arXiv subjects

James E. Lidsey

Publications and source records attributed to James E. Lidsey.

86 records · Page 5Linked to original sources

arXiv1995

Wavefunctions for Highly Anisotropic Homogeneous Cosmologies

The canonical quantization of homogeneous cosmologies is considered in the high anisotropic limit. Exact wavefunctions are found in this limit when the momentum constraints are reduced at the classical level. Lorentzian solutions that represent tunnelling from classically forbidden regimes are identified. Solutions to the modified Wheeler-DeWitt equation are also found for the vacuum Bianchi IX model when a quantum reduction of the momentum constraints is considered.

gr-qc↗

arXiv1995

Quantum Cosmology of Generalized Two--Dimensional Dilaton Gravity Models

The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding Wheeler-DeWitt equation are presented. A wider class of minisuperspace models that can be solved in this fashion is identified. Supersymmetric extensions to the induced gravity theory and the bosonic string theory are then considered and closed-form solutions to the associated quantum constraints are derived. The possibility of applying the third-quantization procedure to two-dimensional dilaton-gravity is briefly discussed.

gr-qc↗

arXiv1994

The Andante Regime of Scalar Field Dynamics

The andante regime of scalar field dynamics in the chaotic inflationary Universe is defined as the epoch when the field is rolling moderately slowly down its interaction potential, but at such a rate that first-order corrections to the slow-roll approximation become important. These conditions should apply towards the end of inflation as the field approaches the global minimum of the potential. Solutions to the Einstein-scalar field equations for the class of power law potentials $V(ϕ) \propto ϕ^{2n}$ are found in this regime in terms of the inverse error function.

astro-ph↗

arXiv1994

Black Holes from Blue Spectra

Blue primordial power spectra with a spectral index $n>1$ can lead to a significant production of primordial black holes in the very early Universe. The evaporation of these objects leads to a number of observational consequences and a model independent upper limit of $n \approx 1.4$. In some cases this limit is strengthened to $n=1.3$. Such limits may be employed to define the boundary to the region of parameter space consistent with generalized inflationary predictions. [To appear in Proceedings of the CASE WESTERN CMB WORKSHOP, April 22-24 1994. Figures available on request from J.H.Gilbert@qmw.ac.uk]

astro-ph↗

arXiv1994

Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra

Blue primordial power spectra have spectral index $n>1$ and arise naturally in the recently proposed hybrid inflationary scenario. An observational upper limit on {\em n} is derived by normalizing the spectrum at the quadrupole scale and considering the possible overproduction of Planck mass relics formed in the final stage of primordial black hole evaporation. In the inflationary Universe with the maximum reheating temperature compatible with the observed quadrupole anisotropy, the upper limit is $n=1.4$, but it is slightly weaker for lower reheat temperatures. This limit applies over 57 decades of mass and is therefore insensitive to cosmic variance and any gravitational wave contribution to the quadrupole anisotropy. It is also independent of the dark matter content of the Universe and therefore the bias parameter. In some circumstances, there may be an extended dust-like phase between the end of inflation and reheating. In this case, primordial black holes form more abundantly and the upper limit is $n=1.3$.

astro-ph↗

arXiv1994

A Potential Window to the GUT

The possibility that the form of the inflationary potential can be reconstructed from a knowledge of the primordial power spectra of scalar (density) and tensor (gravity wave) perturbations is discussed and reviewed. It is suggested that measurements of the scalar spectral index and the amplitude of the tensor spectrum at one scale should be possible in the near future. This would be sufficient to determine whether the potential is convex or concave over the limited region relevant to the formation of large-scale structure in the universe. Such information would provide an `observation' of physics at energy scales above $10^{14}$GeV. $^*$Invited talk presented at {\em The Second Alexander Friedmann International Seminar on Gravitation and Cosmology, St. Petersburg, Russia, 12th-19th September 1993.}

astro-ph↗

arXiv1994

Stringy Quantum Cosmology of the Bianchi Class a

The quantum cosmology of the string effective action is considered within the context of the Bianchi class A minisuperspace. An exact unified solution is found for all Bianchi types and interpreted physically as a quantum wormhole. The solution is generalized for types ${\rm VI_0}$ and ${\rm VII_0}$. The Bianchi type IX wavefunction becomes increasingly localized around the isotropic Universe at large three-geometries.

