Towards a Solution to the H0 Tension: the Price to Pay

Abstract

The tension between current expansion rate H${}_0$ using Planck data and direct model-independent measurements in the local universe has reached a tension above 5$\sigma$ in the context of the $\Lambda$CDM model. The growing tension among early time and local measurements of H${}_0$ has not ameliorated and remains a crucial and open question in cosmology. Solutions to understand this tension are possible hidden sources of systematic error in the observable measurements or modifications to the concordance $\Lambda$CDM model. In this work, we investigate a solution to the H${}_0$ tension by modifying $\Lambda$CDM and we add at early times extra relativistic energy density ${\rho }_{ex}$. In some context this ${\rho }_{ex}$ corresponds to EDE or Bound Dark Energy. We implement our model in CAMB and perform a full COSMO-MC (MCMC) allowing to simultaneously fit the latest data from CMB anisotropies and the value of H${}_0=74.03\pm 1.42,\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ from A. Riess [R-19] \ci{Riess:2019cxk}. The inclusion of ${\rho }_{ex}$ ameliorates the tension between early and late time measurements only slightly and we obtain a value H${}_0=(68.70\pm 0.45$\ksm) still in conflict with local measurements [R-19]. We follow up our analysis by proposing two forecasting standard deviation ${\sigma }_H=1$ and ${\sigma }_H=0.5$ (in units of \ksm) for local distance measurements H${}_0=(74.03\pm {\sigma }_H)$ \ksm. From MCMC we obtain a value of H${}_0=(72.83\pm 0.47)$ \ksm\, at 68\% confidence level for ${\sigma }_H=0.5$, fully consistent with [R-19], while the price to pay is a percentage increase of $0.12\%$ in CMB ${\chi }_{cmb}^2$. Finally, the extra energy density ${\rho }_{ex}$ leaves distinctive imprints in the matter power spectrum at scales $k\sim k_c$ with $k_c=a_{c}H(a_c)$ and in the CMB power spectrum, allowing for independent verification of our analysis.

20 pages, 10 figures

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