[Paper Review] The inhomogeneous equation of state and the road towards the solution of the cosmological constant problem

Hrvoje Štefančić|ArXiv.org|Nov 27, 2008

Cosmology and Gravitation Theories9 references3 citations

TL;DR

This paper proposes a cosmological model with a cosmological constant Λ and a component exhibiting an inhomogeneous equation of state (EOS) to achieve relaxation of the effective cosmological constant to a small positive value. The mechanism dynamically drives the universe toward a de Sitter state with a small effective Λ, even when the true Λ is large, via a parameter b that controls asymptotic behavior, offering a robust, fine-tuning-free path to solving the cosmological constant problem for specific parameter ranges.

ABSTRACT

We present a cosmological model containing a cosmological constant $Λ$ and a component with an inhomogeneous equation of state. We study the form of the inhomogeneous equation of state for which the model exhibits the relaxation of the cosmological constant, i.e. it asymptotically tends to the de Sitter regime characterized by a small positive effective cosmological constant. The effect of the relaxation of the cosmological constant is observed both for negative and positive values of $Λ$ and for a range of model parameters. A special emphasis is put on the study of the details of the CC relaxation mechanism and the robustness of the mechanism to the variation of model parameters. It is found that within the studied model the effective cosmological constant at large scale factor values is small because the absolute value of the real cosmological constant is large.

Motivation & Objective

• To address the cosmological constant problem by proposing a dynamical relaxation mechanism that explains the small observed value of the effective cosmological constant.
• To investigate whether a large fundamental cosmological constant Λ can naturally lead to a small effective Λ through a time-dependent, inhomogeneous equation of state.
• To assess the robustness of the relaxation mechanism under variation of model parameters, particularly the new parameter b introduced in the EOS.
• To explore the physical motivation for the inhomogeneous EOS, linking it to modified gravity or nonlinear viscosity.
• To lay the groundwork for a complete cosmological model that includes matter and radiation, while preserving the CC relaxation mechanism in the late-time de Sitter regime.

Proposed method

• Introduce a new parameter b into the equation of state, modifying the energy density evolution to allow for asymptotic relaxation to a small effective cosmological constant.
• Use the Friedmann equation to derive the H² evolution, showing that the asymptotic H² value depends on the ratio of parameters ξ and λ, with b dominating for large b.
• Analyze the system's behavior in the limit of large scale factor a → ∞, demonstrating that the effective cosmological constant Λ_eff approaches h = |ξ/λ|.
• Study the dependence of Λ_eff on λ and b, showing that for large |λ| and small b, Λ_eff becomes small without requiring fine-tuning of λ.
• Extend the model from previous work [8] by introducing b as a free parameter to explore the limits of the relaxation mechanism.
• Assess the mechanism's robustness by varying b and λ, confirming that the relaxation mechanism persists even for non-zero b, though fine-tuning re-emerges if b is not small.

Experimental results

Research questions

• RQ1 Can a large fundamental cosmological constant Λ naturally lead to a small effective cosmological constant Λ_eff through a dynamical relaxation mechanism?
• RQ2 How does the introduction of a new parameter b in the inhomogeneous equation of state affect the asymptotic behavior of the Hubble parameter and the effective cosmological constant?
• RQ3 Is the relaxation mechanism robust to variations in model parameters, particularly b and λ, and does it remain viable without fine-tuning?
• RQ4 What physical motivations underlie the proposed inhomogeneous equation of state, and how might it be connected to modified gravity or nonlinear viscosity?
• RQ5 Can this relaxation mechanism be embedded into a full cosmological model that includes radiation and matter, preserving the late-time de Sitter behavior?

Key findings

• For vanishing b, the effective cosmological constant Λ_eff approaches h = |ξ/λ|, and if |λ| is large, Λ_eff becomes small without requiring fine-tuning of λ.
• The asymptotic value of H² is determined by the ratio h = |ξ/λ|, and this value becomes fully dominated by b when b grows large.
• When |λ| is large and b is small, the effective cosmological constant is small and naturally arises from the model's dynamics, avoiding fine-tuning of λ.
• Even for non-zero b, the relaxation mechanism persists, but fine-tuning re-enters if b is not small, as b then becomes the dominant parameter determining Λ_eff.
• The model shows that a large Λ does not determine the asymptotic behavior; instead, the system relaxes to a small Λ_eff due to the interplay of λ and b.
• The mechanism is robust for small or vanishing b, supporting the idea that inhomogeneous equations of state offer a viable path toward solving the cosmological constant problem.