Study of f(T) Theory of Gravity in the Framework of Modified Holographic Ricci Dark Energy with Thermodynamical Aspects

This article explores the analysis of modified holographic Ricci dark energy (MHRDE) in the context of \(\varvec{f(T)}\) theory of gravity, with a focus on the validity of thermodynamics for homogenous and isotropic Friedmann-Robertson-Walker (FRW) universe by using hybrid expansion law (HEL) represented as \(\varvec{a(t)} \varvec{=} \varvec{e}^{\varvec{mt}} \varvec{t}^{\varvec{n}}\), where \(\varvec{m, n}\) are constants. The study investigates the dynamics of the accelerating universe across the established \(\varvec{f(T)}\) model, \(\varvec{f(T)} \varvec{=} \varvec{\xi }_{\varvec{1}} \varvec{T} \varvec{+} \varvec{\xi }_{\varvec{2}} \varvec{T}^{\varvec{\xi }_{\varvec{3}}} \varvec{\log } \varvec{T}\), where \(\varvec{\xi }_{\varvec{1}}\varvec{,} \varvec{\xi }_{\varvec{2}}\varvec{,} \varvec{\xi }_{\varvec{3}}\) are constants. The fundamental equations of thermodynamics features of the model have been deliberated. Additionally, the entropy density and temperature of the model are determined. We use the energy conditions in our solutions to identify a range of values for free parameters of the model, ensuring a stable and well-behaved scenario. Furthermore, a detailed examination of the physical and geometrical characteristics of the model has been conducted.