Oscillating scalar fields and the Hubble tension: a resolution with novel signatures

Abstract

We present a detailed investigation of a sub-dominant oscillating scalar field ('early dark energy', EDE) in the context of resolving the Hubble tension. Consistent with earlier work, but without relying on fluid approximations, we find that a scalar field frozen due to Hubble friction until ${\rm log}_{10}(z_c)\sim3.5$, reaching $ρ_{\rm EDE}(z_c)/ρ_{\rm tot}\sim10$%, and diluting faster than matter afterwards can bring cosmic microwave background (CMB), baryonic acoustic oscillations, supernovae luminosity distances, and the late-time estimate of the Hubble constant from the SH0ES collaboration into agreement. A scalar field potential which scales as $V(φ) \propto φ^{2n}$ with $2\lesssim n\lesssim 3.4$ around the minimum is preferred at the 68% confidence level, and the {\em Planck} polarization places additional constraints on the dynamics of perturbations in the scalar field. In particular, the data prefers a potential which flattens at large field displacements. An MCMC analysis of mock data shows that the next-generation CMB observations (i.e., CMB-S4) can unambiguously detect the presence of the EDE at very high significance. This projected sensitivity to the EDE dynamics is mainly driven by improved measurements of the $E$-mode polarization. We also explore new observational signatures of EDE scalar field dynamics: (i) We find that depending on the strength of the tensor-to-scalar ratio, the presence of the EDE might imply the existence of isocurvature perturbations in the CMB. (ii) We show that a strikingly rapid, scale-dependent growth of EDE field perturbations can result from parametric resonance driven by the anharmonic oscillating field for $n\approx 2$. This instability and ensuing potentially nonlinear, spatially inhomogenoues, dynamics may provide unique signatures of this scenario.

Figures (22)

• Figure 1: Contours of constant ${\rm log}_{10}f_{\rm EDE}(z_c)$ (vertical/solid) and ${\rm log}_{10}z_c$ (horizontal/dashed) as a function of the axion mass, $m$, and decay constant, $f$. The red lines show the contours for $n=2$ and the black for $n=3$. Since $H_0 = 100 h\ {\rm km/s/Mpc} = 2.13h \times 10^{-33}\ {\rm eV}$ the mass parameter of the potential that helps to resolve the Hubble tension ranges between $10^{-28}\ {\rm eV} \lesssim m \lesssim 10^{-26} \ {\rm eV}$ and $0.01 \lesssim f/M_{\rm pl}\lesssim 1$.
• Figure 2: The evolution of the fraction of the total energy density in the EDE as a function of redshift for $z_c = 10^4$ and $f_{\rm EDE}(z_c) = 0.1$. Note that as the initial field displacement becomes larger the asymmetry of $f_{\rm EDE}(z)$ and oscillation frequency of the background field increases.
• Figure 3: Posterior distributions of the cosmological parameters reconstructed from a run to all data (including Planck high-$\ell$ polarization) in the $\Lambda$CDM (blue) and EDE (red) cosmology. From top to bottom we show: the $\Lambda$CDM parameters, 2D distributions of $H_0$ and $f_{\rm EDE}(z_c)$ vs a subset of parameters, the 1D posterior distribution of the EDE parameters. We show the SH0ES determination of $H_0$ in the gray bands.
• Figure 4: 2D posterior distribution of a subset of parameters in the $n=3$ case. We compare the results with and without high-$\ell$ TT,TE,EE data.
• Figure 5: Reconstructed 1D posterior of $H_0$ and $f_{\rm EDE}(z_c)$. We compare the results with (blue) and without (red) high-$\ell$ TT,TE,EE data, as well as keeping $\Theta_i$ free (full lines) and enforcing $\Theta_i=0.1$, i.e., the power-law case (dashed lines).