Abstract:
A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models namely large field, small field, hybrid and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.

Abstract:
We revisit the question whether the running-mass inflation model allows the formation of Primordial Black Holes (PBHs) that are sufficiently long-lived to serve as candidates for Dark Matter. We incorporate recent cosmological data, including the WMAP 7-year results. Moreover, we include "the running of the running" of the spectral index of the power spectrum, as well as the renormalization group "running of the running" of the inflaton mass term. Our analysis indicates that formation of sufficiently heavy, and hence long-lived, PBHs still remains possible in this scenario. As a by-product, we show that the additional term in the inflaton potential still does not allow significant negative running of the spectral index.

Abstract:
Without demanding a specific form for the inflaton potential, we obtain an estimate of the contribution to the curvature perturbation generated during the linear era of the hybrid inflation waterfall. The spectrum of this contribution peaks at some wavenumber $k=k_*$, and goes like $k^3$ for $k\ll k_*$, making it typically negligible on cosmological scales. The scale $k_*$ can be outside the horizon at the end of inflation, in which case $\zeta=- (g^2 - \vev{g^2})$ with $g$ gaussian. Taking this into account, the cosmological bound on the abundance of black holes is likely to be satisfied if the curvaton mass $m$ much bigger than the Hubble parameter $H$, but is likely to be violated if $m\lsim H$. Coming to the contribution to $\zeta$ from the rest of the waterfall, we are led to consider the use of the `end-of-inflation' formula, giving the contribution to $\zeta$ generated during a sufficiently sharp transition from nearly-exponential inflation to non-inflation, and we state for the first time the criterion for the transition to be sufficiently sharp. Our formulas are applied to supersymmetric GUT inflation and to supernatural/running-mass inflation

Abstract:
We analyse the reheating in the modification of \nuMSM (Standard Model with three right handed neutrinos with masses below the electroweak scale) where the sterile neutrino providing the Dark Matter is generated in decays of the additional inflaton field. We deduce that due to rather inefficient transfer of energy from the inflaton to the Standard Model sector reheating tends to happen at very low temperature, thus providing strict bounds on the coupling between the inflaton and the Higgs particles. This in turn translates to the bound on the inflaton mass, which appears to be very light 0.1 GeV <~ m_I <~ 10 GeV, or slightly heavier then two Higgs masses 300 GeV <~ m_I <~ 1000 GeV.

Abstract:
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 $\alpha = g^2/4\pi $ 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.

Abstract:
Inflation ends with the formation of a Bose condensate of inflatons. We show that in hybrid inflation models this condensate is typically unstable with respect to spatial perturbations and can fragment to condensate lumps. The case of D-term inflation is considered as an example and it is shown that fragmentation occurs if \lambda > 0.2g, where \lambda is the superpotential coupling and g is the U(1)_{FI} gauge coupling. Condensate fragmentation can result in an effective enhancement of inflaton annihilations over decays as the main mode of reheating. In the case of D-term inflation models in which the Standard Model fields carry U(1)_{FI} charges, if condensate fragmentation occurs then reheating is dominated by inflaton annihilations, typically resulting in the overproduction of thermal gravitinos. Fragmentation may also have important consequences for SUSY flat direction dynamics and for preheating.

Abstract:
We study a recently proposed running kinetic inflation model in which the inflaton potential becomes flat due to rapid growth of the kinetic term at large inflaton field values. As concrete examples, we build a variety of chaotic inflation models in supergravity with e.g. quadratic, linear, and fractional-power potentials. The power of the potential generically increases after inflation, and the inflaton is often massless at the potential minimum in the supersymmetric limit, which leads to many interesting phenomena. First, the light inflaton mass greatly relaxes severe thermal and non-thermal gravitino problems. Secondly, the kination epoch is naturally present after inflation, which may enhance the gravity waves. Thirdly, since the inflaton is light, it is likely coupled to the Higgs sector for successful reheating. The inflaton and its superpartner, inflatino, may be produced at the LHC. Interestingly, the inflatino can be dark matter, if it is the lightest supersymmetric particle.

Abstract:
In conventional scenario of thermal inflation, the requirement that the reheating temperature must be larger than the temperature of the nucleosynthesis puts a lower bound on the mass of the inflaton field. At the same time, the mass of the inflaton field and the height of the potential during thermal inflation are intimately related. With these conditions, the conventional models for thermal inflation are quite restricted. Naively, one can expect that the above constraints may be removed if thermal inflation is realized within the setups for hybrid inflation. In this paper we show why it is difficult to construct hybrid models for thermal inflation within conventional supergravity, and then show a successful example in models for the braneworld. Our mechanism is based on the idea of non-tachyonic brane inflation.

Abstract:
We study the single field slow-roll inflation models that better fit the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study them as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The compute the spectral index n_s of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index d n_s/dln k, derive explicit formulae and provide relevant plots. In new inflation, and for the three years WMAP central value n_s = 0.95, we predict 0.031. Hybrid inflation for mu_0^2>Lambda_0 M_{Pl}^2/192 can fullfill all the present CMB+LSS data. Even if chaotic inflation predicts n_s values compatible with the data, chaotic inflation is disfavoured since it predicts a too high value for the ratio r=0.27. The model which best fits the current data and which best prepares the way to the expected data r < 0.1, is the trinomial potential with negative mass term: new inflation.

Abstract:
We consider the conditions for the decay products of perturbative inflaton decay to thermalize. The importance of considering the full spectrum of inflaton decay products in the thermalization process is emphasized. It is shown that the delay between the end of inflaton decay and thermalization allows the thermal gravitino upper bound on the reheating temperature to be raised from 10^{8} GeV to as much as 10^{12} GeV in realistic inflation models. Requiring that thermalization occurs before nucleosynthesis imposes an upper bound on the inflaton mass as a function of the reheating temperature, m_{S} < 10^{10} (T_{R}/1 GeV)^{7/9} GeV. It is also shown that even in realistic inflation models with relatively large reheating temperatures, it is non-trivial to have thermalization before the electroweak phase transition temperature. Therefore the thermal history of the Universe is very sensitive to details of the inflation model.