  New Early Dark Energy (NEDE) is a component of vacuum energy at the electron
volt scale, which decays in a first-order phase transition shortly before
recombination [arXiv:1910.10739]. The NEDE component has the potential to
resolve the tension between recent local measurements of the expansion rate of
the Universe using supernovae (SN) data and the expansion rate inferred from
the early Universe through measurements of the cosmic microwave background
(CMB) when assuming $\Lambda$CDM. We discuss in depth the two-scalar field
model of the NEDE phase transition including the process of bubble percolation,
collision, and coalescence. We also estimate the gravitational wave signal
produced during the collision phase and argue that it can be searched for using
pulsar timing arrays. In a second step, we construct an effective cosmological
model, which describes the phase transition as an instantaneous process, and
derive the covariant equations that match perturbations across the transition
surface. Fitting the cosmological model to CMB, baryonic acoustic oscillations
and SN data, we report $H_0 = 69.6^{+1.0}_{-1.3} \, \textrm{km}\,
\textrm{s}^{-1}\, \textrm{Mpc}^{-1}$ $(68 \%$ C.L.) without the local
measurement of the Hubble parameter, bringing the tension down to $2.5\,
\sigma$. Including the local input, we find $H_0 = 71.4 \pm 1.0 \,
\textrm{km}\, \textrm{s}^{-1}\, \textrm{Mpc}^{-1}$ $(68 \%$ C.L.) and strong
evidence for a non-vanishing NEDE component with a $\simeq 4\, \sigma$
significance.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory