A promising idea to resolve the long standing Hubble tension is to postulate a new subdominant dark-energy-like component in the prerecombination Universe which is traditionally termed as the early dark energy (EDE). However, as shown in the Refs. [J. C. Hill et al., Early dark energy does not restore cosmological concordance, Phys. Rev. D 102, 043507 (2020), M. M. Ivanov et al.,Constraining early dark energy with large-scale structure, Phys. Rev. D 102, 103502 (2020).] the cosmic microwave background (CMB) and large-scale structure (LSS) data impose tight constraints on this proposal. Here, we revisit these strong bounds considering the Planck CMB temperature anisotropy data at large angular scales and the SPTPol polarization and lensing measurements. As advocated in [A. Chudaykin et al., Combined analysis of Planck and SPTPol data favors the early dark energy models, J. Cosmol. Astropart. Phys. 08 (2020) 013.] another paper, this combined data approach predicts the CMB lensing effect consistent with the $\mathrm{<ruby><rb>\Lambda </rb><rt>らむだ</rt></ruby>}\mathrm{CDM}$ expectation and allows one to efficiently probe both large and small angular scales. Combining Planck and SPTPol CMB data with the full-shape BOSS likelihood and information from photometric LSS surveys in the EDE analysis we found for the Hubble constant $H_0=69.79\pm 0.99\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and for the EDE fraction $f_{\mathrm{EDE}}<0.094(2\mathrm{<ruby><rb>\sigma </rb><rt>しぐま</rt></ruby>})$. These bounds obtained without including a local distance ladder measurement of $H_0$ (SH0ES) alleviate the Hubble tension to a $2.5\mathrm{<ruby><rb>\sigma </rb><rt>しぐま</rt></ruby>}$ level. Including further the SH0ES data we obtain $H_0=71.81\pm 1.19\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and $f_{\mathrm{EDE}}=0.088\pm 0.034$ in full accordance with SH0ES. We also found that a higher value of $H_0$ does not significantly deteriorate the fit to the LSS data. Overall, the EDE scenario is (though weakly) favored over $\mathrm{<ruby><rb>\Lambda </rb><rt>らむだ</rt></ruby>}\mathrm{CDM}$ even after accounting for unconstrained directions in the cosmological parameter space. We conclude that the large-scale Planck temperature and SPTPol polarization measurements along with LSS data do not rule out the EDE model as a resolution of the Hubble tension. This paper underlines the importance of the CMB lensing effect for robust constraints on the EDE scenario.

• Received 16 November 2020
• Accepted 26 January 2021

DOI:https://doi.org/10.1103/PhysRevD.103.043529