[Paper Review] Bulk Viscous cosmological models in Lyra geometry

Anirudh Pradhan, Hare Ram Pandey|ArXiv.org|Jul 9, 2003

Cosmology and Gravitation Theories43 references3 citations

TL;DR

This paper presents exact solutions for spatially homogeneous, locally rotationally symmetric (LRS) Bianchi Type I cosmological models with bulk viscosity in Lyra's geometry, assuming a time-dependent displacement field and a power-law viscosity coefficient. The key result is the derivation of physically viable models with positive energy density and evolving scale factors, showing that bulk viscosity significantly influences cosmic expansion dynamics without requiring a cosmological constant.

ABSTRACT

We have investigated an LRS Bianchi Type I models with bulk viscosity in the cosmological theory based on Lyra's geometry. A new class of exact solutions have been obtained by considering a time-dependent displacement field for a constant value of the deceleration parameter and viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. The physical behaviour of the models is also discussed.

Motivation & Objective

• To explore the effects of bulk viscosity on cosmological evolution within Lyra's geometric framework.
• To construct exact solutions for LRS Bianchi Type I models under a constant deceleration parameter.
• To investigate the role of a time-dependent displacement field in modifying cosmic dynamics without a cosmological constant.
• To analyze the physical viability of the models through energy density and shear behavior.
• To compare the results with standard general relativistic models and assess the relevance for early-universe cosmology.

Proposed method

• Adopted Lyra's geometry with a time-dependent displacement field to model a cosmological constant-like effect.
• Assumed a power-law form for the bulk viscosity coefficient: ξ(t) = ξ₀ρⁿ, where ρ is the energy density.
• Solved the modified Einstein field equations under the LRS Bianchi Type I metric and constant deceleration parameter.
• Used a specific ansatz for the Hubble parameter to derive exact solutions for scale factors and displacement field.
• Analyzed the behavior of energy density, shear scalar, and displacement field over time for different values of the power index n.
• Employed numerical plots to visualize the evolution of energy density and physical parameters under varying model parameters.

Experimental results

Research questions

• RQ1 How does bulk viscosity affect the dynamics of LRS Bianchi Type I models in Lyra's geometry with a time-dependent displacement field?
• RQ2 Can exact solutions be derived for such models under a constant deceleration parameter and power-law viscosity?
• RQ3 What are the physical implications of the energy density and shear scalar behavior in these viscous models?
• RQ4 How does the time-dependent displacement field influence the cosmic expansion and energy density evolution?
• RQ5 Can these models avoid singularities and remain physically viable without a cosmological constant?

Key findings

• For n = 0 (constant viscosity), the energy density remains positive for t > 0 and approaches a constant value, with β² > 0 for t > t_c, indicating a physically viable model.
• For n = 1 (linear viscosity), the energy density becomes negative for a short time interval when b < 2, but recovers to a small positive value, suggesting transient instability.
• In the case b = -1 (constant Hubble parameter), the energy density increases with time and approaches a constant positive value, with β² > 0 under specific conditions on ξ₀ and H₀.
• The critical time t_c for β² = 0 is determined by a nonlinear relation involving H₀, γ, ξ₀, and b, indicating a transition point in model evolution.
• The energy density remains positive when ξ₀ > (γ - 1)/(3H₀) for t > T₃, ensuring physical consistency under certain parameter regimes.
• Numerical plots confirm that the energy density evolves smoothly and remains non-negative in most parameter ranges, supporting the physical viability of the models.