The Hubble constant problem
This parameter measured by low z ( z<1) astrophysical methods (SN1A, for instance) gives a value around 74km/s/ Mpc, but when measured by high z (z >1000) , (Planck) method, we get a value around 67 km/s/Mpc.
Per the accuracy claimed for the experiences, these two values are not compatible.
DESI provides a breaking new information
But, whether the cosmological constant is no longer constant, i.e weakening as pointed out by several experiences (DESI) , then the result of the its value, computed by using the angular distance DA, depending on H0, resulting from the position of the first peak in the RFC, 2 D Fourier transform of the CMB, should increase from 67 km/s/Mpc up to the targeted 74km/s/Mpc, solving then the discrepancy.
Obviously, the mathematical law of its function of z and its physical nature are to be determined.
Per dimensional arguments, as the dimension of the cosmological constant is [L]-2 , and associating L to the size of the universe at the scale of the universe this would induce a law such L(z) = L0(1+z)-2 which will provide a value of about 77.5 km/s/Mpc (in place of 67.27km/s/Mpc) , for z = 1100, higher (about 5%) than the value (74 km/s/Mpc) of the SN1A for z < 1.
This is not a physical example and is just used to show the sensibility of such hypothesis.
Obviously, this would imply to modify the density parameters « omega » for fitting the experimental data at different value of z, this modifying the standard cosmological model.
Let us point out that the weakening of the cosmological constant would change the destiny of the universe, the big rip would likely no longer occur!