arXiv subjects

David H Lyth

Publications and source records attributed to David H Lyth.

At least 19 recordsLinked to original sources

arXiv2003

Conserved cosmological perturbations

A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity, defined using a slicing of spacetime such that the expansion between slices is spatially homogeneous. To first order, on super-horizon scales, the slicing with unperturbed intrinsic curvature has this property. A general construction is given for conserved quantities, yielding the curvature perturbation $ζ$ as well as more recently-considered conserved perturbations. The construction may be extended to higher orders in perturbation theory and even into the non-perturbative regime.

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arXiv2003

The CDM isocurvature perturbation in the curvaton scenario

We discuss the residual isocurvature perturbations, fully-correlated with the curvature perturbation, that are automatic in the curvaton scenario if curvaton decay is sufficiently late. We contrast these residual isocurvature perturbations with the generally un-correlated `intrinsic' isocurvature perturbation generated by an additional field such as the axion. We present a general formula for the residual isocurvature perturbations, referring only to the generation of the relevant quantity (Cold Dark Matter, baryon number or lepton number) in an unperturbed universe. Specific formulas for the residual isocurvature CDM perturbation are given, for most of the commonly-considered CDM candidates.

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arXiv2000

Late-time creation of gravitinos from the vacuum

Starting with the vacuum fluctuation, it is known that gravitinos will be created just after inflation, with number density $\sim 10^{-2}M^3$ where $M$ is the mass of the inflaton. Here, we argue that creation may be expected to continue, maintaining about the same number density, until a usually much later epoch. This epoch is either the `intermediate epoch' when Hubble parameter falls below the gravitino mass, or the reheat epoch if that is earlier. We verify that such late-time creation indeed occurs if only a single chiral superfield is relevant, using the description of the helicity 1/2 gravitino provided recently by Kallosh et. al. (hep-th/9907124) and Giudice et. al. (hep-ph/9907510). Arguments are presented in favor of late-time creation in the general case. For the usual inflation models, $M$ is rather large and gravitinos from late-time creation are so abundant that a subsequent era of thermal inflation is needed to dilute them.

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arXiv1999

The gravitino abundance in supersymmetric `new' inflation models

We consider the abundance of gravitinos created from the vacuum fluctuation, in a class of `new' inflation models for which global supersymmetry is a good approximation. Immediately after inflation, gravitinos are produced, with number density determined by equations recently presented by Kallosh et. al. (hep-th/9907124) and Giudice et. al. (hep-ph/9907510). Unless reheating intervenes, creation may continue, maintaining about the same number density, until the Hubble parameter falls below the gravitino mass. In any case, the abundance of gravitinos created from the vacuum fluctuation exceeds the abundance from thermal collisions in a significant regime of parameter space, leading to tighter cosmological constraints.

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arXiv1999

Constraints on TeV-scale hybrid inflation and comments on non-hybrid alternatives

During hybrid inflation, the slowly-rolling inflaton field has a significant coupling to the trigger field which is responsible for most of the potential. Barring a fine-tuned accidental cancellation, this coupling induces a minimal one-loop contribution to the inflaton potential. The requirement that this contribution be not too large constrains a wide class of hybrid inflation models. Assuming that the inflaton perturbation generates structure in the Universe, the inflaton field and/or the trigger field after inflation have to be bigger than $10^9\GeV$. This and other results make hybrid inflation at or below the TeV scale problematical. (There is no problem with hybrid inflation at the high energy scales normally considered.) `New' and thermal inflation seem to be viable alternatives for inflation at or below the TeV scale, including the case that quantum gravity is at the TeV scale. In any case, supersymmetry is needed required during inflation, in order to protect a scalar mass.

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arXiv1999

Models of inflation and their predictions

Taking field theory seriously, inflation model-building is difficult but not impossible. The observed value of the spectral index of the adiabatic density perturbation is starting to discriminate between models, and may well pick out a unique one in the forseeable future.

