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

Abstract: Cosmological measurements have revealed tensions within the standard $\Lambda$CDM model, notably discrepancies in the Hubble constant and $S_8$ parameter. Additionally, recent observations suggested evidence of a possible non-flat spatial curvature and an anomalous CMB lensing amplitude that beyond the $\Lambda$CDM framework. In this study, we explore whether introducing a variation in the electron mass $m_e$, allowing non-zero spatial curvature $\Omega_K$, and a free lensing amplitude $A_{\rm lens}$ can resolve these persistent tensions. Without relying on any local Universe measurements, we obtain $$H_0 = 69.61^{{+0.60}_{-0.55}} \rm \, km \, s^{-1} \, Mpc<sup>{-1}$$ and $S_8= 0.808\pm0.012$, with $\Delta m_e / m_e = 0.0109<sup>{+0.0066}_{-0.0062}$ and $A_{\rm lens} = 1.030<sup>{+0.039}_{-0.037}$, both of which exceed the $\Lambda$CDM expectations. We find no indication of spatial curvature deviating from flatness, even when including the Cosmic Chronometers and SNe Ia samples. Our results point to a promising direction for cosmological models to reconcile these discrepancies, although more precise data from future experiments will be necessary to clarify these modifications.