A hybrid method for reconstruction of the equation of state of dark energy and its application to Pantheon+SH0ES data
Cosmology aims to understand the physical properties of our Universe on its largest scales. One such feature is the expansion of the Universe, which currently seems to be dominated by a phenomenon referred to as dark energy. The physical nature and properties of dark energy are one of the main topics of investigation of modern cosmology. Observational cosmology aims to reconstruct the evolution and the equation of state of dark energy, while theoretical cosmology aims to provide methods for such reconstructions and models explaining the nature of dark energy. If the equation of state, defined as the ratio of pressure to density $w = p/\rho$, deviates from $-1$, i.e. $w\ne-1$, then this would imply the existence of some sort of dynamical process behind dark energy. Most investigations assume a specific parametric form of $w$, eg. $w(z) = w_{0} + w_a z/(1+z)$, with $z$ being redshift and $w_0$ and $w_a$ being constants. The analysis of the data is then reduced to fitting the model to the data. In this work, we take a different approach. Instead of imposing a predefined parametric form for $w(z)$, we reconstruct the equation of state indirectly from the dimensionless comoving distance $D(z)$ and its derivatives. This avoids assuming a specific physical parametrisation of dark energy, such as the CPL form, but still requires adopting functional representations for the distance--redshift relation itself. The method should therefore be regarded as a hybrid or semi-parametric reconstruction approach: the parametrisation is shifted from the equation of state to the observable distance function. Finally we apply the method to the Pantheon+ SH0ES data. The results are consistent with dark energy being the cosmological constant, i.e. $w = -1$. Future surveys such as LSST will provide more data and narrow down the uncertainty. This in turn will yield tighter constraints on dark energy.