Artificial contradiction between cosmology and particle physics: the Λ problem

Abstract

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.

On the Dilaton Stabilization by Matter

“…At this point it might be helpful to underline that given that the above recurrent picture is realized in Nature, supports the interest of the ideas argued in Ref. (37), about the connections between the cosmological constant and the quantum behavior of matter in such internal universes. An important outcome emerged in the examination of the problem, is that the coexistence of the scalar field as described by the EKG equations including also the dust energy momentum tensor does not allow the existence of static solutions, at least in centrally symmetric configurations, in the absence of Dilaton -matter interaction (26).…”

Universality of the self gravitational potential energy of any fundamental particle

“…This is well in the range of observations [3]. The Hubble radius for today is defined as c/H(t 0 ) ≈ c t 0 and taking this radius as the present reference for the cosmological scale factor, i.e., c t 0 ≈ R(1) we get from (6), (7) and (8) to first order…”

“…It may be linked to the entropy of the universe (with Boltzmann constant k = 1). It is also the order of magnitude of the discrepancy between the values of the cosmological constant Λ, as derived from cosmological information, and from the standard particle theory [7].…”

Non-expanding universe: a cosmological system of units

“…From the assumed (as an angular momentum) and observed constancy of the Planck´s constant ђ (radioactive decay times depend on the 7 th power of ђ, and no time variation in these times has been observed) and (4) one has to assume also that the electronic charge e is a true constant. We have shown elsewhere, Alfonso-Faus [6], that the Planck´s constant for the quantum world is of the order of 1/10 122 . We also showed that this constant is the square of the length of the scale, in a system of units that we adopt in part given by the equality G = c 3 .…”

“…If we take now as the cosmological unit of length the size of the universe ct ≈ 10 28 cm, the cosmological "quantum" of length, then Planck´s constant for the quantum world is the square of the ratio of ct to the Planck´s unit of length L = ct ≈ 10 28 cm = 1 ђ ≡ (ct) 2 c 3 /Gђ ≈ 1/10 122 (6) and from (1), (2) and (6) we get for the cosmological quantum of electrical charge Q ≈ 3.3 10 61 e = 1 (7) This is the same value as has been obtained elsewhere, Alfonso-Faus [7], where we have found equilibrium in the plasma state of the universe with charge (7) pushing outwards against the inward gravitational force. The Debye length of this plasma is a bit larger than the size L in (6). We see that the number of electronic charges in (7) is the same as the number of Planck´s units that could make up for the universe (with a dimensionless scale factor of ∼ 10 61 ).…”