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

TL;DR

This paper sets new upper limits on the energy density of cosmological gravitational waves using CMB and BAO data, explores prior sensitivity, and forecasts future measurement capabilities with upcoming experiments.

Contribution

It provides the first constraints on gravitational wave energy density considering dynamical dark energy and analyzes prior dependence of these limits.

Findings

95% CL upper limits on $oldsymbol{ m{ extbf{ extit{ extOmega}_{ m{gw}}h^{2}}}}$ in standard cosmology.

Prior assumptions significantly affect the constraints, with tighter bounds under log-uniform priors.

Forecasts for future experiments suggest improved sensitivity to gravitational wave energy density.

Abstract

In this work, we derive upper limits on the physical energy-density fraction today of cosmological gravitational waves, denoted by $\Omega_{\rm{gw}}h^{2}$, via analyzing \emph{Planck} \& ACT \& SPT CMB and DESI BAO data combination. In the standard cosmological model, we establish 95\% CL upper limits of $\Omega_{\rm{gw}}h^{2} < 1.0 \times 10^{-6}$ for adiabatic initial conditions and $\Omega_{\rm{gw}}h^{2} < 2.7 \times 10^{-7}$ for homogeneous initial conditions, assuming a uniform prior for $\Omega_{\rm gw}h^{2}$. In light of dynamical dark energy, we get $\Omega_{\rm{gw}}h^{2} < 7.2 \times 10^{-7}$ (adiabatic) and $\Omega_{\rm{gw}}h^{2} < 2.4 \times 10^{-7}$ (homogeneous). In contrast, if a log-uniform prior was assumed for $\Omega_{\rm gw}h^{2}$, 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 $\sigma = 2.5 \times 10^{-7}$ (adiabatic) and $\sigma = 1.0 \times 10^{-7}$ (homogeneous) for ${\Omega_{\rm{gw}}h^{2}}$. 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.