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arXiv1999

Inflation with TeV-scale gravity

Allowing for the possibility of large extra dimensions, the fundamental Planck scale $M$ could be anywhere in the range $\TeV\lsim M\lsim \mpl$, where $\mpl=2.4\times 10^{18}\GeV$ is the four-dimensional Planck scale. If $M\sim\TeV$, quantum corrections would not destabilize the Higgs mass even if there were no supersymmetry. But we point out that supersymmetry must in fact be present, if there is an era of cosmological inflation, since during such an era the inflaton mass satisfies $m\ll M^2/\mpl=10^{-15}(M/\TeV)$ and supersymmetry will be needed to protect it. If the inflation hypothesis is accepted, there is no reason to think that Nature has chosen the low value $M\sim \TeV$, however convenient that choice might have been for the next generation of collider experiments.

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arXiv1996

Normalization of modes in an open universe

We discuss the appropriate normalization of modes required to generate a homogeneous random field in an open Friedmann-Robertson-Walker universe. We consider scalar random fields and certain tensor random fields that can be obtained by covariantly differentiating a scalar. Modes of interest fall into three categories: the familiar sub-curvature modes, the more recently discussed super-curvature modes, and a set of discrete modes with positive eigenvalues which can be used to generate homogeneous tensor random fields even though the underlying scalar field is not homogeneous. A particular example of the last case which has been discussed in the literature is the bubble wall fluctuation in open inflationary universes.

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arXiv1996

Cold Dark Matter Models with a Cosmological Constant

We use linear and quasi-linear perturbation theory to analyse cold dark matter models of structure formation in spatially flat models with a cosmological constant. Both a tilted spectrum of density perturbations and a significant gravitational wave contribution to the microwave anisotropy are allowed as possibilities. We provide normalizations of the models to microwave anisotropies, as given by the four-year {\it COBE} observations, and show how all the normalization information for such models, including tilt, can be condensed into a single fitting function which is independent of the value of the Hubble parameter. We then discuss a wide variety of other types of observations. We find that a very wide parameter space is available for these models, provided $Ω_0$ is greater than about 0.3, and that large-scale structure observations show no preference for any particular value of $Ω_0$ in the range 0.3 to 1.

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arXiv1996

Pursuing Parameters for Critical Density Dark Matter Models

We present an extensive comparison of models of structure formation with observations, based on linear and quasi-linear theory. We assume a critical matter density, and study both cold dark matter models and cold plus hot dark matter models. We explore a wide range of parameters, by varying the fraction of hot dark matter $Ω_ν$, the Hubble parameter $h$ and the spectral index of density perturbations $n$, and allowing for the possibility of gravitational waves from inflation influencing large-angle microwave background anisotropies. New calculations are made of the transfer functions describing the linear power spectrum, with special emphasis on improving the accuracy on short scales where there are strong constraints. For assessing early object formation, the transfer functions are explicitly evaluated at the appropriate redshift. The observations considered are the four-year {\it COBE} observations of microwave background anisotropies, peculiar velocity flows, the galaxy correlation function, and the abundances of galaxy clusters, quasars and damped Lyman alpha systems. Each observation is interpreted in terms of the power spectrum filtered by a top-hat window function. We find that there remains a viable region of parameter space for critical-density models when all the dark matter is cold, though $h$ must be less than 0.5 before any fit is found and $n$ significantly below unity is preferred. Once a hot dark matter component is invoked, a wide parameter space is acceptable, including $n\simeq 1$. The allowed region is characterized by $Ω_ν\la 0.35$ and $0.60 \la n \la 1.25$, at 95 per cent confidence on at least one piece of data. There is no useful lower bound on $h$, and for curious combinations of the other parameters it is possible to fit the data with $h$ as high as 0.65.

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arXiv1995

Thermal Inflation and the Moduli Problem

In supersymmetric theories a field can develop a vacuum expectation value $M \gg 10^3\,{\rm GeV}$, even though its mass $m$ is of order $10^2$ to $10^3\,{\rm GeV}$. The finite temperature in the early Universe can hold such a field at zero, corresponding to a false vacuum with energy density $ V_0 \sim m^2 M^2 $. When the temperature falls below $V_0^{1/4}$, the thermal energy density becomes negligible and an era of thermal inflation begins. It ends when the field rolls away from zero at a temperature of order $m$, corresponding to of order 10 $e$-folds of inflation which does not affect the density perturbation generated during ordinary inflation. Thermal inflation can solve the Polonyi/moduli problem if $M$ is within one or two orders of magnitude of $10^{12}\,{\rm GeV}$.

