ΛCDM is alive and well

Despite its successes, the $\Lambda$CDM model faces several tensions with recent cosmological data and their increased accuracy. The mismatch between the values of the Hubble constant $H_0$ obtained from {some} direct distance ladder measurements and from the cosmic microwave background (CMB) is the most statistically significant, but the amplitude of the matter fluctuations is also regarded as a serious concern, leading to the investigation of a plethora of {alternative} models. Here, we examine the situation from a different perspective. We first show that the combination of several recent measurements from local probes leads to a tight constraint on the present-day matter density $\Omega_m$ as well as on the amplitude of the matter fluctuations, both acceptably consistent with the values inferred from the CMB. Secondly, we address the Hubble tension by assuming that some determinations of the value of $H_0$ are possibly biased. We treat such a bias as a nuisance parameter within $\Lambda$CDM and we examine such ``$\Lambda$CDM$+$ $H_0$ bias'' models on the same statistical grounds as alternative cosmological models. A bias in Planck or in SH0ES produces similar improvements. However we show that a bias in the Cepheids calibration produces improvements in terms of $\Delta AIC$ that supersede existing extended models proposed up to now. In a third step, we show that the value of $\Omega_m$ we obtained from our RSD, Pantheon+ and 3×2pt from DES, combined with SH0ES determination of $H_0$, leads to a precise determination of the density parameter of the Universe $\omega_m = 0.1753 \pm 0.0069$. This measurement provides an additional low-redshift test for cosmological models by comparing it to the preferred value derived from the CMB. From this test, most $\Lambda$CDM extensions seem to be confronted with a new tension as many of them cluster around $\omega_m = 0.14$, while there is no tension with a local $H_0 \sim 67 $ km/s/Mpc. We conclude that a standard $\Lambda$CDM model with an unknown bias in the Cepheids distance calibration represents a model that reaches a remarkable agreement, statistically better than previously proposed extensions without bias for which such a comparison can be performed.