arXiv subjects
Publications and source records attributed to David H. Lyth.
An alternative to a cosmological constant is quintessence, defined as a slowly-varying scalar field potential V(ϕ). If quintessence is observationally significant, an epoch of inflation is beginning at the present epoch, with ϕthe slowly-rolling inflaton field. In contrast with ordinary inflation, quintessence seems to require extreme fine tuning of the potential V(ϕ). The degree of fine-tuning is quantified in various cases.
In a large region of parameter space, the tree-level hybrid inflation model is likely to be be invalidated by loop corrections. In particular, this is likely to be the case if both quartic couplings are of order unity, as is often supposed. It is likely also to be the case if there is an ultra-violet cutoff far below the Planck scale, ($\luv\lsim 10^9\GeV(V_0^{1/4}/1\MeV)^{2/5}$, where $V_0$ is the height of the potential) unless one allows field values bigger than the cutoff.
This is a review of particle-theory models of inflation, and of their predictions for the primordial density perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational cosmology, of elementary field theory and of supersymmetry, that may be of interest in their own right. The spectral index $n(k)$, specifying the scale-dependence of the spectrum of the curvature perturbation, will be a powerful discriminator between models, when it is measured by Planck with accuracy $Δn\sim 0.01$. The usual formula for $n$ is derived, as well as its less familiar extension to the case of a multi-component inflaton; in both cases the key ingredient is the separate evolution of causally disconnected regions of the Universe. Primordial gravitational waves will be an even more powerful discriminator if they are observed, since most models of inflation predict that they are completely negligible. We treat in detail the new wave of models, which are firmly rooted in modern particle theory and have supersymmetry as a crucial ingredient. The review is addressed to both astrophysicists and particle physicists, and each section is fairly homogeneous regarding the assumed background knowledge.
We study in detail a supersymmetric Peccei-Quinn model, which has a DFSZ and a KSVZ version. The fields breaking the Peccei-Quinn (PQ) symmetry correspond to flat directions (flaton fields) and have unsuppressed couplings when PQ symmetry is unbroken. The models have interesting particle physics phenomenology. The PQ scale is naturally generated through radiative corrections; also, in the DFSZ case the $μ$ problem can be solved and neutrino masses can be generated. Cosmologically they lead to a short period of thermal inflation making the axion an excellent dark matter candidate if one of the flaton fields has a positive effective mass-squared at early times but with too low a density in the opposite case. A highly relativistic population of axions is produced by flaton decay during the subsequent reheating, whose density is constrained by nucleosynthesis. We evaluate all of the relevant reaction rates and evaluate the nucleosynthesis constraint. We find that the KSVZ model is practically ruled out, while the DFSZ model has a sizable allowed region of parameter space.
Models of supersymmetric D-term inflation require a new mass scale near 10^{15-16} GeV in order to match the density perturbation spectrum observed by COBE. Attempts to obtain such a scale from the anomalous U(1) of string theories fail in most string models. However there is hope that models based on non-standard embeddings in M-theory can solve the discrepancy. We will show that such models still suffer from the other drawback of D-inflationary models, namely that Planckian field values are required to drive inflation. Thus it is hard to understand why the inflaton potential remains so flat without imposing stringent symmetries on the superpotential. We also examine a fascinating quasi-fixed point behavior for the gauge coupling of the anomalous U(1) in these extra-dimensional models, and show that either the presence of large numbers of fields in the 5-dimensional bulk or strongly suppressed U(1) gauge couplings is required in order to restore naturality to the inflationary potential.
If the inflaton sector is described by softly broken supersymmetry, and the inflaton has unsuppressed couplings, the inflaton mass will run strongly with scale. Four types of model are possible. The prediction for the spectral index involves two parameters, while the COBE normalization involves a third, all of them calculable functions of the relevant masses and couplings. A crude estimate is made of the region of parameter space allowed by present observation.
