Non-expanding interpretation of FLRW metric

It is commonly assumed that the expanding universe rest on general relativity through the Einstein’s field equations and the FLRW metric. In this talk, I will show that it also requires the definition of an external equation d_L=D_M(1+z) to relate the observable luminosity distance d_L to the comoving distance d_M. I will also show that the FLRW may represent a non-expanding universe as well by interpreting the comoving coordinates as luminosity (distance) ones. In such a universe, the observable luminosity distance is directly derived from FLRW metric and the redshift is still explained by the a(t) factor which would be interpreted as a time dilation factor rather than the radio of an expanding universe. This interpretation agrees with the non-expanding luminosity-angular distante relation d_L=d_A(1+z) we have obtained experimentally from SDSS DR15.