[Paper Review] Holographic energy density in the Brans-Dicke theory

Hung-Soo Kim, Yun Soo Myung+1 more|arXiv (Cornell University)|Jan 15, 2005

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper proposes a holographic energy density model within the Brans-Dicke theory to describe dark energy, using the future event horizon as an infrared cutoff. By applying the Bianchi identity as a consistency condition, it shows that the Brans-Dicke scalar naturally generates a dynamical dark energy component, with its equation of state approaching -1 in the late-time universe, consistent with observations.

ABSTRACT

We study cosmological applications of the holographic energy density. Considering the holographic energy density as a dynamical cosmological constant, we need the Brans-Dicke theory as a dynamical framework instead of general relativity. In this case we use the Bianchi identity as a consistency relation to obtain physical solutions. It is shown that the future event horizon as the IR cutoff provides the dark energy in the Brans-Dicke theory. Furthermore the role of the Brans-Dicke scalar is clarified in the dark energy-dominated universe by calculating its equation of state.

Motivation & Objective

• To investigate the cosmological implications of holographic energy density in the Brans-Dicke theory instead of general relativity.
• To determine whether the future event horizon can serve as a viable infrared cutoff for holographic dark energy in a scalar-tensor framework.
• To clarify the dynamical role of the Brans-Dicke scalar field in a dark energy-dominated universe.
• To derive the equation of state of the holographic energy density within the Brans-Dicke framework and assess its consistency with observational constraints.

Proposed method

• Formulate the holographic energy density as a dynamical cosmological constant within the Brans-Dicke theory.
• Use the future event horizon as the infrared cutoff to define the energy density scale.
• Apply the Bianchi identity as a consistency condition to derive physical solutions for the field equations.
• Derive the effective equation of state parameter for the holographic energy density from the field equations.
• Analyze the late-time behavior of the Brans-Dicke scalar field in the context of dark energy domination.
• Solve the modified Friedmann equations under the holographic assumption to determine the evolution of the scalar field and energy density.

Experimental results

Research questions

• RQ1 Can the holographic principle with the future event horizon as an infrared cutoff produce a consistent dark energy model in the Brans-Dicke theory?
• RQ2 How does the Brans-Dicke scalar field evolve in a universe dominated by holographic energy density?
• RQ3 What is the equation of state of the holographic energy density in the Brans-Dicke framework, and does it approach -1 in the late universe?
• RQ4 Is the Bianchi identity sufficient to ensure physical consistency of the solutions in this holographic Brans-Dicke model?
• RQ5 What is the dynamical role of the Brans-Dicke scalar in mediating the effective cosmological constant?

Key findings

• The future event horizon serves as a consistent infrared cutoff for holographic energy density in the Brans-Dicke theory.
• The holographic energy density behaves as a dynamical cosmological constant, with its evolution governed by the Brans-Dicke scalar field.
• The equation of state parameter of the holographic energy density approaches -1 in the late-time universe, consistent with current dark energy observations.
• The Brans-Dicke scalar field plays a crucial role in dynamically generating the effective cosmological constant, avoiding the need for a fixed cosmological constant.
• The Bianchi identity ensures the consistency of the derived solutions, validating the physicality of the model.
• The model provides a self-consistent framework where the holographic principle and scalar-tensor gravity cohere in explaining dark energy.