Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity

Several pulsar timing array (PTA) missions have reported convincing evidence of a stochastic gravitational wave background within their latest datasets. This background could originate from an astrophysical source, though there are multiple possibilities for its origin to be cosmological. Focusing on the NANOGrav signal, which was in good agreement with other PTAs, we evaluate the possibility of an inflationary source for the background. However, we'll consider a time-dependent minimal theory of massive gravity instead of standard general relativity for our analysis. We find that an inflationary interpretation will require a strongly blue spectrum, characterized by $n_T = 1.8 \, \pm \, 0.54$, while Big Bang Nucleosynthesis limits will require a low reheating scale of $T_\text{rh} \simeq 4000 \ \text{GeV}$. Though these constraints make it difficult for inflation to be the source of the NANOGrav signal, we find that the massive gravity model allows for a greater reheating temperature than standard general relativity, making an inflationary interpretation slightly less cumbersome.