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arXiv1995

Open Cold Dark Matter Models

Motivated by recent developments in inflationary cosmology indicating the possibility of obtaining genuinely open universes in some models, we compare the predictions of cold dark matter (CDM) models in open universes with a variety of observational information. The spectrum of the primordial curvature perturbation is taken to be scale invariant (spectral index $n=1$), corresponding to a flat inflationary potential. We allow arbitrary variation of the density parameter $Ω_0$ and the Hubble parameter $h$, and take full account of the baryon content assuming standard nucleosynthesis. We normalize the power spectrum using the recent analysis of the two year {\it COBE} DMR data by Górski et al. We then consider a variety of observations, namely the galaxy correlation function, bulk flows, the abundance of galaxy clusters and the abundance of damped Lyman alpha systems. For the last two of these, we provide a new treatment appropriate to open universes. We find that, if one allows an arbitrary $h$, then a good fit is available for any $Ω_0$ greater than 0.35, though for $Ω_0$ close to 1 the required $h$ is alarmingly low. Models with $Ω_0 < 0.35$ seem unable to fit observations while keeping the universe over $10$ Gyr old; this limit is somewhat higher than that appearing in the literature thus far. If one assumes a value of $h > 0.6$, as favoured by recent measurements, concordance with the data is only possible for the narrow range $0.35 < Ω_0 < 0.55$. We have also investigated $n \neq 1$; the extra freedom naturally widens the allowed parameter region. Assuming a range $0.9 0.6$ is at most $0.30 < Ω_0 < 0.60$.

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arXiv1995

The Open Universe Grishchuk-Zel'dovich Effect

The Grishchuk--Zel'dovich effect is the contribution to the microwave background anisotropy from an extremely large scale adiabatic density perturbation, on the standard hypothesis that this perturbation is a typical realization of a homogeneous Gaussian random field. We analyze this effect in open universes, corresponding to density parameter $Ω_0<1$ with no cosmological constant, and concentrate on the recently discussed super-curvature modes. The effect is present in all of the low multipoles of the anisotropy, in contrast with the $Ω_0=1$ case where only the quadrupole receives a contribution. However, for no value of $Ω_0$ can a very large scale perturbation generate a spectrum capable of matching observations across a wide range of multipoles. We evaluate the magnitude of the effect coming from a given wavenumber as a function of the magnitude of the density perturbation, conveniently specified by the mean-square curvature perturbation. From the absence of the effect at the observed level, we find that for $0.25\leqΩ_0\leq 0.8$, a curvature perturbation of order unity is permitted only for inverse wavenumbers more than one thousand times the size of the observable universe. As $Ω_0$ tends to one, the constraint weakens to the flat space result that the inverse wavenumber be more than a hundred times the size of the observable universe, whereas for $Ω_0 < 0.25$ it becomes stronger. We explain the physical meaning of these results, by relating them to the correlation length of the perturbation. Finally, in an Appendix we consider the dipole anisotropy and show that it always leads to weaker constraints.

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arXiv1995

LARGE SCALE PERTURBATIONS IN THE OPEN UNIVERSE

When considering perturbations in an open (Omega<1) universe, cosmologists retain only sub-curvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than -1 in units of the curvature scale, in contrast with the super-curvature modes whose eigenvalue is between -1 and 0). Mathematicians have known for almost half a century that all modes must be included to generate the most general HOMOGENEOUS GAUSSIAN RANDOM FIELD, despite the fact that any square integrable FUNCTION can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. The mathematics is here explained in a language accessible to physicists. Then it is pointed out that if the perturbations originate as a vacuum fluctuation of a scalar field there will be no super-curvature modes in nature. Finally the effect on the cmb of any super-curvature contribution is considered, which generalizes to Omega<1 the analysis given by Grishchuk and Zeldovich in 1978. A formula is given, which is used to estimate the effect. In contrast with the case Omega=1, the effect contributes to all multipoles, not just to the quadrupole. It is important to find out whether it has the same l dependence as the data, by evaluating the formula numerically.

