Does time or space shape black hole accretion in Rainbow Gravity? Observational constraints from Pantheon+SH0ES, CC+BAO, and joint data
Abstract
Abstract Rainbow gravity extends doubly special relativity to curved spacetimes, leading to an energydependent metric. Within this framework, we study black hole mass accretion using two distinct rainbow function sets. The first, RF1 , modifies the temporal component of the metric, while the second, RF2 , alters the spatial component. Each formulation is coupled with three generalized holographic dark energy models, Tsallis, R´enyi, and Sharma-Mittal, which introduce non-extensive entropy corrections to the standard Bekenstein-Hawking area law. We perform a comprehensive Markov Chain Monte Carlo analysis constrained by Pantheon+SH0ES, CC+BAO, and joint observational data to obtain precise cosmological parameter constraints. In the RF1 framework, the Tsallis exponent is tightly constrained around the Bekenstein-Hawking limit δ = 2.0 } 0.03, while RF2 yields weaker constraints and a higher Hubble constant (H0 ∼ 74 km/s/Mpc). Notably, the two frameworks give rise to quantitatively different accretion histories. Both exhibit monotonic, quintessence-like mass growth ( ρ + p > 0), but RF1 leads to a mass increase of approximately 0.15% from z = 2 to the present, whereas RF2 results in a slightly lower increase of about 0.10%. Our comparative analysis shows that RF1 is more stable and less sensitive to the choice of dataset, while RF2 is phenomenologically richer but more dependent on observational data. These findings directly link the choice of rainbow functions, temporal versus…
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