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Large-scale primordial perturbations have been well constrained by current cosmological observations, but the properties of small-scale perturbations remain elusive. This study focuses on second-order induced gravitational waves generated…

Cosmology and Nongalactic Astrophysics · Physics 2026-02-11 Di Wu , Zhi-Chao Li , Peng-Yu Wu , Fei-Yu Chen , Jing-Zhi Zhou

Pulsar timing arrays (PTAs) are searching for nanohertz-frequency gravitational waves (GWs) through cross-correlation of pulse arrival times from a set of radio pulsars. PTAs have relied upon a frequency-shift formula of the pulse, where…

High Energy Astrophysical Phenomena · Physics 2024-07-03 Ryousuke Kubo , Kakeru Yamahira , Hideki Asada

We develop a full-covariance formalism for pulsar timing array(PTA) -- astrometry verlap reduction function (ORF) estimators and use it to forecast graviton-mass constraints from a nanohertz stochastic gravitational-wave background (SGWB).…

General Relativity and Quantum Cosmology · Physics 2026-04-30 Jing-Hong Han , Zhi-Chao Zhao

We analyze the energy density spectrum of \acp{SIGW} using the NANOGrav 15-year data set, thereby constraining the primordial non-Gaussian parameter $f_{\mathrm{NL}}$. For the first time, we calculate the seventeen missing two-loop diagrams…

Cosmology and Nongalactic Astrophysics · Physics 2023-11-10 Zhe Chang , Yu-Ting Kuang , Di Wu , Jing-Zhi Zhou , Qing-Hua Zhu

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we…

Statistical anisotropy in the nanohertz-frequency gravitational-wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a frequentist statistical framework that intrinsically…

High Energy Astrophysical Phenomena · Physics 2022-12-14 Nihan Pol , Stephen R. Taylor , Joseph D. Romano

The power-law parametrization for the energy density spectrum of gravitational wave (GW) background is a useful tool to study its physics and origin. While scalar induced secondary gravitational waves (SIGWs) from some particular models fit…

General Relativity and Quantum Cosmology · Physics 2023-11-17 Zhu Yi , Qing Gao , Yungui Gong , Yue Wang , Fengge Zhang

The NANOGrav Collaboration recently reported a strong evidence for a stochastic common-spectrum process in the pulsar-timing data. We evaluate the evidence of interpreting this process as mergers of super massive black hole binaries and/or…

Cosmology and Nongalactic Astrophysics · Physics 2021-04-21 Ligong Bian , Rong-Gen Cai , Jing Liu , Xing-Yu Yang , Ruiyu Zhou

We perform a phenomenological comparison of the gravitational wave (GW) spectrum expected from cosmic gauge string networks and superstring networks comprised of multiple string types. We show how violations of scaling behavior and the…

High Energy Physics - Phenomenology · Physics 2024-07-25 Danny Marfatia , Ye-Ling Zhou

Recently, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) claimed the detection of a stochastic common-spectrum process of the pulsar timing array (PTA) time residuals from their 12.5 year data, which might be…

Cosmology and Nongalactic Astrophysics · Physics 2023-08-15 Guillem Domènech , Shi Pi

The NANOGrav, Parkes, European, and International Pulsar Timing Array (PTA) Collaborations have reported evidence for a common-spectrum process that can potentially correspond to a stochastic gravitational wave background (SGWB) in the…

Cosmology and Nongalactic Astrophysics · Physics 2022-06-15 Alberto Roper Pol , Chiara Caprini , Andrii Neronov , Dmitri Semikoz

The evidence of the nano-Hertz stochastic gravitational wave (GW) background is reported by multiple pulsar timing array collaborations. While a prominent candidate of the origin is astrophysical from supermassive black hole binaries,…

Cosmology and Nongalactic Astrophysics · Physics 2023-12-06 Katsuya T. Abe , Yuichiro Tada

In recent years, several pulsar timing array collaborations have reported first hints for a stochastic gravitational wave background at nano-Hertz frequencies. Here we elaborate on the possibility that this signal comes from new physics…

High Energy Physics - Phenomenology · Physics 2023-11-02 Eric Madge , Enrico Morgante , Cristina Puchades-Ibáñez , Nicklas Ramberg , Wolfram Ratzinger , Sebastian Schenk , Pedro Schwaller

The stochastic gravitational wave (GW) background is secondarily and inevitably induced by the primordial curvature perturbations beyond the first order of the cosmological perturbation theory. We analytically calculate the integration…

General Relativity and Quantum Cosmology · Physics 2026-01-15 Takahiro Terada

In this work, we propose a graph-based method implemented on the pulsar timing residuals (PTRs) for stochastic gravitational wave background (SGWB) detection within the nano-Hertz frequency regime and examining uncertainties of its…

Cosmology and Nongalactic Astrophysics · Physics 2026-04-14 M. Alakhras , S. M. S. Movahed

Recently, many different pulsar timing array (PTA) collaborations have reported strong evidence for a common stochastic process in their data sets. The reported amplitudes are in tension with previously computed upper limits. In this paper,…

High Energy Astrophysical Phenomena · Physics 2022-06-29 Aaron D. Johnson , Sarah J. Vigeland , Xavier Siemens , Stephen R. Taylor

Primordial black holes and secondary gravitational waves can be used to probe the small scale physics at very early time. For secondary gravitational waves produced after the horizon reentry, we derive an analytical formula for the time…

General Relativity and Quantum Cosmology · Physics 2019-12-25 Yizhou Lu , Yungui Gong , Zhu Yi , Fengge Zhang

Studies have shown that the use of pulsar timing arrays (PTAs) is among the approaches with the highest potential to detect very low-frequency gravitational waves in the near future. Although the capture of gravitational waves (GWs) by PTAs…

Instrumentation and Methods for Astrophysics · Physics 2020-10-13 MengNi Chen , Yuanhong Zhong , Yi Feng , Di Li , Jin Li

Recent pulsar timing array results, including the NANOGrav 15-year data set, show evidence for a stochastic gravitational-wave background (GWB) in the nanohertz band. We present a Bayesian framework to compare three possible origins: (i) a…

Cosmology and Nongalactic Astrophysics · Physics 2025-10-28 Mengshen Wang , Zuocheng Zhang , Hua Xu

We thoroughly study the induced gravitational wave interpretation of the possible gravitational wave background reported by PTA collaborations, considering the unknown equation of state $w$ of the early universe. We perform a Bayesian…

Cosmology and Nongalactic Astrophysics · Physics 2024-09-02 Guillem Domènech , Shi Pi , Ao Wang , Jianing Wang