  Convincing evidence of a stochastic gravitational wave (GW) background has
been found by the NANOGrav collaboration in the 15-year data set. From this
signal, we can evaluate the possibility of its source being from the early
universe through the tensor perturbations induced by a massive spin-2 graviton
field. We consider a time-dependent model of the minimal theory of massive
gravity (MG), and find values of the graviton mass, mass cutoff time, and
Hubble rate of inflation that amplify the energy spectra of primordial GWs
sufficiently to reproduce the signal from the NANOGrav data within 1-3 standard
deviation. However, a suppression mechanism for high frequency modes must be
introduced to conservatively obey the big bang nucleosynthesis (BBN) bound.
While there are regions of the parameter space that reproduce the signal, it
remains a challenge to simultaneously respect the BBN and cosmic microwave
background (CMB) bounds without making the graviton mass cutoff time too deep
into the matter dominated era.
