Gravitino production in the warm inflationary scenario

The warm inflation scenario [1] is an unusual variant on the inflationary cosmology, in which the inflaton has significant interactions during the inflationary epoch leading to a continuous production of radiation. The backreaction of this production on the inflaton field appears as a viscosity, slowing down the scalar field evolution and hence aiding slow-roll inflation [2]. In such a scenario, inflation can proceed with potentials steeper than those in standard chaotic scenarios. Issues concerning the implementation of warm inflation within a realistic particle physics context have yet to be studied to the same depth as the standard inflationary scenario [3,4]. Nevertheless, given that the warm inflationary scenario is very different phenomenologically from the usual picture, it makes good sense to examine the extent to which its phenomenology is consistent with observations. The two main purposes of inflation are to provide a large, nearly homogeneous, patch in the Universe within which structure formation can take place, and to ensure that unwanted relic particles do not spoil the successes of the standard hot big bang cosmology. The first of these has seen a reasonable amount of study [5], and so we will consider an example of the latter. In the context of modern particle physics, the most troublesome relics are the gravitino and the moduli fields [6]. We will consider the gravitino, whose existence arises as the supersymmetric partner of the graviton, and whose mass is expected to be order of 1 TeV. It is a cosmological threat because if produced in enough abundance in the early Universe, it is sufficiently long lived to survive until after nucleosynthesis, at which point its decays spoil the element abundances [7]. To avoid this, the ratio of gravitino to photon number densities must be below about 10−12. The gravitino may be produced both by interactions within a thermal bath [8] and by various non-thermal processes [9]. In conventional inflationary scenarios, the former gives an important upper limit on the reheat temperature, while the latter may constrain many possible physical processes. In this paper we explore the consequences of gravitino production during and after warm inflation. Warm inflation differs from conventional inflation in that radiation is constantly produced during inflation, and the radiation density decreases monotonically throughout the evolution, with inflation ending when the radiation density overtakes the inflaton energy density. There is therefore continuous gravitino production during inflation, and also no delay in post-inflationary thermal production due to an intervening (p)reheating period. Consequently the gravitino bound is much harder to satisfy. We will show that the abundance of gravitinos produced during inflation is similar to that produced after inflation, and assess the strength of the constraints this imposes on warm inflation model-building.