We explore a model of inflation where the inflaton mass-squared is generated at a high scale by gravity-mediated soft supersymmetry breaking, and runs at lower scales to the small value required for slow-roll inflation. The running is supposed to come from the coupling of the inflaton to a non-Abelian gauge field. In contrast with earlier work, we do not constrain the magnitude of the supersymmetry breaking scale, and we find that the model might work even if squark and slepton masses come from gauge-mediated supersymmetry breaking. With the inflaton and gaugino masses in the expected range, and $α= g^2/4π$ in the range $10^{-2}$ to $10^{-3}$ (all at the high scale) the model can give the observed cosmic microwave anisotropy, and a spectral index in the observed range. The latter has significant variation with scale, which can confirm or rule out the model in the forseeable future.
The potential during inflation must be very flat in, at least, the direction of the inflaton. In renormalizable global supersymmetry, flat directions are ubiquitous, but they are not preserved in a generic supergravity theory. It is known that at least some of them are preserved in no-scale supergravity, and simple generalizations of it. We here study a more realistic generalization, based on string-derived supergravity, using the linear supermultiplet formalism for the dilaton. We consider a general class of hybrid inflation models, where a Fayet-Illiopoulos $D$ term drives some fields to large values. The potential is dominated by the $F$ term, but flatness is preserved in some directions. This allows inflation, with the dilaton stabilized in its domain of attraction, and some moduli stabilized at their vacuum values. Another modulus may be the inflaton.
Particle creation during inflation is considered. It could be important for species whose interaction is of gravitational strength or weaker. A complete but economical formalism is given for spin-zero and spin-half particles, and the particle abundance is estimated on the assumption that the particle mass in the early universe is of order the Hubble parameter $H$. It is roughly the same for both spins, and it is argued that the same estimate should hold for higher spin particles in particular the gravitino. The abundance is bigger than that from the usual particle collision mechanism if the inflationary energy scale is of order $10^{16} GeV$, but not if it is much lower.
If an adiabatic density perturbation is responsible for large scale structure and the cmb anisotropy, its spectral index $n$ will be measured in the forseeable future with an accuracy $Δn\sim .01$. This is precisely the kind of accuracy required to distinguish between many models of inflation. Most of them have an inflationary potential $V\simeq V_0(1\pmμϕ^p)$ with the constant term dominating. Except for $0\lsim p\lsim 2$, the prediction is $n=1\pm (2/N)(p-1)/(p-2)$, where $N$ is the number of $e$-folds of inflation after cosmological scales leave the horizon. It typically lies in the range $0.9\lsim n\lsim 1.1$. For $p=2$ one has $n=1\pm 2\Mpl^2 μ$ where $\Mpl=(8πG)^{-1/2}$. A generic supergravity theory gives contributions of order $\pm H^2$ to the inflaton mass-squared $m^2$ whereas inflation requires $|m^2| << H^2$. Proposals for keeping $m^2$ small are surveyed with emphasis on their implications for $n$. Finally, the case of a multi-component inflaton (as in `double' inflation) is discussed. In all cases, the best method of calculating the spectrum of the adiabatic density perturbation starts with the assumption that, after smoothing on a super-horizon scale, the evolution of the universe along each comoving worldline will be practically the same as in an unperturbed universe with the same initial inflaton field. The possible isocurvature density perturbation is briefly discussed, with a simple derivation of the fact that the low multipoles of the cmb anisotropy are six times as big as for an adiabatic density perturbation.
It is pointed out that hybrid inflation can be implemented with the inflaton field rolling away from the origin instead of towards it. This `inverted' hybrid inflation has a spectral index $ n < 1 $, in contrast with ordinary hybrid inflation which has $ n \gtrsim 1 $, so a measured value of $n$ substantially different from 1 would distinguish the two. Other generalisations of hybrid inflation are also considered.
