Constraining inflation with nonminimal derivative coupling with the Parkes Pulsar Timing Array third data release

Abstract

We study an inflation model with nonminimal derivative coupling that features a coupling between the derivative of the inflaton field and the Einstein tensor. This model naturally amplifies curvature perturbations at small scales via gravitationally enhanced friction, a mechanism critical for the formation of primordial black holes and the associated production of potentially detectable scalar-induced gravitational waves. We derive analytical expressions for the primordial power spectrum, enabling efficient exploration of the model parameter space without requiring computationally intensive numerical solutions of the Mukhanov-Sasaki equation. Using the third data release of the Parkes Pulsar Timing Array (PPTA DR3), we constrain the model parameters characterizing the coupling function: ${\ensuremath{\phi}}_{c}={3.7}_{\ensuremath{-}0.5}^{+0.3}{M}_{\mathrm{P}}$, ${\mathrm{log}}_{10}{\ensuremath{\omega}}_{L}={7.1}_{\ensuremath{-}0.3}^{+0.6}$, and ${\mathrm{log}}_{10}\ensuremath{\sigma}=\ensuremath{-}{8.3}_{\ensuremath{-}0.6}^{+0.3}$ at 90% confidence level. Our results demonstrate the growing capability of pulsar timing arrays to probe early Universe physics, complementing traditional cosmic microwave background observations by providing unique constraints on inflationary dynamics at small scales.