H0 tension or T0 tension?. (arXiv:2005.10656v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Ivanov_M/0/1/0/all/0/1">Mikhail M. Ivanov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ali_Haimoud_Y/0/1/0/all/0/1">Yacine Ali-Haïmoud</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lesgourgues_J/0/1/0/all/0/1">Julien Lesgourgues</a>
We study whether the discrepancy between the local and cosmological
measurements of the Hubble constant $H_0$ can be reformulated as a tension in
the cosmic microwave background (CMB) monopole temperature $T_0$. The latter is
customarily fixed to the COBE/FIRAS best-fit value in CMB anisotropy data
analyses. We show that the primary CMB anisotropies and the shape of the matter
power spectrum are not directly sensitive to $T_0$. They depend only on the
dark matter and baryon densities per CMB photon. Once these ratios are fixed,
$T_0$ only measures the time elapsed since recombination until today. This
results is a nearly perfect geometric degeneracy between $T_0$ and $H_0$. Taken
at face value, this implies that removing the FIRAS prior on $T_0$ is enough to
make the Planck CMB and SH0ES measurements consistent within the base
$Lambda$CDM model without introducing new physics. One may break the
degeneracy by combining Planck with SH0ES, yielding an independent measurement
of $T_0$, which happens to be in a $4sigma$ tension with FIRAS. Therefore, the
Hubble tension can be fully recast into the $T_0$ tension. The agreement with
FIRAS can be restored if we combine Planck with the baryon acoustic oscillation
data instead of SH0ES. Thus, the tension between SH0ES and cosmological
measurements of $H_0$ within $Lambda$CDM persists even if we discard the FIRAS
$T_0$ measurement.
We study whether the discrepancy between the local and cosmological
measurements of the Hubble constant $H_0$ can be reformulated as a tension in
the cosmic microwave background (CMB) monopole temperature $T_0$. The latter is
customarily fixed to the COBE/FIRAS best-fit value in CMB anisotropy data
analyses. We show that the primary CMB anisotropies and the shape of the matter
power spectrum are not directly sensitive to $T_0$. They depend only on the
dark matter and baryon densities per CMB photon. Once these ratios are fixed,
$T_0$ only measures the time elapsed since recombination until today. This
results is a nearly perfect geometric degeneracy between $T_0$ and $H_0$. Taken
at face value, this implies that removing the FIRAS prior on $T_0$ is enough to
make the Planck CMB and SH0ES measurements consistent within the base
$Lambda$CDM model without introducing new physics. One may break the
degeneracy by combining Planck with SH0ES, yielding an independent measurement
of $T_0$, which happens to be in a $4sigma$ tension with FIRAS. Therefore, the
Hubble tension can be fully recast into the $T_0$ tension. The agreement with
FIRAS can be restored if we combine Planck with the baryon acoustic oscillation
data instead of SH0ES. Thus, the tension between SH0ES and cosmological
measurements of $H_0$ within $Lambda$CDM persists even if we discard the FIRAS
$T_0$ measurement.
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