Gravitational waves and primordial black holes from the T-model inflation with Gauss-Bonnet correction

Recently, the worldwide Pulsar Timing Array (PTA) collaborations detected a stochastic gravitational wave(GW) background in the nanohertz range, which may originate from the early universe's inflationary phase. So in this work, we investigated induce GWs in the T-model inflation with Gauss-Bonnet coupling. Consider the scenario of traversing a domain wall in moduli space, we take the coupling coefficient to be an approximately step function. Within suitable parameter regions, the model exhibits de Sitter fixed points, which allows inflation to undergo an ultra-slow-roll phase, which causes the power spectrum to exhibit a peak. Such a peak can induce nanohertz GWs, which provids an explanation for the PTA observational data. Furthermore, we consider the case of multiple domain wall crossings, and adopting a double-step coupling function. In this case, the resulting GW spectrum has two peaks with frequencies around \(10^{-8} \,\text{Hz}\) and \(10^{-2}\,\text{Hz}\), respectively. Which can be observed by the PTA and the space GW detectors simultaneously.Additionally, the reentry of the power spectrum peaks into the horizon leads to the collapse into primordial black holes (PBHs). We calculate the abundance of PBHs and found that the masses is in the range of \(10^{-14} \sim 10^{-13} M_\odot\) and around \(10^{-2} M_\odot\) , which constitute significant components of the current dark matter.