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 $\Lambda$. 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 ($\Lambda \to S_{\mathrm{\Lambda }}$) and energy ($\Lambda \to E_{\mathrm{\Lambda }}$). 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 $\tau (C_2,\Lambda )$ 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.

15 pages

References in corpus (6)

• Phantom Energy and Cosmic Doomsday
• Inflation and de Sitter Thermodynamics
• Holography in a Radiation-dominated Universe with a Positive Cosmological Constant
• The Elliptic Solutions to the Friedmann equation and the Verlinde's Maps
• 20+ years of Inflation
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Cited by in corpus (7)

• Holographic principle and dark energy
• On phantom thermodynamics with negative temperature
• Holographic Cosmological Constant and Dark Energy
• Entropic force and its cosmological implications
• Cosmological Constant and Noncommutativity: A Newtonian point of view
• Parametric solution of certain nonlinear differential equations in cosmology
• Parametric Solution Of Certain Nonlinear Differential Equations In Cosmology II