We perform a comparative analysis of the inflationary dynamics exhibited by three distinct models Mutated Hilltop Inflation (MHI), D-brane derived KKLTI inflation, and nuclear shell model inspired Woods-Saxon potential within the framework of Rastall-Rainbow gravity. This modified theory, which merges an energy-dependent spacetime geometry with a non-conserved energy-momentum tensor, offers a generalized setting for exploring the early universe. For each model, we compute key observables viz., the scalar spectral index n s , the tensor-to-scalar ratio r, and the running of the scalar index n sk and systematically compare their predictions against the latest combined cosmological data sets from Planck, BICEP/Keck, and the Atacama Cosmology Telescope (ACT). Our comparative study reveals that while all three scenarios successfully yield a nearly scale-invariant scalar spectrum (n s ≈ 0.96-0.97) consistent with observations, they display a hierarchy in their predicted tensor amplitudes, with the Woods-Saxon and MHI models producing the most suppressed signals (r ~ 10 -4 ) and the KKLTI model offering a tunable range up to r ~ 10 -3 . The analysis underscores how the Rastall parameter η and the Rainbow parameter ∑ 0 serve as critical tuning parameters, enabling each model to align with current the CMB bound while highlighting the differential flexibility of the Rastall-Rainbow framework in accommodating different inflationary potentials.
Vitohekpon et al. (2026) studied this question.