Modeling a holographic inflationary scenario in the framework of f(T,𝒯) gravity

In the framework of [Formula: see text] gravity, where T denotes the torsion scalar and [Formula: see text] signifies the energy–momentum tensor’s trace, our study explores the realm of holographic inflation. We employed a holographic potential, incorporating three widely recognized inflationary potentials in cosmological research. Our main objective was to determine the range of parameters that govern the interaction between geometry and matter, which plays a crucial role in describing inflationary phenomena in the universe. By calculating the slow-roll parameters, we were able to forecast critical cosmological quantities, including the scalar spectral index [Formula: see text], the tensor-to-scalar ratio r and the tensor spectral index [Formula: see text], all expressed in terms of the potential’s parameters. When comparing these findings with those derived in teleparallel gravity, which is equivalent to General Relativity (GR), we identified the significant impact of the parameter linking geometry and matter. This influence is thoroughly demonstrated through detailed results in various tables, highlighting its role in [Formula: see text] gravity. Our outcomes underscore the strength of the interaction between geometry and matter while showing considerable alignment with the PLANCK 2018 and WMAP data, thereby reinforcing the reliability and relevance of our conclusions.