The Gravitational-Wave Physics II: Progress

TL;DR

This review surveys five years of gravitational-wave progress, weaving together early-universe GW production, GW cosmology, and GW astrophysics with a focus on the authors' work in phase transitions, induced GWs, preheating, standard sirens, and numerical-relativity waveform modeling. It highlights concrete results such as NS maximum-mass constraints from GW170817, finite-element numerical relativity for eccentric BBHs, and SEOBNRE-based waveforms, alongside insights from lensing, SGWB predictions, and PTA science. The work underlines methodological advances and future prospects with multi-band GW networks (LISA/Taiji/TianQin, ET/CE) and SKA-era PTAs, promising precise tests of gravity, cosmology, and stellar remnants. Overall, the paper outlines end-to-end pathways from early-universe signals to robust GW templates and multi-messenger probes, with broad implications for fundamental physics and astrophysics.

Abstract

It has been a half-decade since the first direct detection of gravitational waves, which signifies the coming of the era of the gravitational-wave astronomy and gravitational-wave cosmology. The increasing number of the detected gravitational-wave events has revealed the promising capability of constraining various aspects of cosmology, astronomy, and gravity. Due to the limited space in this review article, we will briefly summarize the recent progress over the past five years, but with a special focus on some of our own work for the Key Project ``Physics associated with the gravitational waves'' supported by the National Natural Science Foundation of China. In particular, (1) we have presented the mechanism of the gravitational-wave production during some physical processes of the early Universe, such as inflation, preheating and phase transition, and the cosmological implications of gravitational-wave measurements; (2) we have put constraints on the neutron star maximum mass according to GW170817 observations; (3) we have developed a numerical relativity algorithm based on the finite element method and a waveform model for the binary black hole coalescence along an eccentric orbit.

Figures (18)

• Figure 1: An overview for GW studies of observational and theoretical issues, the former contains the GW sources, detection and data analysis, while the latter contains the theoretical problems (GW cosmology/astrophysics) and numerical relativity simulation.
• Figure 2: In the left panel, the orange line presents an example of the present energy spectrum of GWs from domain walls, $\Omega_{\mathrm{GW},0}h^{2}$, using the approximation method in Ref. Saikawa:2017hiv, where the tension and annihilation temperature of domain walls are $(5\times 10^{10}\mathrm{GeV})^{3}$ and $10^{7}$GeV. This SGWB can be observed by DECIGO Kawamura:2011zz, BBO Yagi:2011wg, ET Punturo:2010zz and CE Reitze:2019iox. The right panel shows a random realization of the SGWB using the first 50 $l$-modes, where the angular power spectrum is $l(l+1)C_{l}=0.085$, predicted by models with $\phi_{i}\sim H_{\mathrm{inf}}$. Copied from Ref. Liu:2020mru with permission.
• Figure 3: The PBH abundance as a function of $F_\text{NL}$ and $F_\text{NL}^2\mathcal{A}_\mathcal{R}$, where $\mathcal{A}_\mathcal{R}$ is the amplitude of the power spectrum of the curvature perturbation in the Newtonian gauge. The border between the colored and white regions corresponds to $f_\text{PBH}=1$, i.e. PBHs are all the DM. The dashed lines are for $\mathcal{A}_\mathcal{R}=10^{-2}$, $10^{-3}$, and $10^{-4}$ from left to right, while the shaded area is unphysical since $\mathcal{A}_\mathcal{R}>1$. The thick black curve is the absolute constraint that the GW energy density be smaller than the current density of radiation, while the red and blue curves are the sensitivity bound of LISA at $f_\text{GW}=3\times10^{-2}~\text{Hz}$ and $3\times10^{-3}~\text{Hz}$, respectively; they correspond to PBH masses $M_\text{PBH}=10^{20}~\text{g}$ and $10^{22}~\text{g}$. Copied from Ref. Cai:2018dig with permission.
• Figure 4: Typical energy density spectrum of the GWs induced by a non-Gaussian curvature perturbation at second order with $F_\text{NL}>0$. The width of peak is fixed at $10^{-4}~\text{Hz}$. The abundance of the PBHs is fixed to be $f_\text{PBH}=1$ for $M_\text{PBH}=10^{22}~\text{g}$. We draw the induced GW energy density spectrum $\Omega_\text{GW}h^2$ for $F_\text{NL}=0$ (orange dashed), $10$ (red), $20$ (blue), and $50$ (purple). The gray curve is the sensitivity bound of LISA from Ref. Thrane:2013oya. A reference line of the $k^3$ slope is also drawn for comparison. Copied from Ref. Cai:2018dig with permission.
• Figure 5: The energy density spectrum of induced GWs from curvature perturbations with triple $\delta$-peaks at $k_{*1}<k_{*2}<k_{*3}$. The gray lines denote the positions of those would-be peaks at $k_{ij}$ with $i,j=1,2,3$. Copied from Ref. Cai:2019amo with permission.