Constraint on reheating after f(R) inflation from gravitational waves

Abstract

Recently, a combined model of the primordial inflation and the present cosmic acceleration has been proposed in the context of f(R) gravity. This model is composed of the late-time acceleration term and an R2 term, which enables the model to avoid high curvature singularity and describe a quasi-de Sitter inflationary phase in the early Universe. An interesting feature of this model is that the reheating dynamics after the inflation is significantly modified, in contrast to the original R2 model, and affects the shape of a gravitational wave background (GWB) spectrum. Here we investigate the production of a GWB during the inflation and reheating eras in the R2-corrected f(R) model and compute a GWB spectrum. We found that interesting region of the model parameters has already been excluded by the cosmological limit on abundance of GWs.