Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Observational Constraints on Dark Energy Models with $Λ$ as an Equilibrium Point

Andronikos Paliathanasis

TL;DR

This work constrains dark-energy models in which the equation of state parameter $w_d(a)$ obeys an autonomous second-order law with the cosmological constant $\Lambda$ as an equilibrium point. It develops two parametric families of models—linear and logarithmic in the scale factor—based on the asymptotic solutions near the equilibrium and calibrates them against Pantheon+ SN, Cosmic Chronometers, and DESI DR1/DR2 BAO data using Bayesian MCMC and AIC for model selection. The results show that most models fit the data well, with the logarithmic parametrization often performing best or being statistically indistinguishable from $\Lambda$CDM$, while oscillatory or highly-parametric variants are typically disfavored. The paper also proposes a generalized CPL-style class where the equilibrium point is a constant rather than $\Lambda$, which can match or exceed CPL performance, thereby informing the possible dynamical nature of dark energy and guiding future observational tests.

Abstract

We investigate a dynamical reconstruction of the dark energy equation of state parameter by assuming that it satisfies a law of motion described by an autonomous second-order differential equation, with the limit of the cosmological constant as an equilibrium point. We determine the asymptotic solutions of this equation and use them to construct two families of parametric dark energy models, employing both linear and logarithmic parametrization with respect to the scale factor. We perform observational constraints by using the Supernova, the Cosmic Chronometers and the Baryon Acoustic Oscillations of DESI DR2. The constraint parameters are directly related with the initial value problem for the law of motion and its algebraic properties. The analysis shows that most of the models fit the observational data well with a preference to the models of the logarithmic parametrization. Furthermore, we introduce a new class of models as generalizations of the CPL model, for which the equilibrium point is a constant value rather than the cosmological constant. These models fit the data in a similar or better way to the CPL and the $Λ$CDM cosmological models.

Observational Constraints on Dark Energy Models with $Λ$ as an Equilibrium Point

TL;DR

This work constrains dark-energy models in which the equation of state parameter obeys an autonomous second-order law with the cosmological constant as an equilibrium point. It develops two parametric families of models—linear and logarithmic in the scale factor—based on the asymptotic solutions near the equilibrium and calibrates them against Pantheon+ SN, Cosmic Chronometers, and DESI DR1/DR2 BAO data using Bayesian MCMC and AIC for model selection. The results show that most models fit the data well, with the logarithmic parametrization often performing best or being statistically indistinguishable from CDM\Lambda$, which can match or exceed CPL performance, thereby informing the possible dynamical nature of dark energy and guiding future observational tests.

Abstract

We investigate a dynamical reconstruction of the dark energy equation of state parameter by assuming that it satisfies a law of motion described by an autonomous second-order differential equation, with the limit of the cosmological constant as an equilibrium point. We determine the asymptotic solutions of this equation and use them to construct two families of parametric dark energy models, employing both linear and logarithmic parametrization with respect to the scale factor. We perform observational constraints by using the Supernova, the Cosmic Chronometers and the Baryon Acoustic Oscillations of DESI DR2. The constraint parameters are directly related with the initial value problem for the law of motion and its algebraic properties. The analysis shows that most of the models fit the observational data well with a preference to the models of the logarithmic parametrization. Furthermore, we introduce a new class of models as generalizations of the CPL model, for which the equilibrium point is a constant value rather than the cosmological constant. These models fit the data in a similar or better way to the CPL and the CDM cosmological models.

Paper Structure

This paper contains 13 sections, 47 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Cosmological Framework
  3. Dynamical dark energy with $\Lambda$ as an Equilibrium Point
  4. Linear function $\chi\left( a\right) =\frac{a}{a_{0}}$.
  5. Logarithmic function $\chi\left( a\right) =\ln\left( \frac{a}{a_{0}}\right)$
  6. Parametric space
  7. Observational Data
  8. Methodology
  9. Results
  10. $SN+CC$ data
  11. DESI$\ $DR1: $SN+CC+BAO_{1}$ data
  12. DESI$\ $DR2:$~SN+CC+BAO_{2}$ data
  13. Conclusions

Figures (7)

  • Figure 1: Qualitative evolution of $w^{I}\left( z;w_{d}^{1},w_{a}\right) ~$(Left Fig.) and $w^{II}\left( z;w_{d}^{1},w_{a},w_{d}^{2},w_{b}\right)$ (Right Fig.) for different values of the parameters. We observe that for small $Z$ the sets of parameters $\left( w_{d}^{1},w_{a}\right)$ and $\left( w_{d}^{2},w_{b}\right)$ are degenerate.
  • Figure 2: Evolution for the dark energy equation of state parameter $w_{\pm}^{I}\left( z\right) ,w^{II}\left( z\right)$ and $w^{III}\left( z\right)$.
  • Figure 3: Evolution for the dark energy equation of state parameter $w_{\pm}^{IV}\left( z\right) ,w^{V}\left( z\right)$ and $w^{VI}\left( z\right)$.
  • Figure 4: Contour plots for $w_{+}^{I}$ & $w_{-}^{I}$
  • Figure 5: Contour plots for $w^{II}$ & $w^{III}$
  • ...and 2 more figures