gr-qc↗

arXiv1993

Solutions to the Wheeler-Dewitt Equation Inspired by the String Effective Action

The Wheeler-DeWitt equation is derived from the bosonic sector of the heterotic string effective action assuming a toroidal compactification. The spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology is investigated and a suitable change of variables rewrites the equation in a canonical form. Real- and imaginary-phase exact solutions are found and a method of successive approximations is employed to find more general power series solutions. The quantum cosmology of the Bianchi IX universe is also investigated and a class of exact solutions is found.

gr-qc↗

arXiv1993

Tilting the Primordial Power Spectrum with Bulk Viscosity

Within the context of the cold dark matter model, current observations suggest that inflationary models which generate a tilted primordial power spectrum with negligible gravitational waves provide the most promising mechanism for explaining large scale clustering. The general form of the inflationary potential which produces such a spectrum is a hyperbolic function and is interpreted physically as a bulk viscous stress contribution to the energy-momentum of a perfect baryotropic fluid. This is equivalent to expanding the equation of state as a truncated Taylor series. Particle physics models which lead to such a potential are discussed.

astro-ph↗

arXiv1993

On Identifying the Present-Day Vacuum Energy with the Potential Driving Inflation

There exists a growing body of observational evidence supporting a non-vanishing cosmological constant at the present epoch. We examine the possibility that such a term may arise directly from the potential energy which drove an inflationary expansion of the very early universe. To avoid arbitrary alterations in the shape of this potential at various epochs it is necessary to introduce a time-dependent viscosity into the system. The evolution of the effective Planck mass in scalar-tensor theories is a natural candidate for such an effect. In these models there are observational constraints arising from anisotropies in the cosmic microwave background, large-scale galactic structure, observations of the primordial Helium abundance and solar system tests of general relativity. Decaying power law and exponential potentials are considered, but for these models it is very difficult to simultaneously satisfy all of the limits. This may have implications for the joint evolution of the gravitational and cosmological constants.

astro-ph↗

arXiv1993

Reconstructing the Inflaton Potential---Perturbative Reconstruction to Second Order

One method to reconstruct the scalar field potential of inflation is a perturbative approach, where the values of the potential and its derivatives are calculated as an expansion in departures from the slow-roll approximation. They can then be expressed in terms of observable quantities, such as the square of the ratio of the gravitational wave amplitude to the density perturbation amplitude, the deviation of the spectral index from the Harrison--Zel'dovich value, etc. Here, we calculate complete expressions for the second-order contributions to the coefficients of the expansion by including for the first time corrections to the standard expressions for the perturbation spectra. As well as offering an improved result, these corrections indicate the expected accuracy of the reconstruction. Typically the corrections are only a few percent.

astro-ph↗

arXiv1993

Tensor Perturbations in Inflationary Models as a Probe of Cosmology

In principle, the tensor metric (gravity-wave) perturbations that arise in inflationary models can, beyond probing the underlying inflationary model, provide information about the Universe: ionization history, presence of a cosmological constant, and epoch of matter-radiation equality. Because tensor perturbations give rise to anisotropy of the cosmic background radiation (CBR) solely through the Sachs-Wolfe effect we are able to calculate analytically the variance of the multipole moments of this part of the CBR temperature anisotropy. In so doing, we carefully take account of the contribution of tensor perturbations that entered the Hubble radius during both the matter-dominated and radiation-dominated epoch by means of a transfer function. The striking feature in the spectrum of multipole amplitudes is a dramatic fall off for $l\ga \sqrt{1+\zl}$, where $\zl$ is the red shift of the last-scattering surface. ...

astro-ph↗

arXiv1993

Observing the Inflaton Potential

We show how observations of the density perturbation (scalar) spectrum and the gravitational wave (tensor) spectrum allow a reconstruction of the potential responsible for cosmological inflation. A complete functional reconstruction or a perturbative approximation about a single scale are possible; the suitability of each approach depends on the data available. Consistency equations between the scalar and tensor spectra are derived, which provide a powerful signal of inflation.

hep-ph↗

arXiv1993

Reconstructing the Inflaton Potential---in Principle and in Practice

Generalizing the original work by Hodges and Blumenthal, we outline a formalism which allows one, in principle, to reconstruct the potential of the inflaton field from knowledge of the tensor gravitational wave spectrum or the scalar density fluctuation spectrum, with special emphasis on the importance of the tensor spectrum. We provide some illustrative examples of such reconstruction. We then discuss in some detail the question of whether one can use real observations to carry out this procedure. We conclude that in practice, a full reconstruction of the functional form of the potential will not be possible within the foreseeable future. However, with a knowledge of the dark matter components, it should soon be possible to combine intermediate-scale data with measurements of large-scale cosmic microwave background anisotropies to yield useful information regarding the potential.

hep-ph↗