagree. A modified form of the holographic bound that applies to a post-inflationary universe follows from the generalized second law. However, in a spatially closed universe, or inside a black hole event horizon, there is no simple relationship that connects the area of a region to the maximum entropy it can contain.

hep-th↗

arXiv1999

Inhomogeneity and the Post-Inflationary Universe

We discuss the interaction between perturbations in the inflaton and the background during the preheating phase in simple inflationary models. By numerically solving the Einstein field equations we are able to assess the impact of non-linear gravitational effects on preheating, and to assess the accuracy of perturbative discussions of the preheating epoch.

hep-ph↗

arXiv1999

Preheating and the Einstein Field Equations

We inaugurate a framework for studying preheating and parametric resonance after inflation without resorting to any approximations, either in gravitational perturbation theory or in the evolution of the field(s). We do this by numerically solving the Einstein field equations in the post-inflationary universe. In this letter we show how to compare our results to those of gauge invariant perturbation theory. We then verify Finelli and Brandenberger's analysis (hep-ph/9809490) of super-horizon modes in $m^2ϕ^2$ inflation, showing that they are not amplified by resonant effects. Lastly, we make a preliminary survey of the nonlinear couplings between modes, which will be important in models where the primordial metric perturbations undergo parametric amplification.

hep-ph↗

arXiv1998

Chaos after Two-Field Inflation

We show that two-field inflation can be followed by an era in which the field dynamics become chaotic, and discuss the possible consequences of this for two-field inflationary models. [PASCOS conference proceedings - a short version of gr-qc/9711035]

gr-qc↗

arXiv1998

Nonsingular Dilaton Cosmology

We study spatially homogeneous and isotropic solutions to the equations of motion derived from dilaton gravity, in the presence of a special combination of higher derivative terms in the gravitational action. All solutions are nonsingular. For initial conditions resembling those in the pre-big-bang scenario, there are solutions corresponding to a spatially flat, bouncing Universe originating in a dilaton-dominated contracting phase and emerging as an expanding Friedmann Universe.

gr-qc↗

arXiv1997

Chaotic Dynamics and Two-Field Inflation

We demonstrate the existence of chaos in realistic models of two-field inflation. The chaotic motion takes place after the end of inflation, when the fields are free to oscillate and their motion is only lightly damped by the expansion of the universe. We then investigate whether the presence of chaos affects the predictions of two-field models, and show that chaos enhances the production of topological defects and renders the growth rate of the universe sensitively dependent upon the ``initial'' conditions at the beginning of the oscillatory era.

gr-qc↗

arXiv1997

Vacuum fluctuations in axion-dilaton cosmologies

We study axion-dilaton cosmologies derived from the low-energy string effective action. We present the classical homogeneous Friedmann-Robertson-Walker solutions and derive the semi-classical perturbation spectra in the dilaton, axion and moduli fields in the pre-Big Bang scenario. By constructing the unique S-duality invariant field perturbations for the axion and dilaton fields we derive S-duality invariant solutions, valid when the axion field is time-dependent as well as in a dilaton-vacuum cosmology. Whereas the dilaton and moduli fields have steep blue perturbation spectra (with spectral index n=4) we find that the axion spectrum depends upon the expansion rate of the internal dimensions (0.54<n<4) which allows scale-invariant (n=1) spectra. We note that for n<1 the metric is non-singular in the conformal frame in which the axion is minimally coupled.

hep-th↗

arXiv1996

One-Loop Superstring Cosmology and the Non-Singular Universe

We study the cosmological implications of the one-loop terms in the string expansion. In particular, we find non-singular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the non-singular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in the string expansion.

hep-th↗

arXiv1995

An Inflationary Model with an Exact Perturbation Spectrum

We present a new, exact scalar field cosmology for which the spectrum of scalar (density) perturbations can be calculated exactly. We use this exact result to the probe the accuracy of approximate calculations of the perturbation spectrum.

astro-ph↗

arXiv1995

Tree-level String Cosmology

In this paper we examine the classical evolution of a cosmological model derived from the low-energy tree-level limit of a generic string theory. The action contains the metric, dilaton, central charge and an antisymmetric tensor field. We show that with a homogeneous and isotropic metric, allowing spatial curvature, there is a formal equivalence between this system and a scalar field minimally coupled to Einstein gravity in a spatially flat metric. We refer to this system as the shifted frame and using it we describe the full range of cosmological evolution that this model can exhibit. We show that generic solutions begin (or end) with a singularity. As the system approaches a singularity the dilaton becomes becomes large and loop corrections will become important.

hep-th↗

arXiv1994

Inflationary Perturbations and Exponential Potentials

We consider the spectrum of primordial fluctuations produced by inflationary models where the inflaton potential is the sum of two exponential terms. A wide range of spectra result, with the only constraint being that the scalar spectrum must have more tilt than the tensor spectrum. This model can mimic the spectra of most inflationary models, as well as producing combinations of scalar and tensor perturbations not found in common varieties of slow-rolling inflation.

astro-ph↗

arXiv1993

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 powerlaw inflation, we find models where the inflationary period contains eras of both powerlaw and exponential growth.

gr-qc↗

arXiv1992

Calculating the Critical Temperature for Coleman-Weinberg GUTs

We study the finite temperature effective potential of the Higgs scalar in GUTs with Coleman-Weinberg symmetry breaking. The critical temperature is derived without employing a high temperature approximation to the effective potential, and the limitations of such approximations are discussed.

hep-ph↗