Preheating in derivatively coupled inflation models

Abstract

We study preheating in theories where the inflaton couples derivatively to scalar and gauge fields. Such couplings may dominate in natural models of inflation, in which the flatness of the inflaton potential is related to an approximate shift symmetry of the inflaton. We compare our results with previously studied models with non-derivative couplings. For sufficiently heavy scalar matter, parametric resonance is ineffective in reheating the universe, because the couplings of the inflaton to matter are very weak. If scalar matter fields are light, derivative couplings lead to a mild longwavelength instability that drives matter fields to non-zero expectation values. In this case however, long-wavelength fluctuations of the light scalar are produced during inflation, leading to a host of cosmological problems. In contrast, axion-like couplings of the inflaton to a gauge field do not lead to production of long-wavelength fluctuations during inflation. However, again because of the weakness of the couplings to the inflaton, parametric resonance is not effective in producing gauge field quanta.

Gauge field preheating at the end of inflation

“…Ref. [30]. Our model has long been proposed as a mechanism for generating primordial magnetic fields.…”

Thermal history of the universe after inflation

“…Our approach captures this model by now choosing α 3 = 2φ 0 (t) 2 /Λ 2 . It has been found that preheating in models that preserve an inflaton shift symmetry is not efficient [22]. One reason for this is that naively we assume that the energy of the fields can not exceed the cutoff Λ.…”

Reheating induced by competing decay modes

“…Instead of equations (31) and (39), which are valid only in the limit of small ǫ, we use the general equations (18) with L i taken as the numerical value of the band widths for each model. In Figure 2 a), we see that the e-fold time is essentially determined by the contribution of the first instability band, except in the region of very small values of ǫ.…”

“…Since, however, only the contribution of the first instability band is accounted for in the efficiency estimates found in the literature, these estimates remain valid for the multi-frequency model. Now equations (31) and (39) are valid as long as any given mode remains in the resonance band. Due to the expansion, the time interval ∆τ during which a mode remains in the band is ∆τ ≃ L Hm 2 .…”

“…The latter issue has been studied in depth for a large variety of polynomial potentials [16,34,35,36]. The former issue is less well studied and has been the subject of some recent work [37,38,39].…”