Hello, I'm interested in physics and especially cosmology at the moment - and it seems that the mainstream cosmological model should be questioned.

Concordance cosmology seems to have many flaws, it requires inflation, there is the unexplained dark energy and the Hubble tension.

A solution is to change the redshift scale-factor relation from $a=\frac{1}{1+z}$ to $a=\frac{1}{\sqrt{1+z}}$ for reasons here: Cosmology - an expansion of all length scales

This leads to an apparently static universe, but with a redshift and a predicted matter density $\Omega_m$ of between 0.25 and 0.33 as described in the link above - and a cosmological constant of zero.

General Relativity and the Big Bang model seem correct.

To also incorporate the Big Bang model a mechanism is required that allows regions of collapsing matter to 'bounce'. The mechanism seems likely to be a reduction in the strength of gravity for dense regions of matter, or a way whereby General Relativity allows negative pressure to reduce the active gravitational mass sufficiently to allow large outflows of matter from Active Galactic Nuclei.

In this way the universe could be static, but in dynamic equilibrium - and with a redshift.

A solution to Einstein's equations for this model was discussed here Is there a valid solution to Einstein's equations for this cosmological model?

and the full model, including a resolution of the Hubble tension is here https://vixra.org/pdf/2006.0209v2.pdf