Constraining dark energy cosmologies with spatial curvature using Supernovae JWST forecasting

Recent cosmological tensions, in particular, to infer the local value of the Hubble constant $H_0$, have developed new independent techniques to constrain cosmological parameters in several cosmologies. Moreover, even when the concordance Cosmological Constant Cold Dark Matter ($\Lambda$CDM) model has been well constrained with local observables, its physics has shown deviations from a flat background. Therefore, to explore a possible deviation from a flat $\Lambda$CDM model that could explain the $H_0$ value in tension with other techniques, in this paper we study new cosmological constraints in spatial curvature dark energy models. Additionally, to standard current Supernovae Type Ia (SNIa) catalogs, we extend the empirical distance ladder method through an SNIa sample using the capabilities of the James Webb Space Telescope (JWST) to forecast SNIa up to $z \sim 6$, with information on the star formation rates at high redshift. Furthermore, we found that our constraints provide an improvement in the statistics associated with $\Omega_{m}$ when combining SNIa Pantheon and SNIa Pantheon+ catalogs with JW forecasting data.