Expansion Lensing (I) -- A new paradigm for cosmological luminosity-angular distances relation

The Einstein's General Relativity (GR) theory and the Friedmann-Lemaitre-Robertson-Walker (FLRW) metrics define the main equations that rule the history and future of the Universe. The Standard Model for cosmology collects this knowledge along with some other elements as cosmological distances. The link between the theory and observations is performed through some basic cosmological distances definitions as transverse comoving distance $D_M$, luminosity distance $D_L$, angular diameter distance $D_A$ and its relation $D_L=D_A(1+z)^2$. In this paper, Expansion Lensing (EL) is presented. EL is a novel paradigm revealing a new relationship between $D_L$ and $D_A$ in an expanding universe given by $D_L=D_A(1+z)$. EL demonstrates the inverse square law within the FLRW geometry, i.e., the equivalence between transversal comoving distance and luminosity distance. On the other hand, a new surface brightness-luminosity relation -- different from the one proposed by Tolman -- is derived from Cosmic Microwave Background (CMB) equations, providing an independent derivation of the new paradigm. As a consequence, previous cosmology methods and results entrusting on luminosity as observational data must be reviewed. The expansion rate and the relative densities of the dark components of the Universe, as dark matter}and dark energy, should be revised within the new paradigm.Comment: Includes a new section 3.4. Expansion Lensing deduced from surface brightness reasonin