Exploring Modified Gravity: Constraints on the Μ and Σ Parametrization with WMAP, ACT, and SPT

The cosmic acceleration problem remains one of the most significantchallenges in cosmology. One of the proposed solutions to this problem is themodification of gravity on large scales. In this paper, we explore thewell-known $\mu$-$\Sigma$ parametrization scenarios and confront them withobservational data, including the cosmic microwave background (CMB) radiationfrom the Wilkinson Microwave Anisotropy Probe (WMAP), Atacama CosmologyTelescope (ACT), and South Pole Telescope (SPT), as well as large-scalestructure data from the Sloan Digital Sky Survey (SDSS: BAO+RSD) and PantheonSupernovae (SN) catalog. We employ a Bayesian framework to constrain the modelparameters and discuss the implications of our results on the viability ofmodified gravity theories. Our analysis reveals the strengths and limitationsof the $\mu$-$\Sigma$ parametrization and provides valuable insights into thenature of gravity on cosmological scales. From the joint analysis of the ACT +WMAP + SDSS + SN, we find $\mu_0 -1 = 0.02 \pm 0.19$ and $\Sigma_0 -1 = 0.021\pm 0.068$ at 68% CL. In light of the SPT + WMAP + SDSS + SN, we find $\mu_0 -1= 0.07 \pm 0.18$ and $\Sigma_0 -1 = -0.009^{+0.078}_{-0.11}$ at 68% CL. In allthe analyses carried out, we do not find any deviations from the theory ofgeneral relativity. Our results represent an observational update on thewell-known $\mu$-$\Sigma$ parameterization in view of current CMB data,independent and competitive with the constraints obtained with the Planck data.