Role of the cosmological constant in the holographic description of the early universe

Abstract

We investigate the role of the cosmological constant in the holographic description of a radiation-dominated universe C 2 /R 4 with a positive cosmological constant Λ. In order to understand the nature of cosmological term, we first study the Newtonian cosmology. Here we find two aspects of the cosmological term: entropy (Λ → S Λ ) and energy (Λ → E Λ ). Also we solve the Friedmann equation parametrically to obtain another role. In the presence of the cosmological constant, the solutions are described by the Weierstrass elliptic functions on torus and have modular properties. In this case one may expect to have a two-dimensional Cardy entropy formula but the cosmological constant plays a role of the modular parameter τ (C 2 , Λ) of torus. Consequently, the entropy concept of the cosmological constant is very suitable for establishing the holographic entropy bounds in the early universe. This contrasts to the role of the cosmological constant as a dark energy in the present universe.

Parametric solution of certain nonlinear differential equations in cosmology II

“…There energy and matter in the universe are assumed to be a perfect fluid consisting of radiation, non-relativistic matter, and a cosmological constant. The modular property (3.1) and the "chain of connections" of [14] discussed in section 3, and the solution (4.11) in the special Friedmann case (with Q = 0, x 0 = 0) are also discussed in [37], for example, where a holographic description of the early universe is considered.…”

Entropic force and its cosmological implications

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Cosmological Constant and Noncommutativity: A Newtonian Point of View

“…Refs. [7,8]. A great advantage of Newtonian gravity is its simplicity as it is just an external potential in a flat space.…”