Rotherham Hospital.

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Primordial black holes as a tool for constraining non-Gaussianity

Primordial Black Holes (PBH's) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which can not otherwise be constrained, with PBH's only forming from the extremely rare large fluctuations. The number of PBH's formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parameterised by f_nl and g_nl respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even non-linearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as f_nl changes from just -0.5 to 0.5. We find that if PBH's are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative f_nl would be ruled out. Finally we show that g_nl can have an even larger effect on the number of PBH's formed than f_nl.Comment: 9 pages, 5 figures, v2: version to appear in Phys. Rev. D with minor changes, v3: typos corrected (including factor of 1/2 in erfc prefactor), no changes to result

The abundance of relativistic axions in a flaton model of Peccei-Quinn symmetry

Flaton models of Peccei-Quinn symmetry have good particle physics motivation, and are likely to cause thermal inflation leading to a well-defined cosmology. They can solve the $\mu$ problem, and generate viable neutrino masses. Canonical flaton models predict an axion decay constant F_a of order 10^{10} GeV and generic flaton models give F_a of order 10^9 GeV as required by observation. The axion is a good candidate for cold dark matter in all cases, because its density is diluted by flaton decay if F_a is bigger than 10^{12} GeV. In addition to the dark matter axions, a population of relativistic axions is produced by flaton decay, which at nucleosynthesis is equivalent to some number \delta N_\nu of extra neutrino species. Focussing on the canonical model, containing three flaton particles and two flatinos, we evaluate all of the flaton-flatino-axion interactions and the corresponding axionic decay rates. They are compared with the dominant hadronic decay rates, for both DFSZ and KSVZ models. These formulas provide the basis for a precise calculation of the equivalent \delta N_\nu in terms of the parameters (masses and couplings). The KSVZ case is probably already ruled out by the existing bound \delta N_\nu\lsim 1. The DFSZ case is allowed in a significant region of parameter space, and will provide a possible explanation for any future detection of nonzero $\delta N_\nu$

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 $10^{12}\,{\rm GeV}$.Comment: Revised version to appear in Phys Rev D. Improved discussion of the possible effect of parametric resonance. Latex, 31 page

Cosmological consequences of particle creation during inflation

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.Comment: 17 pages, no Figure

Cosmology with a TeV mass GUT Higgs

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.Comment: 4 pages, revte

Exponential potentials and cosmological scaling solutions

We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state $p_\gamma = (\gamma-1) \rho_\gamma$, plus a scalar field $\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa \phi)$ where $\kappa^2 = 8\pi G$. In addition to the well-known inflationary solutions for $\lambda^2 3\gamma$ in which the scalar field energy density tracks that of the barotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where $V(\phi)/\rho_\gamma \to 0$ at late times, are always unstable (except for the cosmological constant case $\gamma = 0$). The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to $\lambda^2 > 20$. We show that standard inflation models are unable to solve this `relic density' problem.Comment: 6 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Matches published versio

Particle physics models of inflation

Inflation models are compared with observation on the assumption that the curvature perturbation is generated from the vacuum fluctuation of the inflaton field. The focus is on single-field models with canonical kinetic terms, classified as small- medium- and large-field according to the variation of the inflaton field while cosmological scales leave the horizon. Small-field models are constructed according to the usual paradigm for beyond Standard Model physicsComment: Based on a talk given at the 22nd IAP Colloquium, ``Inflation +25'', Paris, June 2006 Curve omitted from final Figur

Non-Gaussianities in two-field inflation

We study the bispectrum of the curvature perturbation on uniform energy density hypersurfaces in models of inflation with two scalar fields evolving simultaneously. In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the $\delta N$-formalism, in the slow-roll approximation. In this case, we provide an analytic formula for the nonlinear parameter $f_{NL}$. We apply this formula to double inflation with two massive fields, showing that it does not generate significant non-Gaussianity; the nonlinear parameter at the end of inflation is slow-roll suppressed. Finally, we develop a numerical method for generic two-field models of inflation, which allows us to go beyond the slow-roll approximation and confirms our analytic results for double inflation.Comment: 29 pages, 6 figures. v2, comparison with previous estimates. v3, JCAP version; Revisions based on Referee's comment, corrected typos, added few eqs and refs, conclusions unchange