Cosmic expansion parametrization: Implication for curvature and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> tension
Bikash R. Dinda
Abstract
We propose an analytical parametrization of the comoving distance and Hubble parameter to study the cosmic expansion history beyond the vanilla $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. The parametrization is generalized enough to include the contribution of spatial curvature and to capture the higher redshift behaviors. With this parametrization, we study the late-time cosmic behavior and put constraints on the cosmological parameters like present values of Hubble parameter (${H}_{0}$), matter-energy density parameter (${\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}0}$), spatial curvature energy density parameter (${\mathrm{\ensuremath{\Omega}}}_{\mathrm{k}0}$), and baryonic matter-energy density parameter (${\mathrm{\ensuremath{\Omega}}}_{\mathrm{b}0}$) using different combinations data like CMB (cosmic microwave background), BAO (baryon acoustic oscillation), and SN (Pantheon sample for type Ia supernovae). We also rigorously study the Hubble tension in the framework of late time modification from the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. We find that the late time modification of the cosmic expansion can solve the Hubble tension between CMB and SHOES (local distance ladder observation for ${H}_{0}$), between $\mathrm{CMB}+\mathrm{BAO}$ and SHOES and between $\mathrm{CMB}+\mathrm{SN}$ and SHOES, but the late time modification cannot solve the Hubble tension between $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SN}$ and SHOES. That means CMB, BAO, and SN data combined put strong enough constraints on ${H}_{0}$ (even with varying ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{k}0}$) and on other background cosmological parameters so that the addition of ${H}_{0}$ prior from SHOES (or from similar other local distance observations) cannot significantly pull the ${H}_{0}$ value toward the corresponding SHOES value.