[Paper Review] Interacting R\\'enyi holographic dark energy with parametrization on the interaction term

Umesh Kumar Sharma, Vipin Chandra Dubey|arXiv (Cornell University)|Jan 7, 2020

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes an interacting Rényi holographic dark energy (RHDE) model in a flat Friedmann-Robertson-Walker universe, using the Hubble horizon as the infrared cut-off and three parametrized interaction terms between dark matter and dark energy. The model exhibits late-time accelerated expansion, with the equation of state parameter entering the phantom regime and the squared speed of sound indicating classical stability for certain parameter choices, particularly in models I and III.

ABSTRACT

In the present work, we study the R$\\acute{e}$nyi holographic dark energy model (RHDE) in a flat FRW Universe where the infrared cut-off is taken care by the Hubble horizon and also by taking three different parametrizations of the interaction term between the dark matter and the dark energy. Analyzing graphically, the behavior of some cosmological parameters in particular deceleration parameter, equation of state (EoS) parameter, energy density parameter and squared speed of sound, in the process of the cosmic evolution, is found to be leading towards the late-time accelerated expansion of the RHDE model.

Motivation & Objective

• To explore the cosmological behavior of Rényi holographic dark energy (RHDE) in a flat FRW universe with Hubble horizon as the infrared cut-off.
• To examine the impact of three different parametrizations of the interaction term between dark matter and dark energy on the evolution of cosmological parameters.
• To assess the stability of the RHDE model through the squared speed of sound and determine viable parameter regimes.
• To determine whether the model can reproduce the observed late-time accelerated expansion and address the cosmic coincidence problem.

Proposed method

• The model employs the Rényi entropy formalism to define the energy density of dark energy, with the Hubble horizon as the infrared cut-off.
• Three distinct parametrizations of the interaction term Q are introduced: Q = 3α₁Hρ_tot, Q = 3α₂Hρ_m, and Q = 3δHρ_q, allowing for varied energy transfer dynamics.
• The evolution of key cosmological parameters—deceleration parameter q(z), equation of state ω_D, energy density Ω_D, and squared sound speed v_s²—is derived from the modified energy balance equations.
• Graphical analysis is used to study the time evolution of these parameters across different redshift ranges and parameter values.
• Stability is evaluated by analyzing the sign of the squared speed of sound v_s², with v_s² ≥ 0 indicating classical stability.
• Numerical simulations and plots are used to compare model behavior across different parameter sets (α₁, α₂, δ) and to assess consistency with observational trends.

Experimental results

Research questions

• RQ1 Does the interacting RHDE model with Hubble horizon cut-off produce a transition from early deceleration to late-time acceleration?
• RQ2 How does the choice of interaction parametrization (Q = 3α₁Hρ_tot, Q = 3α₂Hρ_m, Q = 3δHρ_q) affect the evolution of the equation of state parameter ω_D?
• RQ3 What are the conditions under which the RHDE model remains classically stable, as indicated by the squared speed of sound v_s²?
• RQ4 How do the energy density parameters Ω_D evolve over time, and do they align with observational expectations for the future universe?
• RQ5 Which of the three parametrized models (I, II, III) best matches the observed behavior of cosmological parameters like Ω_D and q(z)?

Key findings

• The deceleration parameter q(z) shows a transition from a positive (decelerated) phase in the past to a negative (accelerated) phase at present, consistent with observations, for all three models and parameter choices.
• The equation of state parameter ω_D approaches values below -1, indicating phantom-like behavior, particularly in Models I and II, with Model II remaining in the quintessence regime only when α₂ = 0.
• The dark energy density parameter Ω_D increases monotonically with redshift, approaching 1 in the non-interacting case (α₁ = α₂ = 0), while in interacting cases it stabilizes below 1, indicating a balance between dark matter and dark energy.
• Model II is inconsistent with observed Ω_D evolution for α₂ = 0.09 and α₂ = 0.18, whereas Models I and III show better agreement with observational trends.
• The squared speed of sound v_s² indicates classical stability (v_s² ≥ 0) for Models I and III under specific parameter choices, while instability (v_s² < 0) occurs for certain values of α₁, α₂, and δ, particularly in the past for Model II.
• Model I and III exhibit similar cosmological behavior in the low-redshift region for selected parameters, suggesting robustness in their dynamical evolution.