Lensing amplitude anomaly and varying electron mass alleviate the Hubble and $S_8$ tensions

TL;DR

The paper investigates whether incorporating a time-varying electron mass Δm_e, non-zero spatial curvature Ω_K, and a free CMB lensing amplitude A_lens can alleviate the H0 and S8 tensions. It performs Bayesian analyses with CAMB/HYREC-2/Cobaya and nessai on combinations of Planck and ACT CMB data (with PR3 or PR4 likelihoods), CMB lensing, DESI DR2 BAO, CC, and SN data, exploring degeneracies and recombination-geometry implications. The results show that Planck PR3 analyses favor modest shifts in m_e and a mild lensing anomaly, yielding H0 ≈ 69.6 and S8 ≈ 0.808, while Planck PR4 data push m_e negative with persistent A_lens excess, alleviating only the S8 tension; including late-time probes shifts toward H0 ≈ 70.5 and S8 ≈ 0.813, with limited evidence for curvature. Overall, the extended model can partly reconcile tensions but does not decisively supersede ΛCDM, highlighting the need for future high-precision data from experiments like CMB-S4, the Simons Observatory, Euclid, and LSST to clarify these modifications.

Abstract

Cosmological measurements have revealed tensions within the standard $Λ$CDM model, notably discrepancies in the Hubble constant and $S_8$ parameter. A modified recombination scenario involving a time-varying electron mass has been proposed as a feasible solution to the Hubble tension without exacerbating the $S_8$ tension. Recent observations have further revealed other potential deviations from the $Λ$CDM framework, such as non-flat spatial curvature and an anomalous CMB lensing amplitude. In this study, we explore whether introducing a variation in the electron mass $m_e$, allowing non-zero spatial curvature $Ω_K$, and a free lensing amplitude $A_{\rm lens}$ can resolve these persistent tensions. Using the Planck Public Release (PR) 3 and ACT power spectra, Planck PR4 and ACT lensing maps, together with BAO measurements from DESI DR2, we obtain $H_0 = 69.61^{+0.60}_{-0.55} \rm \, km \, s^{-1} \, Mpc^{-1}$ and $S_8= 0.808\pm0.012$, with $Δm_e / m_e = 0.0109^{+0.0068}_{-0.0066}$ and $A_{\rm lens} = 1.030^{+0.039}_{-0.037}$, both exceeding the $Λ$CDM expectations. We find no indication of spatial curvature deviating from flatness, even when including the Cosmic Chronometers and SNe Ia samples. However, when adopting the latest Planck power spectra likelihoods, NPIPE and HiLLiPoP, we obtain lower electron masses with $Δm_e / m_e = -0.0063^{+0.0095}_{-0.0099}$ and $-0.0095^{+0.0078}_{-0.0079}$, relieving the $S_8$ tension only. The lensing amplitude remains anomalously high, with $A_{\rm lens} = 1.053^{+0.042}_{-0.040}$ and $1.075^{+0.044}_{-0.043}$. Our results point to a promising direction for cosmological models to reconcile the aforementioned discrepancies, although more precise data from future experiments will be necessary to clarify the aforementioned modifications.

Figures (13)

• Figure 1: Ionization history for different values of $\Delta m_e/m_e$. The left panel shows the evolution of $X_e$, while the right panel shows relative deviations with respect to the standard case. All curves are obtained using HYREC-2.
• Figure 2: The CMB temperature power spectra and their variations for different values of $m_e$, $\Omega_K$, and $A_{\rm lens}$, calculated by the cosmological Boltzmann code CAMB with the recombination code HYREC-2.
• Figure 3: Degeneracy between $\Omega_K$ and $A_{\rm lens}$. The blue region shows the posterior result from the combination of the TT/TE/EE power spectra (Planck PR3 + ACT, NPIPE, and HiLLiPoP) and the lensing maps (Planck PR4 + ACT DR6). The pink region further includes BAO measurements from DESI DR2. The dashed grey lines represent the expectations of $\Lambda$CDM model. All contours show 68% and 95% credible intervals.
• Figure 4: Posterior distributions of $\Omega_K$ and $H_0$ in different extended models. In the left panel, he combined data sets include the TT/TE/EE power spectra (Planck and ACT), the lensing maps (Planck PR4 + ACT DR6), and the BAO measurements (DESI DR2). $\Omega_K+A_{\rm lens}+ \Delta m_e$, $\Omega_K+ \Delta m_e$, and $\Omega_K+A_{\rm lens}$ are shown in blue, pink, and purple regions, respectively. The right panel shows the results using the lensing maps, BAO measurements and the PR4 NPIPE or HiLLiPoP likelihoods. The results of the three scenarios The dashed grey line indicates the expectation of $\Lambda$CDM model. The y-axis ranges differ between these two panels and \ref{['fig:omega_k_A']}
• Figure 5: Posterior distributions of $H_0$, $z_{\rm d}$, $r_{\rm d}$, $z_*$, and $r_*$ in different extended models. The definitions of the color regions are same with those in the left panel of \ref{['fig:omega_k']}. All contours show 68% and 95% credible intervals.