Nanohertz Gravitational Waves

TL;DR

This work surveys the emergence of nanohertz gravitational waves, focusing on pulsar timing arrays as detectors of a stochastic GWB and the physical origins behind it. It shows that MBHBs are the dominant astrophysical source in the nano-Hz band, with a characteristic spectrum $h_c(f)\propto f^{-2/3}$ for circular, GW-driven MBHBs, while eccentricity and environmental coupling imprint deviations and potential discriminants. It also surveys early-Universe GWB scenarios (inflation, phase transitions, defects) as alternative or complementary sources detectable by PTAs, astrometry, and future detectors, and discusses how current PTA evidence (HD-correlated signal with $A_{\rm GWB}\sim\text{few}\times10^{-15}$ and $\gamma\approx2.5$–$4$) constrains these possibilities. The review highlights discriminants such as spectral features, discreteness of sources, anisotropies, and multi-messenger implications for the early Universe, dark matter, and exotic objects, underscoring the profound astrophysical and particle-physics insights enabled by nano-Hz GWs.

Abstract

Evidence of a gravitational wave (GW) signal has emerged in pulsar timing array (PTA) data, opening a new window into the nanoHz GW Universe. We explore the physics of GW signals potentially explaining the data, with a primary focus on GW backgrounds (GWBs), considering both astrophysical and cosmological origins. We describe how: (i) An astrophysical nanoHz GWB emerges as the superposition of individual signals from inspiralling massive black-hole binaries (MBHBs); (ii) Environment coupling, eccentricity, and sparse sampling, affect the MBHB signal spectrum and statistical properties, causing great uncertainty in theoretical predictions, but simultaneously offering a handle to discriminate a potential astrophysical origin; (iii) PTA data offers unprecedented opportunities to constrain high-energy physics beyond the standard model, by probing early Universe GWBs, originated during or after inflation; (iv) Different early Universe GWBs, typically created by non-linear and out-of-equilibrium dynamics, can explain the PTA data, as e.g. from inflation scenarios, first order phase transitions, or topological defects; (v) The PTA detection of GWs opens a new window to explore the Universe, with profound implications for astrophysics and particle physics, probing e.g. the equation of state of the early Universe, the origin of the cosmological perturbations, the nature of the dark matter, or whether exotic objects like primordial black holes or cosmic strings exist.

Figures (3)

• Figure 1: The gravitational wave landscape. In the nano-Hz band zoom-in, each lavander diamond is an individual MBHB. The overall GW signal is marked by the light-turquoise jagged line, whereas the residual GWB following subtraction of the loudest source (dark-blue triangles) at each frequency is marked by the dark-turquoise jagged line. Sensitivity curves of various experiments are shown in black, as labeled. We also show the milli-Hz and kilo-Hz band for completeness. In each band, we plot in black GW detectors and with colored lines and marks a variety of resolved GW signals and unresolved GWBs as labeled.
• Figure 2: Left panel: free spectrum showing the PSD of the RMS residuals measured by EPTA+InPTA, NANOGrav and PPTA. Right Panel: 2-D $A_{\rm GWB}$ - $\gamma$ posterior distribution of the GWB parameters as determined from the data (68%, 95% and 99.7% confidence intervals) together with the joint posterior. The vertical dotted line represents $\gamma=13/3$ for reference. Adapted from InternationalPulsarTimingArray:2023mzf.
• Figure 3: Example of a GWB generated from a population of circular, GW driven MBHBs assuming $T\approx 25$ years. The overall GWB (black) is built by the sum of each individual source (orange stars) as described in the text. The spectrum becomes appreciably spiky and departs from the $f^{-2/3}$ PL (dashed purple line) above 10 nHz. Adapted from Ferranti:2024jsh.