Rainbow McVittie Horizons in an Expanding Universe

Abstract

We derive the Friedmann dynamics and apparent-horizon thermodynamics of a spatially flat McVittie spacetime in Gravity's Rainbow and construct a consistent non-accreting perfect-fluid sector with an effective rainbow Hubble rate. The Einstein equations, trapping horizon, surface gravity, Misner--Sharp energy, unified first law, and Clausius relation form a closed thermodynamic system reproducing the Friedmann dynamics. We then introduce a low-energy rainbow deformation and constrain it using 32 cosmic-chronometer measurements and 1580 Pantheon+ light curves with the full covariance matrix. Combined with the Planck matter-density prior, the fit gives $H_0=68.75\pm 2.63\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, ${\Omega }_m=0.3157\pm 0.0070$, and $\epsilon =0.0106_{-0.0231}^{+0.0234}$. The resulting constraints establish the observational viability of small late-time rainbow corrections and place the general-relativistic limit within the preferred parameter region.

23 pages, 10 figures