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

TL;DR

This paper investigates an inflation model with nonminimal derivative coupling, deriving analytical power spectrum expressions, and uses pulsar timing array data to constrain model parameters, highlighting PTA's potential to probe early Universe physics.

Contribution

The paper provides analytical solutions for the primordial power spectrum in a nonminimal derivative coupling inflation model and constrains its parameters using PTA data, enhancing understanding of small-scale inflationary physics.

Findings

Constraints on coupling parameters: $oxed{ ext{phi}_c, ext{omega}_L, ext{sigma}}$ at 90% CL.

PTA data can probe inflationary models at small scales.

Analytical expressions enable efficient parameter exploration.

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: $\phi_c = 3.7^{+0.3}_{-0.5} M_\mathrm{P}$, $\log_{10} \omega_L = 7.1^{+0.6}_{-0.3}$, and $\log_{10} \sigma = -8.3^{+0.3}_{-0.6}$ 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.