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S-inflation:a testable, minimal model of inflation and dark matter

This thesis describes work on inflationary cosmology, specifically in relation to observations. After reviewing the theory of inflation and dark matter, we introduce a model, ‘S-inflation’, in which a gauge singlet scalar S (with quartic self-coupling s) is both thermal relic dark matter and the inflaton. This is made possible by its non-minimal coupling s to gravity, where s √ s ∼ 4.6 × 10 at tree level. Reheating occurs primarily through a stochastic resonance to Higgs bosons, which then annihilate to relativistic particles. Primary importance is given to the predictions the model makes for the Higgs mass (mh), spectral index (n) and S mass (ms). Under reasonable assumptions, 130 GeV 0.966. All of these are in principle within reach of the LHC, Planck and direct detection dark matter experiments, such as XENON100. We then show that the renormalization group improved effective potential is a superior method to the standard Coleman Weinberg potential for calculating inflation observables. Then, we compare the predictions of S-inflation to those of pure Higgs inflation and Higgs inflation with an additional scalar. For mh ≳ 130 GeV, the models are in general distinguishable through the spectral index n, with n > ncl for S-inflation models and n < ncl for Higgs inflation. For N e-foldings of inflation, ncl ≈ 1− 2 N − 3 2N2 ≈ 0.966. We next explain the origin of the apparent violation of unitarity at energy scales greater than Λ ∼ Mp s (Mp is the reduced Planck mass). As we demonstrate, the calculation of the unitarity bound is done perturbatively, while the theory is non-perturbative at the energy of unitarity violation. Therefore, it is not possible to conclude whether or not unitarity is violated in the model. The model may instead be strongly coupled, meaning that the calculation of scattering amplitudes at E ∼ Λ becomes non-perturbative, while the analysis of inflation is unchanged. If unitarity is shown to be violated in the original model, a new, unitarity conserving version i of the model can be considered. This has a simple form in the Einstein frame, and predicts a larger spectral index (n ≈ 0.975) than the original model.