Early-Universe-Physics Independent and Uncalibrated Cosmic Standards: Constraint on $\Omega_{\rm{m}}$ and Implications for the Hubble Tension

To further shed light on whether pre-recombination models can resolve the Hubble tension, we explore constraints on the cosmic background evolution that are insensitive to early-universe physics. The analysis of the cosmic microwave background (CMB) anisotropy has been thought to highly rely on early-universe physics. However, we show that the difference between the sound horizon at recombination and that at the end of the drag epoch is small and insensitive to early-universe physics. This allows us to link the absolute sizes of the two horizons and treat them as free parameters. Jointly, the CMB peak angular size, Baryon Acoustic Oscillations (BAO), and Type Ia supernovae can be used as "early-universe-physics independent and uncalibrated cosmic standards", which measure the cosmic history from recombination to today. They can set strong and robust constraints on the post-recombination cosmic background, especially the matter density parameter with $\Omega_{\rm{m}}=0.302\pm0.008$ ($68\%$ C.L.). When combined with other non-local observations that are independent of or insensitive to early-universe physics, we obtain several constraints on $H_0$ that are currently more consistent with the Planck 2018 result than the local measurement results such as those based on Cepheids. These results suggest a tension between the post-recombination, but non-local, observations and the local measurements. This tension cannot be resolved by modifying the pre-recombination early universe physics.