From A-CDM to extended models: Via equation of state parametrization in f(R) gravity

초록

In this work, we reconstruct the gravitational action f(R) corresponding to various cosmological epochs within the framework of modified gravity. Utilizing the field equations of f(R) gravity, we develop analytical expressions for the gravitational Lagrangian under different equation-of-state (EoS) scenarios, including dust (w = 0), radiation (w = 1/3), stiff fluid (w = 1), curvature-like matter (w = - 1/3), and dark energy (w = -1). The theoretical formulations are calibrated using two independent datasets: the 55-point Observational Hubble Data (OHD) and the 1048-point Pantheon Supernovae Type Ia (SN Ia) compilation, leading to precise constraints on the cosmological parameters H-0 and Omega(m). Our reconstructed f(R) functions reveal distinct redshift-dependent behaviours corresponding to each EoS, with the stiff fluid case exhibiting a particularly steep increase-reaching magnitudes on the order of 1010-and dominant for z >= 0, thus indicating its significance during the early Universe. In contrast, the w = -1 scenario mimics the late-time acceleration consistent with the ACDM model but differs notably in amplitude. Our results demonstrate the capacity of f(R) models to replicate key features of cosmic expansion, including the transition from deceleration to acceleration, and suggest a geometric origin for dark energy effects, potentially obviating the need for additional scalar fields or exotic matter. Furthermore, all reconstructed models satisfy the standard viability conditions (f '(R) > 0, f ''(R) > 0) and naturally recover the Hu-Sawicki limit at low curvature and the Starobinsky-like R2 behaviour at high curvature, reinforcing their theoretical consistency across epochs.

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