We present a flat (K = 0) cosmological model, described by a perfect fluid with the "constants" G, c and Λ varying with cosmological time t. We introduce Planck´s "constant" in the field equations through the equation of state for the energy density of radiation. We then determine the behaviour of the "constants" by using the zero divergence of the second member of the modified Einstein´s field equations i.e. div(

Abstract. It is shown that the usual choice of units obtained by taking G = c = ђ = 1, giving the Planck‚s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ђ. We note that the choice of ђ = 1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ђ ≈ 1/10 122 , while the choice of ђ = 1 corresponds to the cosmological scale. This is due to the scale factor of 10 61 that converts the Planck scale to the cosmological scale. By choosing the ratio G/c 3 = constant = 1, which includes the choice G = c = 1, and the momentum conservation mc = constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c 2 = r g , the gravitational radius of m, is constant. For a quantum black hole we prove that ђ ≈ r g 2 ≈ (mc) 2 . We also prove that the product Λђ is a general constant of order one, for any scale. The cosmological scale implies Λ ≈ ђ ≈ 1, while the Planck scale gives Λ ≈ 1/ђ ≈ 10 122 . This explains the Λ problem. We get two scales: the cosmological quantum black hole (QBH), size  10 28 cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size  10 -13 cm, as well as the Planck‚ scale, size  10 -33 cm.

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's constant that "absorbs" the well known large number 10 120 . With this new Planck's constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zel'dovich formula, for the cosmological constant , is equivalent to the Weinberg's 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's principle). The usual cosmological 's 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 10 61 converts 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 a(t) ≈ const · t. This constant is just the speed of light today. Then the Hubble parameter is exactly H = a(t) /a(t) = 1/t.

The fine structure constant α includes the speed of light as given by α = e 2 4πε 0 c . It is shown here that, following a T Hεµ formalism, interpreting the permittivity ǫ0 and permeabiliy µ0 of free space under Lorentz local and position invariance, this is not the case. The result is a new expression as α = e 2 4π in a new system of units for the charge that preserves local and position invariance. Hence, the speed of light does not explicitly enter in the constitution of the fine structure constant. The new expressions for the Maxwell's equations are derived and some cosmological implications discussed.La constant de la structure fine insére aussi la vitesse de la lumière en accord avec la formula α = e 2 4πε 0 c . On démontre avec ce travail que, suivant le formulisme T Hεµ et interprétant la permitivité ε0 et la pérmeabilité µ0 du vide selon l'invariant de Lorentz local et de position, cette formula n'est pas l'adéquate. La nouvelle expression es α = e 2 4π . dans un système d'unités neuf pour la chargeélectrique, système qui préserve l'invariant local et de position. Par conséquent, la vitesse de la lumière ne rentre pas dans la constitution du constant de la structure fine. On deduit les nouvelles expressions deséquations de Maxwell et on débat certaines inplications cosmologiques.

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