Touch of neutrinos on the vacuum metamorphosis: Is the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> solution back?

With the entrance of cosmology in its new era of high precision experiments, low- and high-redshift observations set off tensions in the measurements of both the present-day expansion rate (${H}_{0}$) and the clustering of matter (${S}_{8}$). We provide a simultaneous explanation of these tensions using the Parker-Raval vacuum metamorphosis (VM) model with the neutrino sector extended beyond the three massless Standard Model flavors and the curvature of the universe considered as a model parameter. To estimate the effect on cosmological observables we implement various extensions of the VM model in the standard cosmomc pipeline and establish which regions of parameter space are empirically viable to resolve the ${H}_{0}$ and ${S}_{8}$ tensions. We constrain the parameter space employing the following datasets: (i) the cosmic microwave temperature and polarization data from the Planck mission, (ii) baryon acoustic oscillations (BAO) measurements, and (iii) the Pantheon sample of Supernovae type Ia. We find that the likelihood analyses of the physically motivated VM model, which has the same number of free parameters as in the spatially flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, always gives ${H}_{0}$ in agreement with the local measurements (even when BAO or Pantheon data are included) at the price of much larger ${\ensuremath{\chi}}^{2}$ than $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. The inclusion of massive neutrinos and extra relativistic species quantified through two well-known parameters $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ and ${N}_{\mathrm{eff}}$, does not modify this result, and in some cases improves the goodness of the fit. In particular, for the original $\mathrm{VM}+\ensuremath{\sum}{m}_{\ensuremath{\nu}}+{N}_{\mathrm{eff}}$ and the Planck+BAO+Pantheon dataset combination, we find evidence for $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.8{0}_{\ensuremath{-}0.22}^{+0.18}\text{ }\text{ }\mathrm{eV}$ at more than $3\ensuremath{\sigma}$, no indication for extra neutrino species, ${H}_{0}=71.0\ifmmode\pm\else\textpm\fi{}1.2\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ in agreement with local measurements, and ${S}_{8}=0.755\ifmmode\pm\else\textpm\fi{}0.032$ that solves the tension with the weak lensing measurements.

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