Tachyonic Preheating in Palatini $R^2$ Inflation

Abstract

We study preheating in the Palatini formalism with a quadratic inflaton potential and an added αR 2 term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when α 10 13 and that the energy density of the fragmented field grows with the rate Γ/H ≈ 0.011×α 0.31 . The model extends the family of plateau models with similar preheating behaviour. Although it contains non-canonical quartic kinetic terms in the Einstein frame, we show that, in the first approximation, these can be neglected during both preheating and inflation.

General Analytical Conditions for Inflaton Fragmentation: Quick and Easy Tests for its Occurrence

“…The same lower bound of 10 13 was later found in Ref. [20] by performing a numerical analysis of tachyonic preheating in this model.…”

“…The polynomial expansion of a general potential is expected to have a leading-order quartic or cubic interactions for a symmetric potential or an asymmetric potential, respectively. The fragmentation condition (20) can then be converted into a bound on the model parameters. In the following two subsections, we discuss the case of a symmetric and an asymmetric potential respectively and obtain the condition on the model parameters for fragmentation to occur.…”

“…where we used the fact that the potential is dominated by the quadratic term so that H 0 = mR/( √ 6M P ). Therefore, the fragmentation condition (20), S max > 10, will be satisfied if…”

“…Let us consider the quadratic inflation model in the Palatini formulation with an R 2 term added [19,20]. The action is given in the Jordan frame by…”

“…As our aim is to apply our general analytical conditions to a specific model, we do not discuss the detailed computational steps. Readers may refer to Refs [19,20]…”