Rainbow f(R) Inflation: de Sitter-Quintessence Phases
Year: 2025
Type: article
Abstract: In this study, we investigate the inflationary dynamics of Rainbow f ( R ) gravity characterized by f ( R ) ≃ αR n , with the rainbow deformation and . The effects of the rainbow parameter λ and the curvature exponent n on inflationary observables are analyzed under the Atacama Cosmology Telescope (ACT) constraint 0.9709 < n s < 0.9777. Numerical results reveal a clear correlation among n, λ , and the tensor-to-scalar ratio r , such that decreasing n corresponds to increasing λ , accompanied by a growth in r within observational limits. Negative values of λ (typically for n ≈ 3) yield a quasi–de Sitter inflationary phase with a nearly constant Hubble parameter and suppressed tensor modes, while positive λ (for n ≲ 2.2) drive a quintessence–like inflationary regime with enhanced expansion and a time-dependent curvature. Using power–law solutions a ( t )∝ t p , we relate the expansion exponent to the number of e -folds N ≃ 50–60. Small deviations between the matter and effective equations of state indicate a mild breaking of , suggesting the emergence of matter–like behavior within the quintessence–like inflationary field. At low curvature, we further show that a logarithmic Nojiri–Odintsov correction f ( R ) ≃ α ′ln ( R / μ 2 ) naturally dominates the dynamics, giving rise to a late–time quintessence phase ( for ) that asymptotically approaches a de Sitter attractor ( as ϵ 1 → 0 or ). Thus, the combined R n and logarithmic contributions provide a unified geometric framework in which early–time inflation and late–time cosmic acceleration naturally arise from different curvature regimes of Rainbow f ( R ) gravity, consistent with ACT observational data.
Source: Physics Letters B
Author: A.I. Keskin
Institution: Batman University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416939402