Symmetry of Cosmological Observables, a Mirror World Dark Sector, and the Hubble Constant

We find that a uniform scaling of the gravitational free-fall rates and photon-electron scattering rate leaves most dimensionless cosmological observables nearly invariant. This result opens up a new approach to reconciling cosmic microwave background and large-scale structure observations with high values of the Hubble constant $H_0$: Find a cosmological model in which the scaling transformation can be realized without violating any measurements of quantities not protected by the symmetry. A “mirror world” dark sector allows for effective scaling of the gravitational free-fall rates while respecting the measured mean photon density today. Further model building might bring consistency with the two constraints not yet satisfied: the inferred primordial abundances of deuterium and helium.

Figure 1

CMB temperature (TT) and polarization (EE) power spectra with (red and green) and without (blue) scaling by $\lambda =1.1$ from the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model for dataset 1. Both $\lambda =1.1$ cases are scaled by use of the mirror world dark sector, with (red) and without (green) scaling of the photon scattering rate. Data points are from Planck 2018 [147]. Fractional differences with the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model are shown in the second and bottom panels.

Figure 2

Constraints on parameters from datasets 1 and 2 given models $A$, $B$, and $C$ (see Tables 1 and 2). Top left panel: the (unnormalized) posterior probability density of $H_0$. Other panels: the 68% and 95% contours of equal probability density in the $H_0-Y_P$, $H_0-f_{\mathrm{ADM}}$, and $H_0-T_D/T_{\gamma }$ planes. The gray band “R21” shows the $1\sigma$ and $2\sigma$ constraint on $H_0$ from R21. The purple band “A21” shows the same for $Y_P$ from ([157] hereafter A21).