New constraints on cosmological gravitational waves from CMB and BAO in light of dynamical dark energy

TL;DR

The paper probes the cosmological gravitational-wave background by constraining the present-day energy density $Ω_{gw}h^{2}$ using state-of-the-art CMB (Planck, ACT, SPT) and BAO (DESI) data, under adiabatic and homogeneous initial conditions and within ΛCDM and CPL dynamical-dark-energy models. It demonstrates that GW perturbations affect both the expansion history and perturbation evolution, implemented via the CLASS code, and shows that bounds are sensitive to priors, with homogeneous initial conditions yielding consistently tighter constraints. The results place stringent, model-robust benchmarks in the $f≳10^{-15}$ Hz band and forecast substantial improvements from next-generation surveys (LiteBIRD, CMB-S4, CSST BAO), enabling potential detections at the few-sigma level and enabling joint cosmological- and direct-detection GW analyses. Overall, the work provides a framework for model-agnostic constraints on the cosmological GW background and highlights the synergy between CMB, BAO, and future GW probes.

Abstract

In this work, we derive upper limits on the physical energy-density fraction today of cosmological gravitational waves, denoted by $Ω_{\rm{gw}}h^{2}$, via analyzing \emph{Planck} \& ACT \& SPT CMB and DESI BAO data combination. In the standard cosmological model, we establish 95\% CL upper limits of $Ω_{\rm{gw}}h^{2} < 1.0 \times 10^{-6}$ for adiabatic initial conditions and $Ω_{\rm{gw}}h^{2} < 2.7 \times 10^{-7}$ for homogeneous initial conditions, assuming a uniform prior for $Ω_{\rm gw}h^{2}$. In light of dynamical dark energy, we get $Ω_{\rm{gw}}h^{2} < 7.2 \times 10^{-7}$ (adiabatic) and $Ω_{\rm{gw}}h^{2} < 2.4 \times 10^{-7}$ (homogeneous). In contrast, if a log-uniform prior was assumed for $Ω_{\rm gw}h^{2}$, these constraints can become tighter by a factor of $\sim4$, suggesting the results to be prior-sensitive. Furthermore, we project the sensitivity achievable with LiteBIRD \& CMB Stage-IV measurements of CMB and CSST observations of BAO, forecasting 68\% CL uncertainties of $σ= 2.5 \times 10^{-7}$ (adiabatic) and $σ= 1.0 \times 10^{-7}$ (homogeneous) for ${Ω_{\rm{gw}}h^{2}}$. The constraints we obtained in this work provide critical benchmarks for exploring the cosmological origins of gravitational waves within the frequency band $f \gtrsim 10^{-15}$\,Hz and potentially enable joint analysis with direct gravitational-wave detection sensitive to this regime.

Figures (4)

• Figure 1: Effect of adiabatic versus homogeneous initial conditions on the CMB temperature angular power spectrum. Here, we consider only the $\Lambda$CDM model for the sake of illustration.
• Figure 2: Same as Table \ref{['tab:1']}, but we depict one- and two-dimensional posterior distributions of parameters. The dark and light shaded regions denote 68% and 95% confidence intervals, respectively.
• Figure 3: Same as Table \ref{['tab:1-logUniform']}, but we depict one- and two-dimensional posterior distributions of parameters. The dark and light shaded regions denote 68% and 95% confidence intervals, respectively.
• Figure 4: One-dimensional posterior distributions of $\Omega_{\rm gw}h^{2}$ obtained from the data combination of CSST Gong:2019yxt, LiteBIRD LiteBIRD:2022cnt, and S4 CMB-S4:2016ple. Each fiducial model is determined by the upper-limit value of $\Omega_{\rm gw}h^{2}$ and the central values of other parameters provided in Table \ref{['tab:1']}.