Number counts against K-corrections

Having based on the analysis of Pietronero and collaborators the galaxy number counts can be considered as an evidence of that the geometry of the universe is euclidean and that the K-corrections are absent. In such a universe measuring the cosmological redshift of the object and measuring the flux from the object are inconsistent. It is considered the model of the universe which describes the above properties. Authors of [1],[2] claimed that galaxies have a fractal distribution with constant D ≈ 2 up to the deepest scales probed until now 1000 h Mpc and may be even more. They showed that modification of the euclidean geometry and the K-corrections are not very relevant in the range of the present data. The use of K-corrections leads to the unstable behaviour of the number counts, with fractal dimension D increasing systematically to substantially larger values as a function of the depth of the volume limited sample. Quantitatively this behaviour can be explained as the effect of K-corrections applied to an underlying galaxy distribution with fractal dimension D ≈ 2. The use of the FRW geometry instead of the euclidean geometry is equivalent to an effective K-correction. So similar to the use of Kcorrections the use of the FRW geometry leads to the unstable behaviour of the number counts as a function of depth. The number counts can be considered as an evidence of that the geometry of the universe is euclidean rather than FRW and that the K-corrections are spurious. Let us study the universe with euclidean geometry. It should be noted that here euclidean geometry is conceived as a real background of the universe not as an approximation of the FRW geometry. In the euclidean geometry, the radial distance r and the angular diameter distance rθ are the same and are given by r = rθ = c H0 z 1 + z . (1) The luminosity distance is given by rL = r(1 + z) = rθ(1 + z) = c H0 z. (2) From this it follows that the intrinsic luminosity of the object L and the observed flux F are related as F ∝ L r L ∝ L r(1 + z) ∝ L r θ (1 + z) . (3) In the case of FRW geometry, the intrinsic luminosity of the object L and the observed flux F are related as F ∝ L r L ∝ L r θ (1 + z) . (4)