PBHs and GWs from $\mathbb{T}^2$-inflation and NANOGrav 15-year data

In this paper, we propose a novel mechanism in $\mathbb{T}^2$-inflation to enhance the power spectrum large enough to seed primordial black holes (PBHs) formation. To accomplish this, we consider the coupling function between the inflaton field and $\mathbb{T}^2= T_{\mu \nu}T^{\mu \nu}$ term. PBHs formed within this scenario can contribute partially or entirely to dark matter (DM) abundance. Furthermore, the amplification in the scalar power spectrum will concurrently produce significant scalar-induced gravitational waves (SIGWs) as a second-order effect. In addition, the energy spectrum associated with SIGWs can be compatible with the recent NANOGrav 15-year stochastic gravitational wave detection and fall into the sensitivity range of other forthcoming GW observatories.