Cosmological Acceleration as a Consequence of Quantum de Sitter Symmetry

Abstract

Physicists usually understand that physics cannot (and should not) derive that c ≈ 3·10 8 m/s andh ≈ 1.054·10 −34 kg·m 2 /s. At the same time they usually believe that physics should derive the value of the cosmological constant Λ. We first prove that three parameters defining transitions from more general theories to less general ones are (c,h, R) where R is the parameter defining contraction from the de Sitter (dS) or anti-de Sitter (AdS) algebra to the Poincare algebra. The quantity R is fundamental to the same extent as c andh. In particular, a question why R is as is does not arise, and the answer is simply that R has its value because people want to measure distances in meters. The quantity Λ has a physical meaning only on classical level and equals Λ = ±3/R 2 for dS and AdS spaces, respectively. As a consequence of the fact that quantum dS and AdS symmetries are more general than Poincare symmetry, the cosmological constant problem does not arise, Λ is necessarily not zero and there is no need to involve dark energy for explaining the cosmological acceleration. In the case of those symmetries all physical quantities are dimensionless and no system of units is needed. In particular, the quantities (c,h, s), which are the basic quantities in the modern system of units, are not so fundamental as in relativistic quantum theory, time is not strongly continuous and description of the inflationary stage of the Universe by times (10 −36 s, 10 −32 s) has no physical meaning. Following our previous publications, we consider a system of two free bodies in dS invariant quantum mechanics and show that in semiclassical approximation the dS repulsion is the same as in General Relativity. This result is obtained without using geometry of dS space, metric and connection but simply as a consequence of quantum dS symmetry.

The Problem of Particle-Antiparticle in Particle Theory

“…However, as discussed in detail in Refs. [2,3,4], in quantum theory the concept of space-time background does not have a physical meaning. Although for constructing modern theories of elementary particles local Lagrangians are used, the goal of the theory is to construct the S-matrix in momentum space, and, when this construction has been accomplished, one can forget about space-time background.…”

“…A detailed discussion of the both contractions is described in a vast literature, in particular, in Refs. [2,3,4] where it has been proposed the following Definition: Let theory A contain a finite nonzero parameter and theory B be obtained from theory A in the formal limit when the parameter goes to zero or infinity. Suppose that, with any desired accuracy, theory A can reproduce any result of theory B by choosing a value of the parameter.…”

“…As proved in Refs. [2,3,4], dS and AdS symmetries are more general (fundamental) than Poincare symmetry. The latter is a special degenerate case of the former in the formal limit R → ∞.…”

“…Then, as proved in Refs. [2,3,4], classical theory is a special degenerate case of quantum one in the formal limit h → 0, and nonrelativistic theory (NT) is a special degenerate case of relativistic one (RT) in the formal limit c → ∞. In the literature the above facts are explained from physical considerations but, as shown in Refs.…”

“…In the literature the above facts are explained from physical considerations but, as shown in Refs. [2,3,4] they can be proved mathematically by using properties of Lie algebras.…”