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

PPTA Collaboration; Chang Han; Li-Yang Chen; Zu-Cheng Chen; Chengjie Fu; Puxun Wu; Hongwei Yu; N. D. Ramesh Bhat; Xiaojin Liu; Valentina Di Marco; Saurav Mishra; Daniel J. Reardon; Christopher J. Russell; Ryan M. Shannon; Lei Zhang; Xingjiang Zhu; Andrew Zic

doi:10.1103/PhysRevD.111.L061304

Letter

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

Chang Han^1,2, Li-Yang Chen^3,1,2, Zu-Cheng Chen^1,2,*, Chengjie Fu^4,†, Puxun Wu^1,2,‡, Hongwei Yu^1,2,§, N. D. Ramesh Bhat⁵, Xiaojin Liu⁶, Valentina Di Marco^7,8,9 et al. (PPTA Collaboration)

Valentina Di Marco^7,8,9, Saurav Mishra¹⁰, Daniel J. Reardon^10,11, Christopher J. Russell¹², Ryan M. Shannon^10,11, Lei Zhang^13,10, Xingjiang Zhu^6,14, and Andrew Zic^9,11 (PPTA Collaboration)

¹Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081, China
²Institute of Interdisciplinary Studies, Hunan Normal University, Changsha, Hunan 410081, China
³College of Physics and Engineering Technology, Chengdu Normal University, Chengdu, Sichuan 611130, China
⁴Department of Physics, Anhui Normal University, Wuhu, Anhui 241002, China
⁵International Centre for Radio Astronomy Research, Curtin University, Bentley, Western Australia 6102, Australia
⁶Department of Physics, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China
⁷School of Physics and Astronomy, Monash University, Clayton Victoria 3800, Australia
⁸OzGrav: The ARC Center of Excellence for Gravitational Wave Discovery, Clayton Victoria 3800, Australia
⁹Australia Telescope National Facility, CSIRO, Space and Astronomy, PO Box 76, Epping, New South Wales 1710, Australia
¹⁰Centre for Astrophysics and Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
¹¹OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, Hawthorn Victoria 3122, Australia
¹²CSIRO Scientific Computing, Australian Technology Park, Locked Bag 9013, Alexandria, New South Wales 1435, Australia
¹³National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100101, China
¹⁴Institute for Frontier in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China

^*Contact author: zuchengchen@hunnu.edu.cn
^†Contact author: fucj@ahnu.edu.cn
^‡Contact author: pxwu@hunnu.edu.cn
^§Contact author: hwyu@hunnu.edu.cn

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Phys. Rev. D 111, L061304 – Published 10 March, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L061304

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: $ϕ_{c} = {3.7}_{- 0.5}^{+ 0.3} M_{P}$ , $\log_{10} ω_{L} = {7.1}_{- 0.3}^{+ 0.6}$ , and $\log_{10} σ = - {8.3}_{- 0.6}^{+ 0.3}$ 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.

Physical Review D

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

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

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