Constraining dark energy using the cross correlations of weak lensing with post-reionization probes of neutral hydrogen

Abstract

We investigate the prospects of detecting the cross correlation of CMBR weak-lensing convergence field with the large scale tracers of the underlying dark matter distribution in the post-reionization epoch. The cross-correlation is then used to make error projections for dark energy equation of state (EoS)for models with a time evolving dark energy. We study the cross-correlation angular power spectrum of the weak-lensing field with the Lyman-$\alpha$ forest and the redshifted HI 21 cm signal from the post reionization epoch. The angular power spectra is expressed as a line of sight average over the tomographic slices. We find that on using multiple $400$ hrs observation with an extended uGMRT like instrument or with a BOSS like survey with quasar (QSO) density of $16 {\rm deg}^{-2}$ the cross-correlation with weak-lensing convergence field covering half the sky can be detected at a very high SNR ($>20$). The cross-correlation of weak-lensing with Lyman-$\alpha$ forest allows the $1-\sigma$ errors on the dark energy EoS parameters for different parametrizations to be constrained at a level of precision comparable to combined Planck+SNIa+BAO+HST projections. The 21-cm weak-lensing cross-correlation is found to provide strong constraints on the present value of the dark energy EoS parameter at $4\%$ for the 7CPL model. The constraints on $w_a$ is comparable ($\sim 12\%$) for models other than the 7CPL model. We also find that the CPL parametrization may not be the best constrained parametrization for dark energy evolution. The cross-correlation of CMBR weak-lensing with the post-reionization probes of neutral hydrogen thus holds the potential to give us valuable understanding about the nature of evolving dark energy.