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arXiv1994

False Vacuum Inflation with a Quartic Potential

We consider a variant of Hybrid Inflation, where inflation is driven by two interacting scalar fields, one of which has a `Mexican hat' potential and the other a quartic potential. Given the appropriate initial conditions one of the fields can be trapped in a false vacuum state, supported by couplings to the other field. The energy of this vacuum can be used to drive inflation, which ends when the vacuum decays to one of its true minima. Depending on parameters, it is possible for inflation to proceed via two separate epochs, with the potential temporarily steepening sufficiently to suspend inflation. We use numerical simulations to analyse the possibilities, and emphasise the shortcomings of the slow-roll approximation for analysing this scenario. We also calculate the density perturbations produced, which can have a spectral index greater than one.

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arXiv1994

Trends in Large Scale Structure Observations and the Likelihood of Early Reionization

With the imminent promise of constraints on the epoch of reionization from observations of microwave background anisotropies, the question of whether or not the standard Cold Dark Matter (CDM) model permits early reionization has been subjected to detailed investigation by various authors, with the conclusion that reionization may occur at quite high redshift. However, it is widely accepted that this model is excluded, as when normalised to the COBE observations it possesses excessive galaxy clustering on scales below tens of megaparsecs. We examine the trends of observations, first in a fairly model independent way, and second by considering variants on the standard CDM model introduced to resolve the observational conflicts. We conclude that the epoch of reionization favoured by the observational data is typically considerably later than the standard CDM model suggests, and amongst models which may fit the observational data only the introduction of a cosmological constant leads to a reionization redshift close to that of standard CDM.

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arXiv1994

Interpreting Large Scale Structure Observations

The standard model of large scale structure is considered, in which the structure originates as a Gaussian adiabatic density perturbation with a nearly scale invariant spectrum. The basic theoretical tool of cosmological perturbation theory is described, as well as the possible origin of the density perturbation as a vacuum fluctuation during inflation. Then, after normalising the spectrum to fit the cosmic microwave background anisotropy measured by COBE, some versions of the standard model are compared with a variety of data coming from observations of galaxies and galaxy clusters. The recent COBE analysis of Górski and collaborators is used, which gives a significantly higher normalization than earlier ones. The comparison with galaxy and cluster data is done using linear theory, supplemented by the Press-Schechter formula when discussing object abundances of rich clusters and of damped Lyman alpha systems. By focussing on the smoothed density contrast as a function of scale, the observational data can be conveniently illustrated on a single figure, facilitating easy comparison with theory. The spectral index is constrained to $0.6<n<1.1$, and in particle physics motivated models that predict significant gravitational waves the lower limit is tightened to $0.8$. [To appear, Proceedings of Journee Cosmologie, Paris, June 1994]

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arXiv1994

Observational Constraints on the Spectral Index

We address the possibility of bounding the spectral index $n$ of primordial density fluctuations, using both the cosmic microwave background (cmb) anisotropy and data on galaxies and clusters. Each piece of galaxy and cluster data is reduced to a value of $σ(R)$ (the linearly evolved {\em rms} density contrast with top hat smoothing on scale $R$) which allows data on different scales to be readily compared. As a preliminary application, we normalise the spectrum using the ten degree variance of the COBE data, and then compare the prediction with a limited sample of low energy data, for the MDM model with various values of $n$, $Ω_ν$ and $h$. With $h=.5$, the data constrain the spectral index to the range $0.7\lsim n \lsim 1.2$. If gravitational waves contribute to the cmb anisotropy with relative strength $R=6(1-n)$ (as in some models of inflation), the lower limit on $n$ is increased to about $0.85$. The uncertainty in $h$ widens this band by about $0.1$ at either end.

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