Inflationary interpretation of the gravitational-wave signal in the European Pulsar Timing Array DR2 with constraints

The second data release of the European Pulsar Timing Array (EPTA) collaboration provides evidence for the presence of a gravitational-wave (GW) background. In this work, we explore a potential cosmological interpretation of this signal in terms of inflationary scenarios. We parametrize the tensor power spectrum in terms of the tensor-to-scalar ratio $r$, the tensor spectral index $n_t$, the reheating temperature $T_{\text{rh}}$, and the cut-off frequency $f_{\text{end}}$. We incorporate all relevant observational constraints, including those from the Cosmic Microwave Background, Big Bang Nucleosynthesis, and LIGO-Virgo-KAGRA observations. We demonstrate that imposing these constraints consistently reduces the region of parameter space that provides a viable interpretation of the EPTA signal, to $-11.66 \lesssim \log_{10}r \lesssim -1.45$, $1.32 \lesssim n_t \lesssim 2.47$, $1.78\text{ MeV} \lesssim T_{\text{rh}} \lesssim 28.2\text{ GeV}$, and $75.86\text{ nHz} \lesssim f_{\text{end}} \lesssim 14.45\text{ Hz}$ at the 95% confidence level. This favours the scenario in which the GW spectrum in the EPTA frequency band originates from tensor modes that re-entered the Hubble radius during the radiation-dominated era, allowing for a higher $r$ and a flatter spectrum. However, $T_{\text{rh}}$ must take very low values, which are challenging to explain theoretically.