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

Abstract

We present a detailed investigation of a subdominant 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 ${\mathrm{log}}_{10}({z}_{c})\ensuremath{\sim}3.5$, reaching ${\ensuremath{\rho}}_{\mathrm{EDE}}({z}_{c})/{\ensuremath{\rho}}_{\mathrm{tot}}\ensuremath{\sim}10%$ 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 that scales as $V(\ensuremath{\phi})\ensuremath{\propto}{\ensuremath{\phi}}^{2n}$ with $2\ensuremath{\lesssim}n\ensuremath{\lesssim}3.4$ around the minimum is preferred at the 68% confidence level, and the Planck polarization places additional constraints on the dynamics of perturbations in the scalar field. In particular, the data prefer a potential that flattens at large field displacements. A Markov-chain Monte Carlo analysis of mock data shows that the next-generation CMB observations (i.e., CMB-S4) can unambiguously detect the presence of the EDE at a 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 $n\ensuremath{\approx}2$. This instability and ensuing potentially nonlinear, spatially inhomogeneous, dynamics may provide unique signatures of this scenario.