arXiv subjects

Andrew R Liddle

Publications and source records attributed to Andrew R Liddle.

At least 55 records · Page 3Linked to original sources

arXiv2006

The consistency equation hierarchy in single-field inflation models

Inflationary consistency equations relate the scalar and tensor perturbations. We elucidate the infinite hierarchy of consistency equations of single-field inflation, the first of which is the well-known relation A_T^2/A_S^2 = -n_T/2 between the amplitudes and the tensor spectral index. We write a general expression for all consistency equations both to first and second-order in the slow-roll expansion. We discuss the relation to other consistency equations that have appeared in the literature, in particular demonstrating that the approximate consistency equation recently introduced by Chung and collaborators is equivalent to the second consistency equation of Lidsey et al. (1997).

astro-ph↗

arXiv2005

Dynamics of assisted quintessence

We explore the dynamics of assisted quintessence, where more than one scalar field is present with the same potential. For potentials with tracking solutions, the fields naturally approach the same values; in the context of inflation this leads to the assisted inflation phenomenon where several fields can cooperate to drive a period of inflation though none is able to individually. For exponential potentials, we study the fixed points and their stability confirming results already in the literature, and then carry out a numerical analysis to show how assisted quintessence is realized. For inverse power-law potentials, we find by contrast that there is no assisted behaviour; indeed those are the unique (monotonic) potentials where several fields together behave just as a single field in the same potential. More generally, we provide an algorithm for generating a single-field potential giving equivalent dynamics to multi-field assisted quintessence.

astro-ph↗

arXiv2005

Stochastic approaches to inflation model building

While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by fundamental physics considerations or by simplicity. An alternative is to generate large numbers of models via a random generation process, such as the flow equations approach. The flow equations approach is known to predict a definite structure to the observational predictions. In this paper, we first demonstrate a more efficient implementation of the flow equations exploiting an analytic solution found by Liddle (2003). We then consider alternative stochastic methods of generating large numbers of inflation models, with the aim of testing whether the structures generated by the flow equations are robust. We find that while typically there remains some concentration of points in the observable plane under the different methods, there is significant variation in the predictions amongst the methods considered.

astro-ph↗

arXiv2005

Bayesian model selection and isocurvature perturbations

Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the performance of cosmological models including isocurvature modes with the purely adiabatic case; this framework automatically and consistently penalizes models which use more parameters to fit the data. We compute the Bayesian evidence for fits to a dataset comprised of WMAP and other microwave anisotropy data, the galaxy power spectrum from 2dFGRS and SDSS, and Type Ia supernovae luminosity distances. We find that Bayesian model selection favours the purely adiabatic models, but so far only at low significance.

astro-ph↗

arXiv2004

Braneworld flow equations

We generalize the flow equations approach to inflationary model building to the Randall-Sundrum Type II braneworld scenario. As the flow equations are quite insensitive to the expansion dynamics, we find results similar to, though not identical to, those found in the standard cosmology.

astro-ph↗

arXiv2004

The Cosmological Parameters

Pre-publication version withdrawn at the request of the journal. Final version now available in Reviews of Particle Physics at http://pdg.lbl.gov/2004/reviews/contents_sports.html

hep-ph↗

arXiv2004

The Cosmological Parameters

This is a new review article for The Review of Particle Physics 2004 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters as at the end of 2003. Topics included are Parametrizing the Universe; Extensions to the standard model; Probes; Bringing observations together; Outlook for the future.

astro-ph↗

arXiv2004

On the inflationary flow equations

I explore properties of the inflationary flow equations. I show that the flow equations do not correspond directly to inflationary dynamics. Nevertheless, they can be used as a rather complicated algorithm for generating inflationary models. I demonstrate that the flow equations can be solved analytically and give a closed form solution for the potentials to which flow equation solutions correspond. I end by considering some simpler algorithms for generating stochastic sets of slow-roll inflationary models for confrontation with observational data.

astro-ph↗

arXiv2003

How long before the end of inflation were observable perturbations produced?

We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $λϕ^4$ model which reduces the uncertainties in that case and favours a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $aH$. Finally, we discuss the impact of non-standard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.

astro-ph↗

arXiv2003

Observational constraints on braneworld chaotic inflation

We examine observational constraints on chaotic inflation models in the Randall-Sundrum Type II braneworld. If inflation takes place in the high-energy regime, the perturbations produced by the quadratic potential are further from scale-invariance than in the standard cosmology, in the quartic case more or less unchanged, while for potentials of greater exponent the trend is reversed. We test these predictions against a data compilation including the WMAP measurements of microwave anisotropies and the 2dF galaxy power spectrum. While in the standard cosmology the quartic potential is at the border of what the data allow and all higher powers excluded, we find that in the high-energy regime of braneworld inflation even the quadratic case is under strong observational pressure. We also investigate the intermediate regime where the brane tension is comparable to the inflationary energy scale, where the deviations from scale-invariance prove to be greater.

astro-ph↗

arXiv2003

The power spectrum amplitude from clusters revisited: σ_8 using simulations with preheating and cooling

The amplitude of density perturbations, for the currently-favoured LambdaCDM cosmology, is constrained using the observed properties of galaxy clusters. The catalogue used is that of Ikebe et al. (2002). The cluster temperature to mass relation is obtained via N-body/hydrodynamical simulations including radiative cooling and preheating of cluster gas, which we have previously shown to reproduce well the observed temperature--mass relation in the innermost parts of clusters (Thomas et al. 2002). We generate and compare mock catalogues via a Monte Carlo method, which allows us to constrain the relation between X-ray temperature and luminosity, including its scatter, simultaneously with cosmological parameters. We find a luminosity-temperature relation in good agreement with the results of Ikebe et al. (2002), while for the matter power spectrum normalization, we find $σ_8 = 0.78_{-0.06}^{+0.30}$ at 95 per cent confidence for $Ω_0 = 0.35$. Scaling to WMAP's central value of $Ω_0 = 0.27$ would give a best-fit value of $σ_8 \simeq 0.9$.

