Kinetic axion F(R) gravity inflation

In this work we investigate the quantitative effects of the misalignment kinetic axion on R2 inflation. Due to the fact that the kinetic axion possesses a large kinetic energy that dominates its potential energy, during inflation its energy density redshifts as stiff matter fluid and evolves in a constant-roll way, making the second slow-roll index to be nontrivial. At the equations of motion level, the R2 term dominates the evolution; thus the next possible effect of the axion could be found at the cosmological perturbations level, via the second slow-roll index which is nontrivial. As we show, the latter elegantly cancels from the observational indices; however, the kinetic axion extends the duration of the inflationary era to an extent that it may cause a 15% decrease in the tensor-to-scalar ratio of the vacuum R2 model. This occurs because as the R2 model approaches its unstable quasi-de Sitter attractor in the phase space of F(R) gravity due to the (R2) fluctuations, the kinetic axion dominates over the R2 inflation and in effect the background equation of state is described by a stiff era, or equivalently a kination era, different from the ordinary radiation domination era. This in turn affects the duration of the inflationary era, increasing the e-foldings number up to 5e-foldings in some cases, depending on the reheating temperature, which in turn has a significant quantitative effect on the observational indices of inflation and especially on the tensor-to-scalar ratio.