Kahler potentials for the MSSM inflation and the spectral index

Recently it has been argued that some of the fine-tuning problems of the MSSM inflation associated with the existence of a saddle point along a flat direction may be solved naturally in a class of supergravity models. Here we extend the analysis and show that the constraints on the Kahler potentials in these models are considerably relaxed when the location of the saddle point is treated as a free variable. We also examine the effect of supergravity corrections on inflationary predictions and find that they can slightly alter the value of the spectral index. As an example, for flat direction field values $|\bar{\phi}_0|=1\times10^{-4}M_P$ we find $n\sim0.92 ... 0.94$ while the prediction of the MSSM inflation without any corrections is $n\sim0.92$.Comment: 13 pages, one figure. Typos corrected and a reference adde

Supergravity origin of the MSSM inflation

We consider the supergravity origin of the recently proposed MSSM inflationary model, which relies on the existence of a saddle point along a dimension six flat direction. We derive the conditions that the Kahler potential has to satisfy for the saddle point to exist irrespective of the hidden sector vevs. We show that these conditions are satisfied by a simple class of Kahler potentials, which we find to have a similar form as in various string theory compactifications. For these potentials, slow roll MSSM inflation requires no fine tuning of the soft supersymmetry breaking parameters.Comment: v3: 10 pages, no figures; version accepted for publication. Typos correcte

A-term inflation and the smallness of the neutrino masses

The smallness of the neutrino masses may be related to inflation. The minimal supersymmetric Standard Model (MSSM) with small Dirac neutrino masses already has all the necessary ingredients for a successful inflation. In this model the inflaton is a gauge-invariant combination of the right-handed sneutrino, the slepton, and the Higgs field, which generate a flat direction suitable for inflation if the Yukawa coupling is small enough. In a class of models, the observed microwave background anisotropy and the tilted power spectrum are related to the neutrino masses.Comment: 13 pages, 1 figure, uses JHEP3.cls, minor modifications, final version accepted for publication in JCA

Supersymmetric Thermalization and Quasi-Thermal Universe: Consequences for Gravitinos and Leptogenesis

Motivated by our earlier paper \cite{am}, we discuss how the infamous gravitino problem has a natural built in solution within supersymmetry. Supersymmetry allows a large number of flat directions made up of {\it gauge invariant} combinations of squarks and sleptons. Out of many at least {\it one} generically obtains a large vacuum expectation value during inflation. Gauge bosons and Gauginos then obtain large masses by virtue of the Higgs mechanism. This makes the rate of thermalization after the end of inflation very small and as a result the Universe enters a {\it quasi-thermal phase} after the inflaton has completely decayed. A full thermal equilibrium is generically established much later on when the flat direction expectation value has substantially decareased. This results in low reheat temperatures, i.e., $T_{\rm R}\sim {\cal O}({\rm TeV})$, which are compatible with the stringent bounds arising from the big bang nucleosynthesis. There are two very important implications: the production of gravitinos and generation of a baryonic asymmetry via leptogenesis during the quasi-thermal phase. In both the cases the abundances depend not only on an effective temperature of the quasi-thermal phase (which could be higher, i.e., $T\gg T_{\rm R}$), but also on the state of equilibrium in the reheat plasma. We show that there is no ``thermal gravitino problem'' at all within supersymmetry and we stress on a need of a new paradigm based on a ``quasi-thermal leptogenesis'', because in the bulk of the parameter space the {\it old} thermal leptogenesis cannot account for the observed baryon asymmetry.Comment: 53 pages. Final version published in JCA

Towards constraints on the SUSY seesaw from flavour-dependent leptogenesis

We systematically investigate constraints on the parameters of the supersymmetric type-I seesaw mechanism from the requirement of successful thermal leptogenesis in the presence of upper bounds on the reheat temperature $T_\mathrm{RH}$ of the early Universe. To this end, we solve the flavour-dependent Boltzmann equations in the MSSM, extended to include reheating. With conservative bounds on $T_\mathrm{RH}$, leading to mildly constrained scenarios for thermal leptogenesis, compatibility with observation can be obtained for extensive new regions of the parameter space, due to flavour-dependent effects. On the other hand, focusing on (normal) hierarchical light and heavy neutrinos, the hypothesis that there is no CP violation associated with the right-handed neutrino sector, and that leptogenesis exclusively arises from the CP-violating phases of the $U_\text{MNS}$ matrix, is only marginally consistent. Taking into account stricter bounds on $T_\mathrm{RH}$ further suggests that (additional) sources of CP violation must arise from the right-handed neutrino sector, further implying stronger constraints for the right-handed neutrino parameters.Comment: 42 pages, 12 figures; final version published in JCAP; numerical results for the efficiency factor can be downloaded from http://www.newphysics.eu/leptogenesis