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

TL;DR

The paper argues that supersymmetric flat directions naturally delay thermalization after inflation, creating a quasi-thermal Universe with a suppressed reheat temperature $T_{ m R}$. This slow thermalization mitigates the gravitino problem and motivates a quasi-thermal leptogenesis framework, where baryon asymmetry can be generated during the quasi-thermal phase and depends on the plasma composition. It further explores how different SUSY realizations (gravity mediation, gauge mediation, split SUSY) modify the thermal history and the viability of leptogenesis and gravitino constraints. Together, these results indicate that SUSY flat directions can reconcile high-scale inflation with gravitino bounds and point to a new paradigm for baryogenesis via quasi-thermal processes. The insights have broad implications for inflationary model-building and early-Universe cosmology within SUSY and string-inspired theories.

Abstract

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.