Constraining early dark energy with gravitational waves before recombination

We show that the nonperturbative decay of ultralight scalars into Abelian gauge bosons, recently proposed as a possible solution to the Hubble tension, produces a stochastic background of gravitational waves which is constrained by the cosmic microwave background. We simulate the full nonlinear dynamics of resonant dark photon production and the associated gravitational-wave production, finding the signals to exceed constraints for the entire parameter space we consider. Our findings suggest that gravitational-wave production from the decay of early dark energy may provide a unique probe of these models.

Figure 1

Total energy in the gauge fields (top) and the fractional energy in the dULS sector (bottom) as a function of redshift for various couplings $\alpha$ indicated in the legend. All simulations fix $m_{\varphi }={10}^{-26}\mathrm{eV}$, $f=1.5\times {10}^{17}\mathrm{GeV}$, and $\theta =2$. Dashed and solid vertical lines indicate, respectively, matter-radiation equality and the favored redshift of the transition from dark energy to matter from the analysis of Ref. [18].

Figure 2

Present-day gravitational-wave spectrum emitted by recombination (i.e., evaluated at $z\approx 1100$), fixing $m_{\varphi }={10}^{-26}\mathrm{eV}$ and varying $\alpha$ (top), and fixing $\alpha =70$ and varying $m_{\varphi }$ (bottom). All simulations set $f=1.5\times {10}^{17}\mathrm{GeV}$ and $\theta =2$. In black is the upper bound as constrained by the CMB, computed in Ref. [54].

Figure 3

Polarization components of the present-day gravitational-wave spectrum emitted by recombination (i.e., evaluated at $z\approx 1100$) for $\alpha =50$ (top) and 70 (bottom). The plus and minus polarizations are in blue and red, respectively, while the total signal is portrayed in dashed black. Both panels fix $m_{\varphi }={10}^{-26}\mathrm{eV}$, $f=1.5\times {10}^{17}\mathrm{GeV}$, and $\theta =2$. In solid black is the upper bound as constrained by the CMB, computed in Ref. [54].