Pulsar timing arrays (PTAs) have recently provided compelling evidence for a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, offering a unique window into fundamental physics. Here, we explore implications for symmetric teleparallel $f(Q)$ gravity, a theory in which deviations from General Relativity (GR) arise through the non-metricity scalar $f(Q)$. Crucially, tensor modes propagate at the speed of light in this framework. However, their amplitude undergoes a modified damping during their evolution. We adopt a model-independent parameterization and derive an analytic approximation to the tensor mode transfer function to obtain the spectral energy density of primordial inflationary gravitational waves. Comparison with the NANOGrav 15-year and IPTA second data releases show that the inferred damping parameter $n$ remains consistent with GR, yet allows small deviations that could be observable. We then conduct a Fisher information matrix forecasts which demonstrate that the Square Kilometre Array (SKA) observatory will improve these constraints by several orders of magnitude, offering the potential to distinguish $f(Q)$ gravity from GR with high precision. These results highlight PTAs as powerful probes of non-metricity-based modifications to gravity.
Pulsar timing experiments are currently searching for gravitational waves, and this dissertation focuses on the development and study of the pulsar timing residual models used for continuous wave searches. The first goal of this work is to re-present much of the fundamental physics and mathematics concepts behind the calculations and theory used in pulsar timing. While there exist many reference sources in the literature, I try to offer a fully self-contained explanation of the fundamentals of this research which I hope the reader will find helpful. The next goal broadly speaking has been to f…
We study the observation of stochastic gravitational-wave background (SGWB) made by pulsar-timing arrays in the spherical harmonic space. Instead of using the Shapiro time delay, we keep the Sachs-Wolfe line-of-sight integral for the timing residual of an observed pulsar. We derive the power spectrum of the timing residual, from which the overlap reduction functions and the bipolar spherical harmonics coefficients are constructed for the SGWB intensity and polarization anisotropies. We have reproduced the previous results, noting that we have developed a fast algorithm for computing accurate o…
Gravitational waves provide a new probe of the Universe which can reveal a number of cosmological and astrophysical phenomena that cannot be observed by electromagnetic waves. Different frequencies of gravitational waves are detected by different means. Among them, precision measurements of pulsar timing provides a natural detector for gravitational waves with light-year scale wavelengths. In this review, first a basic framework to detect a stochastic gravitational wave background using pulsar timing array is introduced, and then possible interpretations of the latest observational result of 1…
Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spect…
Pulsar timing provides a sensitive probe of small-scale structure. Gravitational perturbations arising from an inhomogeneous environment could manifest as detectable perturbations in the pulsation phase. Consequently, pulsar timing arrays have been proposed as a probe of dark matter substructure on mass scales as small as $10^{-11} M_\odot$. Since the small-scale mass distribution is connected to early-Universe physics, pulsar timing can therefore constrain the thermal history prior to Big Bang nucleosynthesis (BBN), a period that remains largely unprobed. We explore here the prospects for pul…
Any unambiguous detection of a stochastic gravitational wave background by a pulsar timing array will rest on the measurement of a characteristic angular correlation between pulsars. The ability to measure this correlation will depend on the geometry of the array. However, spatially correlated sources of noise, such as errors in the planetary ephemeris or clock errors, can produce false-positive correlations. The severity of this contamination will also depend on the geometry of the array. This paper quantifies these geometric effects with a spherical harmonic analysis of the pulsar timing res…
Ultra-light Dark Matter (ULDM) models are suitable candidates for the cosmological Dark Matter that may leave characteristic imprints in many observables. Among other probes, signatures of ULDM can be searched for in pulsar timing data. In this work we describe the effects of spin-2 ULDM on pulsar timing arrays, extending previous results on lower spins. Spin-2 ULDM is universally coupled to standard matter with dimensionless strength $α$. We estimate that current data could constrain this coupling in the mass range $m\lesssim4\times10^{-22}$ eV at the $10^{-5}$ to $10^{-6}$ level, which is th…
Non-Gaussian timing residual skewness in pulsar timing arrays
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Leibnitz Universität Hannover（马克斯·普朗克引力物理研究所（爱因斯坦研究所），莱布尼茨汉诺威大学）；Department of Physics, National Central University（国立中央大学物理系）；Institute of Physics, Academia Sinica（台湾中央研究院物理研究所）；Institute of Astronomy and Astrophysics, Academia Sinica（台湾中央研究院天文及天文物理研究所）
We study the ultralight vector dark matter with a mass around $10^{-23}\,\mathrm{eV}$. The vector field oscillating coherently on galactic scales induces oscillations of the spacetime metric with a frequency around nHz, which is detectable by pulsar timing arrays. We find that the pulsar timing signal due to the vector dark matter has nontrivial angular dependence unlike the scalar dark matter and the maximal amplitude is three times larger than that of the scalar dark matter.
Detecting Chiral Gravitational Wave Background with a Dipole Pulsar Timing Array
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙木理论研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（台湾大学梁氏宇宙学与粒子天体物理学研究中心）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
We study how to probe bispectra of stochastic gravitational waves with pulsar timing arrays. The bispectrum is a key to probe the origin of stochastic gravitational waves. In particular, the shape of the bispectrum carries valuable information of inflation models. We show that an appropriate filter function for three point correlations enables us to extract a specific configuration of momentum triangles in bispectra. We also calculate the overlap reduction functions and discuss strategy for detecting the bispectrum with multiple pulsars.
The coherent oscillation of ultralight dark matter in the mass regime around $10^{-23}$ eV induces changes in gravitational potential with the frequency in the nanohertz range. This effect is known to produce a monochromatic signal in the pulsar timing residuals. Here we discuss a multifield scenario that produces a wide spectrum of frequencies, such that the ultralight particle oscillation can mimic the pulsar timing signal of stochastic common spectrum process. We discuss how ultralight dark matter with various spins produces such a wide band spectrum on pulsar timing residuals and perform t…
