arXiv subjects

Andrew R Liddle

Publications and source records attributed to Andrew R Liddle.

136 records · Page 8Linked to original sources

arXiv1994

Second-Order Reconstruction of the Inflationary Potential

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, $n$ and $n_T$, and their contributions to the variance of the quadrupole CBR temperature anisotropy, $S$ and $T$. In addition, there is a ``consistency relation'' between these quantities: $n_T= -{1\over 7}{T\over S}$. We discuss the overall strategy of perturbative reconstruction and derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, all in terms of $n$, $n_T$, $S$, $T$, and $dn/d\ln k$. We also obtain the second-order consistency relation, $n_T =-{1\over 7}{T\over S}[1+0.11{T\over S} + 0.15 (n-1)]$. As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Padé approximant as a greatly improved alternative.

astro-ph↗

arXiv1994

Texture-Induced Microwave Background Anisotropies

We use numerical simulations to calculate the cosmic microwave background anisotropy induced by the evolution of a global texture field, with special emphasis on individual textures. Both spherically symmetric and general configurations are analysed, and in the latter case we consider field configurations which exhibit unwinding events and also ones which do not. We compare the results given by evolving the field numerically under both the expanded core (XCORE) and non-linear sigma model (NLSM) approximations with the analytic predictions of the NLSM exact solution for a spherically symmetric self-similar (SSSS) unwinding. We find that the random unwinding configuration spots' typical peak height is 60--75\% and angular size typically only 10\% of those of the SSSS unwinding, and that random configurations without an unwinding event nonetheless may generate indistinguishable hot and cold spots. The influence of these results on analytic estimates of texture induced microwave anisotropies is examined, and comparison made with other numerical work.

astro-ph↗

arXiv1994

False Vacuum Inflation with Einstein Gravity

We investigate chaotic inflation models with two scalar fields, such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to Linde's second-order `Hybrid Inflation'; with the false vacuum dominating, inflation differs from the usual true vacuum case both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation can be very close to 1, or it can be around ten percent higher. The energy scale at the end of inflation can be anywhere between $10^{16}$\,GeV and $10^{11}$\,GeV, though reheating is prompt so the reheat temperature can't be far below $10^{11}\,$GeV. Topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they can have significant effects. Because false vacuum inflation occurs with the inflaton field far below the Planck scale, it is easier to implement in the context of supergravity than standard chaotic inflation. That the inflaton mass is small compared with the inflationary Hubble parameter is still a problem for generic supergravity theories, but remarkably this can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic, superstring

astro-ph↗

arXiv1993

Extended Inflation with a Curvature-Coupled Inflaton

We examine extended inflation models enhanced by the addition of a coupling between the inflaton field and the space-time curvature. We examine two types of model, where the underlying inflaton potential takes on second-order and first-order form respectively. One aim is to provide models which satisfy the solar system constraints on the Brans--Dicke parameter $ω$. This constraint has proven very problematic in previous extended inflation models, and we find circumstances where it can be successfully evaded, though the constraint must be carefully assessed in our model and can be much stronger than the usual $ω> 500$. In the simplest versions of the model, one may avoid the need to introduce a mass for the Brans--Dicke field in order to ensure that it takes on the correct value at the present epoch, as seems to be required in hyperextended inflation. We also briefly discuss aspects of the formation of topological defects in the inflaton field itself.

astro-ph↗

arXiv1993

Can the Gravitational Wave Background from Inflation be Detected Locally?

