Zel’dovich Λ and Weinberg’s relation: an explanation for the cosmological coincidences

Abstract

In 1937 Dirac proposed the large number hypothesis (LNH). The idea was to explain that these numbers were large because the Universe is old. A time variation of certain constants was assumed. So far, no experimental evidence has significantly supported this time variation. Here we present a simplified cosmological model. We propose a new cosmological system of units, including a cosmological Planck constant that absorbs the well known large number 10120. With this new Planck constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zeldovich formula, for the cosmological constant, is equivalent to the Weinberg relation. The immediate conclusion is that the speed of light c must be proportional to the Hubble parameter H, and therefore decrease with time. We find that the gravitational radius of the Universe and its size are one and the same constant (Mach principle). The usual cosmological omega parameters for mass, lambda and curvature turn out to be all constants of order one. The anthropic principle is not necessary in this theory. It is shown that a factor of 1061converts in this theory a Planck fluctuation (a quantum black hole) into a cosmological quantum black hole: the Universe today. General relativity and quantum mechanics give the same local solution of an expanding Universe with the law const. t. This constant is just the speed of light today. Then the Hubble parameter is exactly H = 1/t.