Inflation generates gravitational waves, which may be observable in the low multipoles of the cosmic microwave background (cmb) anisotropy but only if the inflaton field variation is at least of order the Planck scale. Such a large variation would imply that the model of inflation cannot be part of an ordinary extension of the standard model, and combined with the detection of the waves it would also suggest that the inflaton field cannot be one of the superstring moduli. Another implication of observable gravitational waves would be a potential $V^{1/4}=2$ to $4\times 10^{16}\GeV$, which is orders of magnitude bigger than is expected on the basis of particle theory. It might emerge in a hybrid inflation model where most of the energy density comes from the Higgs sector of a GUT, but only if both the vacuum expectation values {\em and the masses } of the Higgs fields are of this order.
Currently favoured extensions of the Standard Model typically contain `flaton fields' defined as fields with large vacuum expectation values (vevs) and almost flat potentials. If a flaton field is trapped at the origin in the early universe, one expects `thermal inflation' to take place before it rolls away to the true vacuum, because the finite-temperature correction to the potential will hold it at the origin until the temperature falls below $1\TeV$ or so. In the first part of the paper, that expectation is confirmed by an estimate of the finite temperature corrections and of the tunneling rate to the true vacuum, paying careful attention to the validity of the approximations that are used. The second part of the paper considers topological defects which may be produced at the end of an era of thermal inflation. If the flaton fields associated with the era are GUT higgs fields, then its end corresponds to the GUT phase transition. In that case monopoles (as well as GUT higgs particles) will have to be diluted by a second era of thermal inflation. Such an era will not affect the cosmology of GUT strings, for which the crucial parameter is the string mass per unit length. Because of the flat Higgs potential, the GUT symmetry breaking scale required for the strings to be a candidate for the origin of large scale structure and the cmb anisotropy is about three times bigger than usual, but given the uncertainties it is still compatible with the one required by the unification of the Standard Model gauge couplings. The cosmology of textures and of global monopoles is unaffected by the flatness of the potential.
The most natural way to break the GUT gauge symmetry is with a Higgs field whose vacuum expectation value is of order $10^{16}\,\mbox{GeV}$ but whose mass is of order $10^2$ to $10^3\,\mbox{GeV}$. This can lead to a cosmological history radically different from what is usually assumed to have occurred between the standard inflationary and nucleosynthesis epochs, which may solve the gravitino and Polonyi/moduli problems in a natural way.
When considering perturbations in an open 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 {\em homogeneous Gaussian random field}, despite the fact that any square integrable {\em function} can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. This article summarizes recent work with A. Woszczyna. The mathematics is briefly explained in a language accessible to physicists. Then the effect on the cmb of any super-curvature contribution is considered, which generalizes to $Ω_0<1$ the analysis given by Grishchuk and Zeldovich in 1978.
Recent work is reported on inflation model building in the context of supergravity and superstrings, with special emphasis on False Vacuum (`Hybrid') Chaotic Inflation. Globally supersymmetric models do not survive in generic supergravity theories, but fairly simple conditions can be formulated which do ensure successful supergravity inflation. The conditions are met in some of the versions of supergravity that emerge from superstrings.
This is a somewhat extended version of the original July 93 report. It is proved that the cosmological density perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric perturbation. In addition, assuming the usual adiabatic initial condition on the density perturbation, we show that the dipole of the anisotropy measures our peculiar velocity relative to the average peculiar velocity within the last scattering surface of the microwave background, thus defining its frame of reference.
Saxino decay can generate significant cosmological entropy, and hence dilute theoretical estimates of the present mass density of a given particle species. The dilution factor depends on the saxino and axion masses, and is constrained by the requirement that saxino decay should not affect nucleosynthesis, as well as by the usual requirement that the axion density be less than the critical density. The latter constraint is evaluated carefully, under both the Harari-Sikivie and Davis proposals about the emission spectrum from axionic strings. Uncertainties are carefully evaluated, points of principle are addressed, and with an eye to future numerical simulation the spacing and typical oscillation wavelength of the strings are represented by parameters varying in the range 1 to 3. Within the constraints, the entropy dilution varies from 1 to $10^{-4}$. Only saxinos originating from thermal equilibrium are considered, so that more dilution might arise from non-thermal saxinos.