The Cosmic Background Explorer (COBE) detection of microwave background anisotropies may contain a component due to gravitational waves generated by inflation. It is shown that the gravitational waves from inflation might be seen using `beam-in-space' detectors, but not the Laser Interferometer Gravity Wave Observatory (LIGO). The central conclusion, dependent only on weak assumptions regarding the physics of inflation, is a surprising one. The larger the component of the COBE signal due to gravitational waves, the {\em smaller} the expected local gravitational wave signal.

gr-qc↗

arXiv1993

The Inflationary Energy Scale

The energy scale of inflation is of much interest, as it suggests the scale of grand unified physics and also governs whether cosmological events such as topological defect formation can occur after inflation. The COBE results are used to limit the energy scale of inflation at around 60 $e$-foldings from the end of inflation. An exact dynamical treatment based on the Hamilton-Jacobi equations is then used to translate this into limits on the energy scale at the end of inflation. General constraints are given, and then tighter constraints based on physically motivated assumptions regarding the allowed forms of density perturbation and gravitational wave spectra. These are also compared with the values of familiar models.

astro-ph↗

arXiv1993

Inflation and Mixed Dark Matter Models

Recent large scale structure observations, including COBE, have prompted many authors to discuss modifications of the standard Cold Dark Matter model. Two of these, a tilted spectrum and a gravitational wave contribution to COBE, are at some level demanded by theory under the usual assumption that inflation generates the primeval perturbations. The third, whose motivation comes by contrast from observation, is the introduction of a component of hot dark matter to give the Mixed Dark Matter model. We discuss the implication of taking these modifications together. Should Mixed Dark Matter prove necessary, very strong constraints on inflationary models will ensue.

astro-ph↗

arXiv1993

The Cold Dark Matter Density Perturbation

This is a review of the Cold Dark Matter model of structure formation, and its variants. The approach is largely from first principles, the main aim being to impart a basic understanding of the relevant theory with an eye to the likely intense activity of the next few years, but the current observational status of the model is also critically assessed. The evolution of adiabatic and isocurvature density perturbations is described, and their effect on the large scale cmb anisotropy calculated as well as that of any gravitational waves. The generation of all three types of perturbation during inflation is described, and the normalisation and spectral indices are calculated in terms of the inflationary potential and its first and second derivatives. The comparison of the theory with each type of observation is described, starting with the COBE data and moving down in scale to the non-linear regime. Constraints on the spectrum of the adiabatic density perturbation are exhibited, the spectrum being parametrised by its normalisation and its degree of tilt. Finally extensions of the CDM model are considered, which replace some of the cold dark matter by hot dark matter or a cosmological constant.

astro-ph↗

arXiv1993

Perturbation Spectra from Intermediate Inflation

We investigate models of `intermediate' inflation, where the scale factor $a(t)$ grows as $a(t) = \exp (A t^f)$, $0 < f < 1$, $A$ constant. These solutions arise as exact analytic solutions for a given class of potentials for the inflaton $ϕ$. For a simpler class of potentials falling off as a power of $ϕ$ they arise as slow-roll solutions, and in particular they include, for $f = 2/3$, the class of potentials which give the Harrison--Zel'dovich spectrum. The perturbation spectral index $n$ can be greater than unity on astrophysical scales. It is also possible to generate substantial gravitational waves while keeping the scalar spectrum close to scale-invariance; this latter possibility performs well when confronted with most observational data.

astro-ph↗

arXiv1992

COBE, Gravitational Waves, Inflation and Extended Inflation

We analyse the implications for inflationary models of the cosmic microwave background (cmb) anisotropy measured by COBE. Vacuum fluctuations during inflation generate an adiabatic density perturbation, and also gravitational waves. The ratio of these two contributions to the cmb anisotropy is given for an arbitrary slow-roll inflaton potential. Results from the IRAS/QDOT and POTENT galaxy surveys are used to normalise the spectrum of the density perturbation on the scale $20h^{-1}\Mpc$, so that the COBE measurement on the scale $10^3h^{-1}\Mpc$ provides a lower bound on the spectral index $n$. For `power law' and `extended' inflation, gravitational waves are significant and the bound is $n>0.84$ at the $2$-sigma level. For `natural' inflation, gravitational waves are negligible and the constraint is weakened to $n>0.70$, at best marginally consistent with a recent proposal for explaining the excess clustering observed in the APM galaxy survey. Many versions of extended inflation, including those based on the Brans--Dicke theory, are ruled out, because they require $n\lsim 0.75$ in order that bubbles formed at the end of inflation should not be observed now in the cmb.

astro-ph↗