astro-ph↗

arXiv2003

Constraining slow-roll inflation with WMAP and 2dF

We constrain slow-roll inflationary models using the recent WMAP data combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the slow-roll parameters to be $0 < ε_1 < 0.032$ and $ε_2 + 5.0 ε_1 = 0.036 \pm 0.025$. For inflation models $V \propto ϕ^α$ we find that $α< 3.9, 4.3$ at the 2$σ$ and $3σ$ levels, indicating that the $λϕ^4$ model is under very strong pressure from observations. We define a convergence criterion to judge the necessity of introducing further power spectrum parameters such as the spectral index and running of the spectral index. This criterion is typically violated by models with large negative running that fit the data, indicating that the running cannot be reliably measured with present data.

astro-ph↗

arXiv2003

K-essence and the coincidence problem

K-essence has been proposed as a possible means of explaining the coincidence problem of the Universe beginning to accelerate only at the present epoch. We carry out a comprehensive dynamical systems analysis of the k-essence models given so far in the literature. We numerically study the basin of attraction of the tracker solutions and we highlight the behaviour of the field close to sound speed divergences. We find that, when written in terms of parameters with a simple dynamical interpretation, the basins of attraction represent only a small region of the phase space.

astro-ph↗

arXiv2003

Cosmological perturbations and the reionization epoch

We investigate the dependence of the epoch of reionization on the properties of cosmological perturbations, in the context of cosmologies permitted by WMAP. We compute the redshift of reionization using a simple model based on the Press-Schechter approximation. For a power-law initial spectrum we estimate that reionization is likely to occur at a redshift $z_{reion} = 17^{+10}_{-7}$, consistent with the WMAP determination based on the temperature-polarization cross power spectrum. We estimate the delay in reionization if there is a negative running of the spectral index, as weakly indicated by WMAP. We then investigate the dependence of the reionization redshift on the nature of the initial perturbations. We consider chi-squared probability distribution functions with various degrees of freedom, motivated both by non-standard inflationary scenarios and by defect models. We find that in these models reionization is likely occur much earlier, and to be a slower process, than in the case of initial gaussian fluctuations. We also consider a hybrid model in which cosmic strings make an important contribution to the seed fluctuations on scales relevant for reionization. We find that in order for that model to agree with the latest WMAP results, the string contribution to the matter power spectrum on the standard $8 h^{-1} Mpc$ scale is likely to be at most at the level of one percent, which imposes tight constraints on the value of the string mass per unit length.

astro-ph↗

arXiv2003

Primordial black holes in braneworld cosmologies: astrophysical constraints

In two recent papers we explored the modifications to primordial black hole physics when one moves to the simplest braneworld model, Randall--Sundrum type II. Both the evaporation law and the cosmological evolution of the population can be modified, and additionally accretion of energy from the background can be dominant over evaporation at high energies. In this paper we present a detailed study of how this impacts upon various astrophysical constraints, analyzing constraints from the present density, from the present high-energy photon background radiation, from distortion of the microwave background spectrum, and from processes affecting light element abundances both during and after nucleosynthesis. Typically, the constraints on the formation rate of primordial black holes weaken as compared to the standard cosmology if black hole accretion is unimportant at high energies, but can be strengthened in the case of efficient accretion.

astro-ph↗

arXiv2003

A new view of k-essence

K-essence models, relying on scalar fields with non-canonical kinetic terms, have been proposed as an alternative to quintessence in explaining the observed acceleration of the Universe. We consider the use of field redefinitions to cast k-essence in a more familiar form. While k-essence models cannot in general be rewritten in the form of quintessence models, we show that in certain dynamical regimes an equivalence can be made, which in particular can shed light on the tracking behaviour of k-essence. In several cases, k-essence cannot be observationally distinguished from quintessence using the homogeneous evolution, though there may be small effects on the perturbation spectrum. We make a detailed analysis of two k-essence models from the literature and comment on the nature of the fine tuning arising in the models.

astro-ph↗

arXiv2002

Microwave background constraints on inflationary parameters

We use a compilation of cosmic microwave anisotropy data (including the recent VSA, CBI and Archeops results), supplemented with an additional constraint on the expansion rate, to directly constrain the parameters of slow-roll inflation models. We find good agreement with other papers concerning the cosmological parameters, and display constraints on the power spectrum amplitude from inflation and the first two slow-roll parameters, finding in particular that $ε_1 < 0.057$. The technique we use for parametrizing inflationary spectra may become essential once the data quality improves significantly.

astro-ph↗

arXiv2002

Primordial black holes in braneworld cosmologies: Accretion after formation

We recently studied the formation and evaporation of primordial black holes in a simple braneworld cosmology, namely Randall-Sundrum Type II. Here we study the effect of accretion from the cosmological background onto the black holes after formation. While it is generally believed that in the standard cosmology such accretion is of negligible importance, we find that during the high-energy regime of braneworld cosmology accretion can be the dominant effect and lead to a mass increase of potentially orders of magnitude. However, unfortunately the growth is exponentially sensitive to the accretion efficiency, which cannot be determined accurately. Since accretion becomes unimportant once the high-energy regime is over, it does not affect any constraints expressed at the time of black hole evaporation, but it can change the interpretation of those constraints in terms of early Universe formation rates.

astro-ph↗