Hubble Tension as a Window on the Gravitation of the Dark Matter Sector

A simple and minimal extension of the standard cosmological $\mathrm{\Lambda }\mathrm{CDM}$ model in which dark matter experiences an additional long-range scalar interaction is demonstrated to alleviate the long-lasting Hubble tension while primordial nucleosynthesis predictions remain unaffected and passing by construction all current local tests of general relativity. The theoretical formulation of this $\mathrm{\Lambda }\beta \mathrm{CDM}$ model and its comparison to astrophysical observations are presented to prove its ability to fit existing data and potentially resolve the tension.

Figure 1

From top to bottom: ${\rho }_{\mathrm{D}}$, which exhibits a departure from pure dust between equivalence and recombination; the effective equation of state (12); the strength of the scalar coupling $\alpha$ that shows that DM gravity is stronger at high $z$ but similar as in the visible sector today; the CMB visibility function; and the evolution of the energy densities in units of $3H^2(a)/8\pi G$, proving that $\phi$ remains subdominant at all times. All curves correspond to the best fit parameters of the $\mathrm{base}+\mathrm{BAO}(z>1)+H_0$ dataset, i.e., ${\mathrm{\Omega }}_{\mathrm{b}0}{h}^2=0.02250$, ${\mathrm{\Omega }}_{\mathrm{m}}=0.2619$, $h=0.7240$, $\ln ({10}^{10}{A}_s)=3.0569$, $n_s=0.9741$, ${\tau }_{\mathrm{reio}}=0.0601$, $\beta =0.2509$, and ${\phi }_i=0.7159$.

Figure 2

Black: residuals of TT, TE, and EE spectra of the $\mathrm{\Lambda }\mathrm{CDM}$ best fit (from Planck data only) [2] with Planck data. Red: differences between our $\mathrm{\Lambda }\beta \mathrm{CDM}$ best fit spectra [obtained with the base $\mathrm{dataset}+\mathrm{BAO}(z>1)+H_0$] and the former spectra.

Figure 3

Statistical comparison of the $\mathrm{\Lambda }\mathrm{CDM}$ and $\mathrm{\Lambda }\beta \mathrm{CDM}$ to cosmological data focusing on the four parameters $(H_0,{\mathrm{\Omega }}_{\mathrm{m}},S_8,t_{\mathrm{U}})$ in order to highlight the Hubble tension. See Ref. [14] for a full analysis and details. Plots were performed with getdist [28].