Cooling-heating properties of the FRW universe in gravity with a generalized conformal scalar field

In this paper, within the framework of modified gravity involving a conformal scalar field, we investigate the Joule-Thomson expansion of the Friedmann-Robertson-Walker (FRW) universe to identify cooling and heating regions. We observe a divergence in the Joule-Thomson coefficient (μ), precisely at the apparent horizon ($R_A=\sqrt{-2\alpha }$) of the FRW universe, under conditions of negative gravitational coupling ($\alpha <0$), which aligns with a thermodynamic singularity. Furthermore, we determine the inversion temperature and pressure for the FRW universe, and elucidate the salient features of inversion and isenthalpic curves in the temperature-pressure (T-P) plane. We compare these findings with results obtained under Einstein gravity, discussing the influence of the modification term on the cooling and heating properties of the FRW universe. This work presents insights into the formation of cooling and heating regions within the FRW universe, contributing to a deeper understanding of the physical mechanisms behind cosmic expansion history.