Warm inflation in hybrid metric-Palatini gravity under standard and irreversible thermodynamical approach

Abstract

Abstract The idea of hybrid metric-Palatini $$f({\mathcal {X}})$$ f ( X ) gravity (HMPG) is a blend of Einstein Hilbert (EH) action having non-linear function f(R) and linear scalar curvature R by Palatini gravity. The goal of this paper is to investigate the warm inflationary model (WIM) via standard and irreversible thermodynamical approach in $$f({\mathcal {X}})$$ f ( X ) gravity. We start our work by obtaining the field equations (FEs) for HMPG and then investigate the cosmic inflation in $$f({\mathcal {X}})$$ f ( X ) theory of gravity by looking at cosmic parameters such as slow-roll parameters, spectral index $$(n_s)$$ ( n s ) , running of spectral index $$(\alpha _s)$$ ( α s ) and tensor-to-scalar ratio (r). Next, the early universe is considered as an open system. The thermodynamics and dynamical equations in $$f({\mathcal {X}})$$ f ( X ) gravity are applied to interacting cosmic fluid, which leads us to adapt the basic formalism of WIM. This analysis is done using Higgs Potential (HP). Numerical results of the thermodynamical equations such as scale factor (a(t)), scalar-field energy density $$(\rho _\varphi )$$ ( ρ φ ) and radiation energy density $$(\rho _\gamma )$$ ( ρ γ ) , number of scalar-field particles $$(n_\varphi )$$ ( n φ ) and temperature $$({\mathcal {T}})$$ ( T ) are derived and presented graphically using slow-roll approach and defining several dimensionless variables. From obtained results, we calculate cosmic parameters. In the end, we constraint the model parameters, and compare our calculated results to the Planck-2018 data.