中国物理B ›› 2025, Vol. 34 ›› Issue (2): 20402-020402.doi: 10.1088/1674-1056/ad9a98

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Probing the shape of the primordial curvature power spectrum and the energy scale of reheating with pulsar timing arrays

Lele Fan(范乐乐)1,2, Jie Zheng(郑捷)2, Fengge Zhang(张丰阁)2, and Zhi-Qiang You(尤志强)2,†   

  1. 1 School of Physics, Henan Normal University, Xinxiang 453007, China;
    2 Henan Academy of Sciences, Zhengzhou 450046, China
  • 收稿日期:2024-09-11 修回日期:2024-11-21 接受日期:2024-12-05 出版日期:2025-02-15 发布日期:2025-01-15
  • 通讯作者: Zhi-Qiang You E-mail:you_zhiqiang@whu.edu.cn
  • 基金资助:
    ZQY is supported by the National Natural Science Foundation of China (Grant No. 12305059), the Joint Fund of Henan Province Science and Technology R&D Program (Grant No. 235200810111), and the Startup Research Fund of Henan Academy of Sciences (Grant No. 241841224). FGZ is supported by the National Natural Science Foundation of China (Grant No. 12305075). JZ is supported by the National Natural Science Foundation of China (Grant No. 12403002) and the Startup Research Fund of Henan Academy of Sciences (Grant No. 241841221).

Probing the shape of the primordial curvature power spectrum and the energy scale of reheating with pulsar timing arrays

Lele Fan(范乐乐)1,2, Jie Zheng(郑捷)2, Fengge Zhang(张丰阁)2, and Zhi-Qiang You(尤志强)2,†   

  1. 1 School of Physics, Henan Normal University, Xinxiang 453007, China;
    2 Henan Academy of Sciences, Zhengzhou 450046, China
  • Received:2024-09-11 Revised:2024-11-21 Accepted:2024-12-05 Online:2025-02-15 Published:2025-01-15
  • Contact: Zhi-Qiang You E-mail:you_zhiqiang@whu.edu.cn
  • Supported by:
    ZQY is supported by the National Natural Science Foundation of China (Grant No. 12305059), the Joint Fund of Henan Province Science and Technology R&D Program (Grant No. 235200810111), and the Startup Research Fund of Henan Academy of Sciences (Grant No. 241841224). FGZ is supported by the National Natural Science Foundation of China (Grant No. 12305075). JZ is supported by the National Natural Science Foundation of China (Grant No. 12403002) and the Startup Research Fund of Henan Academy of Sciences (Grant No. 241841221).

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摘要： Recent observations by pulsar timing array collaborations have detected a stochastic common-spectrum signal, which may originate from scalar-induced gravitational waves generated by primordial curvature perturbations during inflation. Using the NANOGrav 15-year data set, we explore this hypothesis by constraining the primordial curvature power spectrum and reheating energy scale. We model the primordial power spectrum with a lognormal form and consider reheating with the equation of state parameter $w=1/6$. Our Bayesian analysis reveals a narrow peak in the primordial power spectrum (the width of the spectrum $\Delta < 0.05$ at the $95%$ confidence level) and constrains the reheating temperature to be $0.03 {\rm GeV} \lesssim T_{\rm rh} \lesssim 7.2$ GeV. The best-fit SIGW spectrum shows a characteristic turning point near $f \sim 10^{-8.1}$ Hz, marking the transition from reheating to radiation domination, providing a unique probe of the properties of the early Universe.

关键词: gravitational waves, pulsars

Abstract: Recent observations by pulsar timing array collaborations have detected a stochastic common-spectrum signal, which may originate from scalar-induced gravitational waves generated by primordial curvature perturbations during inflation. Using the NANOGrav 15-year data set, we explore this hypothesis by constraining the primordial curvature power spectrum and reheating energy scale. We model the primordial power spectrum with a lognormal form and consider reheating with the equation of state parameter $w=1/6$. Our Bayesian analysis reveals a narrow peak in the primordial power spectrum (the width of the spectrum $\Delta < 0.05$ at the $95%$ confidence level) and constrains the reheating temperature to be $0.03 {\rm GeV} \lesssim T_{\rm rh} \lesssim 7.2$ GeV. The best-fit SIGW spectrum shows a characteristic turning point near $f \sim 10^{-8.1}$ Hz, marking the transition from reheating to radiation domination, providing a unique probe of the properties of the early Universe.

Key words: gravitational waves, pulsars

中图分类号:  (Gravitational waves)

  • 04.30.-w
97.60.Gb (Pulsars)