Easing cosmic tensions with an open and hotter universe

Despite the great observational success of the standard cosmological model some discrepancies in the inferred parameter constraints have manifested among a number of cosmological data sets. These include a tension between the expansion rate of our Cosmos as inferred from the cosmic microwave background (CMB) and as found from local measurements, the preference for an enhanced amplitude of CMB lensing, a somewhat low quadrupole moment of the CMB fluctuations as well as a preference for a lower amplitude of matter fluctuations in large-scale structure surveys than inferred from the CMB. We analyze these observational tensions under the addition of spatial curvature and a free CMB background temperature that may deviate from its locally measured value. With inclusion of these parameters, we observe a trend in the parameter constraints from CMB and baryon acoustic oscillation data towards an open and hotter universe with larger current expansion rate, standard CMB lensing amplitudes, lower amplitude of matter fluctuations, and marginally lower CMB quadrupole moment, consistently reducing the individual tensions among the cosmological data sets. Combining this data with local distance measurements, we find a preference for an open and hotter universe beyond the 99.7% confidence level. Finally, we briefly discuss a local void as a possible source for a deviation of the locally measured CMB temperature from its background value and as mimic of spatial curvature for CMB photons. This interpretation implies a $\sim 20\%$ underdensity in our local neighborhood of $\sim 10–100\mathrm{Mpc}$ in diameter, which is well within cosmic variance.

Figure 1

The combination of all data sets (Planck with lensing, BAO, and R19) shows a preference for an open (${\mathrm{\Omega }}_k>0$) and hotter ($T_0>T_{\mathrm{FIRAS}}=2.7255$) universe. The contours indicate 68.3%, 95.4%, and 99.7% confidence levels.

Figure 2

With the additional variation of ${\mathrm{\Omega }}_k$ and $T_0$ there is no longer any noteworthy preference for an enhanced amplitude of CMB lensing $A_L>1$. The CMB and BAO data also favour a larger current expansion rate $H_0$ in better agreement with local measurements as well as a lower amplitude of matter fluctuations ${\sigma }_8$ as preferred by large-scale structure surveys. A further effect is a marginal lowering of the predicted CMB quadrupole towards the measurement. Error bars represent marginalized 68.3% confidence levels.