Abstract
We present a cosmological model that incorporates a minimally coupled canonical scalar field, dark energy, and dark matter components of the cosmos within the context of general relativity (GR) based gravity. Using the first integral method, we solve the homogeneous scalar field equation with the Higgs potential and obtain some new analytical solutions for the scalar field \(\phi\) . These solutions are effective in explaining the Universe’s late-time acceleration phase. We use the \(\chi^{2}\) -minimization technique to compare our theoretical findings with a variety of observational data in order to evaluate the validity of this theoretical model. We make use of the observational data from three compilations of the Type Ia supernovae (SN Ia) dataset: the Union 2.1 compilation, the joint light-curve analysis (JLA), and the Pantheon sample. We calculate the current values of some significant cosmological parameters, such as the present values of the Hubble parameter ( \((H_{0})\) and the deceleration parameter ( \((q_{0})\) ), and these values are in good agreement with the most recent observational evidence. As a function of redshift \(z\) , we also look at the evolution of the Equation of State parameters ( \(w_{\textrm{DE}}(z)\) and \(w_{\phi}(z)\) ), the density parameters, the potential ( \(V(z)\) ), and the deceleration parameter ( \(q(z)\) ).
