Conformally Interacting Dark Energy with Early and Late-Time Measurements

The conformal interacting dark energy (CIDE) model is investigated by introducing a scalar field representing dark energy (DE) coupled to dark matter (DM) via a conformal transformation, thereby yielding a class of scalar-tensor theories. The interaction term $Q$, that indicts the flow of energy between the dark sectors is proportional to the trace of the energy momentum tensor of the DM fluid, $T_{\mu \nu }^{\mathrm{D}\mathrm{M}}$, as $Q=\frac{C^{\mathrm{\prime }}(\phi )}{2C(\phi )}{g}^{\mu \nu }{T}_{\mu \nu }^{\mathrm{D}\mathrm{M}}$, where $C(\phi )$ is the conformal function of a scalar potential (coupling) field. We assume the power-law parametrization $C(\phi )\propto (1+\phi {)}^m$, with $m$ a coupling parameter, and determine the direction and magnitude of the energy flow between the DM and DE components. The dynamical nature of DE is modeled by the two conformal interacting scenarios, CIDE and $w$CIDE, with $w$ the DE equation of state parameter. To test the viability of each model, we constrain them using a combination of early- and late-time cosmological data, namely: CMB measurements from the South Pole Telescope, Planck 2018, and the Atacama Cosmology Telescope (DR6) ($\mathtt{\text{CMB}}\mathtt{\text{SPA}}$); BAO data from the Dark Energy Survey ($\mathtt{\text{DESI}}\mathtt{\text{DR2}}\mathtt{\text{BAO}}$); and Supernova Type Ia distance compilations ($\mathtt{\text{PantheonPlus,}}\mathtt{\text{PantheonPlus}}\mathtt{\text{+}}\mathtt{\text{SH0ES,}}\mathtt{\text{Union3}}$, and $\mathtt{\text{DES}}\mathtt{\text{Dovekie}}$). Parameter inference is performed with Monte Carlo Markov Chain ($\mathtt{\text{MCMC}}$) simulations using $\mathtt{\text{COBAYA}}$ and a modified $\mathtt{\text{CLASS}}$. Further statistical analysis using the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) is summarized to assess the viability of the model in comparison with the standard cosmological model, investigating the model’s potential to alleviate the $H_0$ and $S_8$ tensions.