Cosmological Dynamics in f(R) Gravity Models through Cosmographic Energy Conditions

Abstract A proposed f ( R ) functional form’s constraints caused by energy conditions are presented. Raychaudhuri’s equation and the premise that gravity is attractive are both used to derive null and strong energy conditions for the proposed f ( R ) gravity model. Furthermore, the weak and dominant energy conditions are established by analysing the energy conditions induced by an effective energy-momentum tensor for the f ( R )-theory of gravity. The most recent estimates of the cosmographic parameters that mimic Chaplygin gas-type dark energy are used on the parameters of a pair of f ( R ) models as a tangible extension of the energy conditions to the Robertson-Walker universe. It is found that under the various values of the coupling parameters the proposed f ( R ) model satisfy null, weak and dominant energy conditions while strong energy conditions are breached. Further, constraining the coupling parameters as a result of energy conditions, our analysis shows that the proposed model accurately captures the observed cosmic acceleration, as indicated by key parameters such as the effective equation of state ( ω eff ), and the deceleration parameter ( q ). Through a geometric analysis of cosmographic parameters, we observe deviations of f ( R ) gravity from the ΛCDM model. We identify distinct evolutionary pathways that resemble characteristics of either quintessence or Chaplygin gas dark energy across various epochs, indicating a dynamic rate of cosmic acceleration. Our findings highlight the significant influences of coupling parameters and initial conditions on the cosmic evolution.