A disformally coupled quintessence mimicking the ΛCDM background - Dusoye, Avishek (Department of Mathematics and Applied Mathematics, 2023)
Although the currently-accepted Concordance model of the Universe has been very successful observationally, it cannot resolve two main issues. Firstly, it cannot untangle the unknown nature of the cosmological constant in the Einstein Field Equations, which is responsible for the accelerated cosmological expansion. Secondly, it cannot explain the σ8 tension, which occurs because the constraints upon galactic clustering by the Cosmic Microwave Background Planck experiments diverge from the large-scale measurement by the Dark Energy Survey. As an alternative to the cosmological constant, this thesis will be using a scalar field, namely the quintessence. Our studied cosmological model assumes that the quintessence is coupled with a generic fluid. It also assumes a theory of gravity with two geometries. The gravitational geometry describes the curvature of space-time while the physical geometry describes the propagation of matter fields. The conformal transformation, which relates the gravitational metric and the physical metric, is extended here to a disformal transformation. In this thesis, the disformally coupled quintessence model mimics the expansion history of the Concordance model, in order to reproduce its observational success and yet have additional degrees of freedom to attempt to address those two issues. Using this approach, the quintessential potential is not specified. The dynamical system for our model is analysed using phase portraits for various studied scenarios. We investigate the expansion history of the DCQ model, where the quintessence couples disformally with dark matter (Scenario I). Our investigation confirms that the quintessential mass influences the disformal characteristics of the dynamical system. Furthermore, the evolution of the density perturbations for the disformally coupled dark matter is reviewed. A disformal effect due to the quintessential mass is seen in the growth rate of the cosmological structures on large scales. The disformal parameter renders no appreciable effect on the evolution of total matter perturbation. A Bayesian analysis of the relevant parameters for the perturbative model (i.e., conformal parameter and quintessential mass) is then carried out using the Redshift Space Distortion data to constrain the best-fit parameters, which might elucidate the σ8 tension. The best fit set of parameters indicates that the data prefers the model to behave conformally.