No-go guide for late-time solutions to the Hubble tension: Matter perturbations

The Hubble tension seems to be a crisis with $\sim 5\sigma$ discrepancy between the most recent local distance ladder measurement from type Ia supernovae calibrated by Cepheids and the global fitting constraint from the cosmic microwave background data. To narrow down the possible late-time solutions to the Hubble tension, we have used in a recent study [Phys. Rev. D 105, L021301 (2022)] an improved inverse distance ladder method calibrated by the absolute measurements of the Hubble expansion rate at high redshifts from the cosmic chronometer data, and found no appealing evidence for new physics at the late time beyond the $\mathrm{\Lambda }\mathrm{CDM}$ model characterized by a parametrization based on the cosmic age. In this paper, we further investigate the perspective of this improved inverse distance ladder method by including the late-time matter perturbation growth data. Independent of the dataset choices, model parametrizations, and diagnostic quantities ($S_8$ and $S_{12}$), the new physics at the late time beyond the $\mathrm{\Lambda }\mathrm{CDM}$ model is strongly disfavored so that the previous late-time no-go guide for the Hubble tension is further strengthened.

Figure 1

The comparison of various BAO length scales ($D_M$ in red, $D_V$ in blue, and $D_H$ in green) among the exact $\mathrm{\Lambda }\mathrm{CDM}$ model (solid), the Taylor expansions of $\mathrm{\Lambda }\mathrm{CDM}$ model in terms of the redshift $z$ (dash-dotted) and redshift $y\equiv 1-a=z/(1+z)$ (dotted), and the PAge presentation of $\mathrm{\Lambda }\mathrm{CDM}$ model (dash) with respect to the BAO data we use. The fiducial cosmology is assumed with ${\mathrm{\Omega }}_m=0.3156$, $H_0=67.27\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ from Planck 2018 [10].

Figure 2

The relative errors for various BAO length scales with $\mathrm{PAge}/\mathrm{MAPAge}$ representation for the $\mathrm{\Lambda }\mathrm{CDM}$ model with respect to the exact $\mathrm{\Lambda }\mathrm{CDM}$ model in the same fiducial cosmology as Fig. 1.

Figure 3

The comparison between the best-fit models from $\mathrm{\Lambda }\mathrm{CDM}$ (blue dashed curve), PAge (orange solid curve) and MAPAge (green dashed curve) with respect to the 2018 RSD dataset (top panel) and 2021 RSD dataset (bottom panel).

Figure 4

Model comparison from fitting the $\mathrm{\Lambda }\mathrm{CDM}$ (blue), PAge (orange), and MAPAge (green) models to the background IDL ($\mathrm{CC}+\mathrm{BAO}+\mathrm{SNe}$) data (top) and perturbative IDL data ($\mathrm{RSD}+\mathrm{CC}+\mathrm{BAO}+\mathrm{SNe}$) with inclusions of RSD 2018 (medium) and RSD 2021 (bottom) data.

Figure 5

Data comparison from fitting the background IDL without RSD data (blue) and the perturbative IDL data ($\mathrm{RSD}+\mathrm{CC}+\mathrm{BAO}+\mathrm{SNe}$) with inclusions of RSD 2018 (green) and RSD 2021 (orange) data to the $\mathrm{\Lambda }\mathrm{CDM}$ (top), PAge (medium), and MAPAge (bottom) models.