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We propose an analytical parametrization of the comoving distance and Hubbleparameter to study the cosmic expansion history beyond the vanilla $\Lambda$CDMmodel. The parametrization is generalized enough to include the contribution ofspatial curvature and to capture the higher redshift behaviors. With thisparameterization, we study the late time cosmic behavior and put constraints onthe cosmological parameters like present values of Hubble parameter ($H_{0}$),matter energy density parameter ($\Omega_{m0}$), spatial curvature energydensity parameter ($\Omega_{k0}$) and baryonic matter energy density parameter($\Omega_{b0}$) using different combinations data like CMB (Cosmic microwavebackground), BAO (baryon acoustic oscillation), and SN (Pantheon sample fortype Ia supernovae). We also rigorously study the Hubble tension in theframework of late time modification from the standard $\Lambda$CDM model. Wefind that the late time modification of the cosmic expansion can solve theHubble tension between CMB $\&$ SHOES (local distance ladder observation for$H_{0}$), between CMB+BAO $\&$ SHOES and between CMB+SN $\&$ SHOES, but thelate time modification can not solve the Hubble tension between CMB+BAO+SN andSHOES. That means CMB, BAO, and SN data combined put strong enough constraintson $H_{0}$ (even with varying $\Omega_{k0}$) and on other backgroundcosmological parameters so that the addition of $H_{0}$ prior from SHOES (orfrom similar other local distance observations) can not significantly pull the$H_{0}$ value towards the corresponding SHOES value.

Cosmic expansion parametrization: Implication for curvature and $\text{H}_{0}$ tension