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
$log_10(z_c)\sim3.5$, reaching $\rho_EDE(z_c)/\rho_\rm
tot\sim10$%, 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 $V(\phi) \phi^2n$ with $2n3.4$ 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 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 $n2$. This instability and ensuing
potentially nonlinear, spatially inhomogenoues, dynamics may provide unique
signatures of this scenario.
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