Reheating matters: Starobinsky inflation in light of joint CMB+BAO results and gravitational-wave forecasts
It has been noted in the literature that, if post-inflationary reheating is dominated by a stiff fluid with equation of state (EoS) $p>ρ/3$, then the predictions of Starobinsky inflation for the scalar spectral index could be made to agree with measurements from the combined CMB+BAO datasets performed by the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) collaborations. However, a side-effect of such a stiff epoch is the blue-tilting of the primordial gravitational-wave (GW) spectrum. In this work, we explore the observational consequences of this blue-tilting in three scenarios: (i) a purely stiff-dominated reheating, (ii) a more realistic case where reheating is first dominated by a matter-like fluid (corresponding to inflaton oscillations around the bottom of a quadratic potential well) later followed by a stiff epoch, and (iii) a case analogous to the previous one, but with an earlier radiation-dominated instead of matter-dominated epoch. We show that in all cases the $1σ$ region allowed by recent CMB+BAO data is already excluded by constraints on the amount of radiation present during Big Bang Nucleosynthesis (BBN). Moreover, in a considerable fraction of the remaining $2σ$ region we find that the blue-tilting would be severe enough to make the primordial spectrum detectable in future interferometers such as Einstein Telescope, LISA, DECIGO, and BBO, thus rendering these scenarios testable by these experiments.