The European Pulsar Timing Array's second data release shows evidence for a low-frequency gravitational-wave background. This paper asks whether that signal could come from inflation — the very early, rapid expansion of the Universe. The authors model the primordial gravitational-wave spectrum with four parameters and, after including other observations, find a limited region of parameters that could work: log10(r) between −11.66 and −1.45, tensor spectral index n_t between 1.32 and 2.47, reheating temperature T_rh between 1.78 MeV and 28.2 GeV, and a high‑frequency cutoff f_end between 75.86 nHz and 14.45 Hz (95% confidence).

To reach these numbers the team combined the EPTA DR2 timing data — 10.3 years of measurements of 25 millisecond pulsars — with independent physical limits from the cosmic microwave background (CMB), Big Bang nucleosynthesis (BBN), and the LIGO–Virgo–KAGRA (LVK) detectors. They sampled model parameters directly inside a Markov Chain Monte Carlo (MCMC) pipeline so those external constraints were enforced consistently. Compared with earlier studies, they also allowed a free high‑frequency cutoff f_end that represents the end of inflation and the start of reheating.

At a simple level the four parameters mean this. The tensor‑to‑scalar ratio r measures how strong primordial gravitational waves were, compared with the density fluctuations we see in the CMB. The tensor spectral index n_t describes how that wave power changes with frequency (a “blue” tilt means more power at higher frequencies). The reheating temperature T_rh marks when the hot, radiation‑dominated Universe begins after inflation. The cutoff f_end sets the highest frequency in the inflationary spectrum. The authors assumed a constant n_t across all frequencies and used a reheating model computed for a quadratic inflaton potential, noting that some spectral details depend on that choice.