[Paper Review] K-essence scalar field as dynamical dark energy

L. C. Garcia, Juan Manuel Tejeiro+1 more|arXiv (Cornell University)|Oct 18, 2012

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes a K-essence scalar field as a dynamical dark energy model that tracks during radiation domination (achieving ωₚ ≈ 1/3) and evolves toward ωₚ → -1 at late times, mimicking a cosmological constant. Using an effective redshift-dependent parametrization of the equation of state and fitting to Type Ia supernovae luminosity distances, the model successfully reproduces late-time acceleration while increasing the primordial ⁴He abundance during Big Bang Nucleosynthesis due to enhanced Hubble expansion, bringing predictions into better agreement with observations.

ABSTRACT

We study an early dark energy (EDE) model as a K-essence scalar field in the framework of FLRW universe using an effective parametrization of the state equation as a function of the redshift $z$ with the tracker condition during radiation domination, but also demanding an accelerated expansion of the universe at late times emulating cosmological constant. We found all the dynamical variables of the EDE system. We use the luminosity distances of the SNIA to get the best estimations for the free parameters of the model and also, we constrain the model using primordial abundances of light nuclei in BBN theory. We summarize the necessary conditions to achieve BBN predictions and the accelerated expansion of the universe at late times.

Motivation & Objective

• To develop a dynamical dark energy model that explains late-time cosmic acceleration without fine-tuning initial conditions.
• To incorporate a non-negligible energy density from a K-essence scalar field during radiation domination, affecting Big Bang Nucleosynthesis (BBN) dynamics.
• To constrain the model using observational data from Type Ia supernovae (SNIa) and BBN predictions, particularly for ⁴He and ⁷Li abundances.
• To test whether the model can simultaneously satisfy late-time acceleration and improved agreement with primordial light element abundances.
• To provide a parametrization of the K-essence equation of state that avoids attractor fine-tuning and allows for analytical tractability.

Proposed method

• Formulate the K-essence scalar field Lagrangian using a non-canonical kinetic term Q(v) and a field-dependent function K(φ), enabling tracker behavior during radiation domination.
• Derive the energy density and pressure of the field from the Lagrangian, and express the effective equation of state ωₚ(z) as a redshift-dependent parametrization to fit SNIa data.
• Use the χ² minimization technique with the Union SNIa dataset to constrain the free parameters of the effective equation of state, particularly the field's contribution during radiation (parameterized by b).
• Incorporate the K-essence field’s energy density into the Hubble parameter to modify the BBN reaction network, using the Public Big Bang Nucleosynthesis code to compute light element abundances.
• Compute the baryon-to-photon ratio η_B and Ω_Bh² from the model’s predictions and compare them with observational bounds from WMAP and other datasets.
• Analyze the sound speed C_s² to ensure perturbative stability of the K-essence field throughout cosmic evolution.

Experimental results

Research questions

• RQ1 Can a K-essence scalar field with a redshift-dependent equation of state reproduce the observed late-time acceleration of the universe while remaining subdominant during radiation and matter eras?
• RQ2 How does a non-zero energy density of the K-essence field during radiation domination affect the primordial abundances of ⁴He and ⁷Li in Big Bang Nucleosynthesis?
• RQ3 To what extent can the model’s parameters be constrained by fitting to Type Ia supernovae luminosity distances, and how do they compare to ΛCDM?
• RQ4 Does the model avoid the fine-tuning problem of initial field conditions due to its tracker-like behavior during radiation domination?
• RQ5 What is the impact of the K-essence field on the Hubble expansion rate during BBN, and how does this alter the neutron-to-proton freeze-out and subsequent ⁴He production?

Key findings

• The model achieves a tracker-like behavior during radiation domination with ωₚ ≈ 1/3, ensuring minimal fine-tuning of initial conditions.
• The effective equation of state ωₚ(z) successfully fits the SNIa Union dataset, with best-fit parameters derived via χ² minimization.
• At late times (z ≈ 0), the field asymptotically approaches ωₚ → -1, emulating a cosmological constant and reproducing late-time acceleration.
• The inclusion of the K-essence field during radiation domination increases the Hubble expansion rate, leading to faster reaction rates and a higher predicted ⁴He mass fraction, which remains within observational bounds.
• For b = 0.2 (maximum radiation-era contribution), the model predicts Ω_Bh² = 0.02692 and η_B × 10¹⁰ = 6.73, compared to ΛCDM’s 0.02218 and 6.20, respectively, showing improved agreement with WMAP data.
• The model’s predictions for ⁴He abundance are consistent with observations, suggesting it can alleviate discrepancies in BBN without requiring new physics beyond the K-essence field.