[Paper Review] Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology

A. Hernández-Almada, Genly León+6 more|arXiv (Cornell University)|Dec 8, 2021

Cosmology and Gravitation Theories92 references60 citations

TL;DR

This paper investigates Kaniadakis horizon-entropy cosmology, a modified gravity model derived from the gravity-thermodynamics conjecture using Kaniadakis entropy, which introduces an effective dark energy sector. Using Bayesian MCMC analysis on observational data (H(z), SNIa, HII galaxies, SLS, BAO), it finds the Kaniadakis parameter ≈ 0, a Hubble constant h ≈ 0.708, and a transition redshift z_T ≈ 0.715, suggesting alleviation of the H₀ tension. Phase-space analysis confirms late-time dark energy dominance and rules out bounce solutions.

ABSTRACT

We study the scenario of Kanadiakis horizon entropy cosmology which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from Cosmic chronometers, Supernova Type Ia, HII galaxies, Strong lensing systems, and Baryon acoustic oscillations observations and we apply a Bayesian Markov Chain Monte Carlo analysis to construct the likelihood contours for the model parameters. We find that the Kaniadakis parameter is constrained around 0, namely, around the value where the standard Bekenstein-Hawking is recovered. Concerning the normalized Hubble parameter, we find $h=0.708^{+0.012}_{-0.011}$, a result that is independently verified by applying the $\mathbf{\mathbb{H}}0(z)$ diagnostic and, thus, we conclude that the scenario at hand can alleviate the $H_0$ tension problem. Regarding the transition redshift, the reconstruction of the cosmographic parameters gives $z_T=0.715^{+0.042}_{-0.041}$. Furthermore, we apply the AICc, BIC and DIC information criteria and we find that in most datasets the scenario is statistical equivalent to $\Lambda$CDM one. Moreover, we examine the Big Bang Nucleosynthesis (BBN) and we show that the scenario satisfies the corresponding requirements. Additionally, we perform a phase-space analysis, and we show that the Universe past attractor is the matter-dominated epoch, while at late times the Universe results in the dark-energy-dominated solution. Finally, we show that Kanadiakis horizon entropy cosmology accepts heteroclinic sequences, but it cannot exhibit bounce and turnaround solutions.

Motivation & Objective

• To test Kaniadakis horizon-entropy cosmology against observational data, including H(z), SNIa, HII galaxies, strong lensing, and BAO.
• To constrain the Kaniadakis parameter β and the Hubble parameter h using Bayesian Markov Chain Monte Carlo (MCMC) methods.
• To assess the model’s viability through information criteria (AICc, BIC, DIC) and compare it with ΛCDM.
• To perform a dynamical systems analysis to determine the stability of equilibrium points and the late-time behavior of the universe.
• To investigate whether the model can support bounce or turnaround solutions.

Proposed method

• Apply the gravity-thermodynamics conjecture using Kaniadakis-modified entropy to derive modified Friedmann equations with an effective dark energy term.
• Use observational datasets: Cosmic Chronometers (H(z)), SNIa, HII galaxies, strong lensing systems (SLS), and BAO to constrain model parameters.
• Perform Bayesian MCMC analysis to compute likelihood contours and extract posterior distributions for β, h, and Ωₘ⁰.
• Conduct a dynamical systems analysis by transforming the Friedmann equations into a one-dimensional autonomous system, identifying equilibrium points and their stability.
• Apply the H₀(z) diagnostic to independently verify the Hubble parameter constraint.
• Use information criteria (AICc, BIC, DIC) to compare model performance with ΛCDM.

Experimental results

Research questions

• RQ1 Can Kaniadakis horizon-entropy cosmology alleviate the H₀ tension observed in Planck and SH0ES measurements?
• RQ2 What are the observational constraints on the Kaniadakis parameter β and the normalized Hubble parameter h?
• RQ3 How does the model's dynamical behavior compare to ΛCDM, particularly in terms of equilibrium points and late-time attractors?
• RQ4 Does the model support bounce or turnaround solutions, and what is the phase-space structure of its cosmological evolution?
• RQ5 How does the model compare to ΛCDM in terms of statistical goodness-of-fit using AICc, BIC, and DIC?

Key findings

• The Kaniadakis parameter β is constrained to β ≈ 0, indicating recovery of the standard Bekenstein-Hawking entropy in the limit of the model.
• The normalized Hubble parameter is constrained to h = 0.708⁺⁰.⁰¹²₋₀.⁰¹₁ for Λ ≠ 0, which is 2.67σ below the Planck value and 1.74σ below the SH0ES value, suggesting potential alleviation of the H₀ tension.
• The transition redshift from deceleration to acceleration is z_T = 0.715⁺⁰.⁰⁴²₋₀.⁰⁴¹, consistent with ΛCDM within 1σ.
• The AICc suggests statistical equivalence between the Kaniadakis model and ΛCDM, while BIC indicates strong evidence against the model, and DIC shows moderate to strong tension depending on the dataset.
• Phase-space analysis confirms the matter-dominated epoch as a past attractor and dark-energy-dominated solution as a late-time attractor, with no stable bounce or turnaround solutions.
• The model supports heteroclinic sequences but cannot exhibit bounce or turnaround behavior due to the absence of required dynamical conditions in the phase space.