Alleviating the $H_0$ tension in Rastall gravity

Abstract

The persistent discrepancy between local determinations of the Hubble constant $H_0$ and the Planck 2018 value ($67.4\pm 0.5\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$) within $\hat{I}›$CDM remains a central challenge in precision cosmology. We investigate the Hubble tension in $\hat{I}›$CDM and its Rastall extension (R-$\hat{I}›$CDM) for flat, open, and closed geometries. We analyze three primary dataset combinations: D${}_1$ (late-time probes: SN + $H(z)$ + $f\ddot{I}{ƒ}_8$), D${}_2$ (late-time probes combined with DESI DR2 BAO and BBN), and D${}_3$ (late-time probes combined with BAO and Planck 2018 CMB distance priors). Parameters are constrained via Markov Chain Monte Carlo sampling, and tensions with SH0ES ($73.2\pm 1.3\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$) and Planck are expressed in units of the combined uncertainty. In addition, we include a Planck-only configuration (D${}_4$) as a reference baseline to isolate early-Universe constraints on $H_0$. Within $\hat{I}›$CDM, D${}_1$ and D${}_2$ yield $H_0\simeq 70.75$-$71.43\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, reducing the SH0ES discrepancy to $1.11\ddot{I}ƒ$--$1.63\ddot{I}ƒ$ while maintaining a $3.62\ddot{I}ƒ$-$4.23\ddot{I}ƒ$ tension with Planck. Including CMB distance priors (D${}_3$) shifts the result to $H_0\simeq 67.18$--$67.55\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, consistent with Planck at $0.09\ddot{I}ƒ$-$0.38\ddot{I}ƒ$ but increasing the SH0ES discrepancy to $4.25\ddot{I}ƒ$-$4.51\ddot{I}ƒ$.

40 pages, 8 figures