A comprehensive data-driven odyssey to explore the equation of state of dark energy

Abstract: For the first time, we reconstruct the dark energy equation of the state parameter $w$ from the combination of background and perturbation observations, specifically combining the Hubble parameter data from cosmic chronometer observations and the logarithmic growth rate data from the growth rate observations. We do this analysis using posterior Gaussian process regression without considering any specific cosmological model or parametrization. However there are three main assumptions: (I) a flat Friedmann-Lema^itre-Robertson-Walker (FLRW) metric is considered for the cosmological background, (II) there is no interaction between dark energy and matter sectors, and (III) for the growth of inhomogeneity, sub-Hubble approximation and linear perturbations are considered. This study is unique in the sense that the reconstruction of $w$ is independent of any derived parameters such as the present values of the matter-energy density parameter and Hubble parameter. From the reconstruction, we look at how the dark energy equation of state evolves between redshifts 0 and 1.5, finding a slight hint of dynamical behavior in dark energy. However, the evidence is not significant. We also find a leaning towards non-phantom behavior over phantom behavior. We observe that the $\Lambda$CDM model ($w=-1$) nearly touches the lower boundary of the 1$\sigma$ confidence region in the redshift range $0.6 \lesssim z \lesssim 0.85$. However, it comfortably resides within the 2$\sigma$ confidence region in the whole redshift range under investigation, $0\leq z \leq 1.5$. Consequently, the non-parametric, model-independent reconstruction of dark energy provides no compelling evidence to deviate from the $\Lambda$CDM model when considering cosmic chronometer and growth rate observations.