[Paper Review] Constraints over Cosmological Constant and Quintessence Fields in an Accelerating Universe

V. B. Johri|arXiv (Cornell University)|Jul 6, 2000

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates constraints on the cosmological constant (Λ) and quintessence fields in an accelerating universe using astrophysical observations. By applying nucleosynthesis and galaxy formation constraints, it derives limits on Ωϕ and the tracking parameter ε ≈ 0.75 at z=0, showing that cosmic acceleration begins earlier in ΛCDM than in QCDM cosmology, with Λ ≈ 6.99×10⁻⁵⁷ (in cgs units), consistent with observational estimates.

ABSTRACT

A brief account of the current cosmological observations is given and their implications for QCDM and $Λ$CDM cosmologies are discussed. The nucleosynthesis and the galaxy formation constraints have been used to put limits on $Ω_ϕ$ during cosmic evolution, and develop a realistic approach to the tracking behaviour of quintessence fields. The astrophysical constraints are applied to interpolate the value of the tracking parameter $ε\simeq 0.75$ at the present epoch and also to find the lower and the upper limits for $Λ$ in the accelerating universe. It is shown that the transition from deceleration to acceleration in the cosmic expansion occurs earlier in $Λ$CDM cosmology compared to QCDM cosmology.

Motivation & Objective

• To constrain the cosmological constant (Λ) and quintessence fields using astrophysical observations.
• To determine the transition redshift from deceleration to acceleration in ΛCDM and QCDM cosmologies.
• To derive theoretical limits on Λ based on matter clumping and structure formation constraints.
• To analyze the tracking behavior of quintessence fields and their evolution during cosmic expansion.
• To compare the viability of QCDM and ΛCDM models under observational constraints.

Proposed method

• Uses energy density and pressure equations for scalar fields: ρϕ = ½φ̇² + V(ϕ), pϕ = ½φ̇² - V(ϕ).
• Applies the equation of motion for scalar fields: φ̈ + 3Hφ̇ + V’(ϕ) = 0, with wϕ = pϕ/ρϕ.
• Employs the energy conservation law: dρϕ/dt + 3H(1 + wϕ)ρϕ = 0, leading to ρϕ ∝ a⁻³⁽¹⁺wϕ⁾.
• Derives analytical solutions for scale factor a(t) and Hubble parameter H(t) in ΛCDM during matter domination: a ∝ sinh²/³(3/2 √(Λ/3) ct).
• Applies constraints from galaxy formation (q > 0) and CMB observations (Ωm ≈ 0.35, ΩX ≈ 0.75) to limit Λ.
• Uses redshift-dependent bounds: Λ < 4.2×10⁻⁵⁷(1+z)³ and Λ > 4.2×10⁻⁵⁷, leading to Λ ≈ 6.99×10⁻⁵⁷ at z=0.

Experimental results

Research questions

• RQ1 What are the theoretical limits on the cosmological constant Λ derived from nucleosynthesis and galaxy formation constraints?
• RQ2 How does the transition redshift from deceleration to acceleration differ between ΛCDM and QCDM cosmologies?
• RQ3 What is the value of the tracking parameter ε for quintessence fields at the present epoch, and how does it affect cosmic evolution?
• RQ4 How do the energy density and equation of state of quintessence fields evolve during cosmic history under observational constraints?
• RQ5 What is the consistency of the derived Λ value with observational estimates based on H₀ and ΩΛ?

Key findings

• The tracking parameter for quintessence fields is constrained to ε ≈ 0.75 at the present epoch (z=0).
• The upper limit for the cosmological constant is Λ < 33.5×10⁻⁵⁷ (in cgs units), derived from galaxy formation constraints up to z=2.
• The lower limit for Λ is Λ > 4.2×10⁻⁵⁷, derived from the condition that cosmic acceleration begins when q=0.
• The derived value of Λ ≈ 6.99×10⁻⁵⁷ is in good agreement with the observational estimate of 7.74×10⁻⁵⁷ based on H₀ = 65 km/Mpc/s and ΩΛ = 0.65.
• The transition to accelerated expansion occurs earlier in ΛCDM cosmology (zc ≈ 0.54) than in QCDM cosmology (zc ≈ 0.419), indicating a faster onset of acceleration in ΛCDM.
• The analytical solution for scale factor in ΛCDM reduces to the Einstein-de Sitter model in the limit Λ → 0, confirming consistency with standard cosmology.