[Paper Review] Data Analysis of three parameter models of deceleration parameter in FRW Universe

Amine Bouali, Himanshu Chaudhary+3 more|arXiv (Cornell University)|Apr 25, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This study proposes four three-parameter parametrizations of the deceleration parameter $q(z)$ to model the transition from cosmic deceleration to acceleration in a flat Friedmann-Lemaítre-Robertson-Walker (FLRW) universe. Using H(z), Pantheon SNIa, BAO, and CMB data with MCMC fitting, it constrains model parameters and evaluates cosmographic, statefinder, and Om diagnostics. The key result is that Model 3 (M3) shows the highest viability, with a late-time deceleration parameter of $q(-1) \approx -0.7$ and consistent behavior with $\Lambda$CDM at high redshift, suggesting it as a strong alternative to $\Lambda$CDM.

ABSTRACT

Constraining the dark energy deceleration parameter is one of the fascinating topics in the recent cosmological paradigm. This work aims to reconstruct the dark energy using parametrization of the deceleration parameter in a flat FRW universe filled with radiation, dark energy, and pressure-less dark matter. Thus, we have considered four well-motivated parameterizations of q(z), which can provide the evolution scenario from the deceleration to acceleration phase of the Universe. We have evaluated the expression of the corresponding Hubble parameter of each parametrization by imposing it into the Friedmann equation. We have constrained the model parameter through H(z), Pantheon, and baryons acoustic oscillation (BOA) data. Next, we have estimated the best-fit values of the model parameters by using Monte Carlo Markov Chain (MCMC) technique and implementing H(z)+ BAO+SNe-Ia dataset. Then we analyzed the cosmographic parameter, such as deceleration, jerk, and snap parameters, graphically by employing the best-fit values of the model parameter. Moreover, we have analyzed statefinder and Om diagnostics parameters for each scenario to discriminate various dark energy models. Using the information criteria, the viability of the models have examined. In the end, we have analogized our outcomes with the standard ΛCDM model to examine the viability of our models

Motivation & Objective

• To reconstruct dark energy dynamics through parametrized deceleration parameter $q(z)$ in a flat FLRW universe.
• To test four well-motivated three-parameter $q(z)$ models that describe the transition from deceleration to acceleration.
• To constrain model parameters using up-to-date observational datasets: $H(z)$, Pantheon SNIa, BAO, and CMB.
• To evaluate model viability using cosmographic parameters, statefinder, $Om$ diagnostic, and information criteria.
• To compare all models with the standard $\Lambda$CDM model to assess their relative probability and physical plausibility.

Proposed method

• Four three-parameter parametrizations of $q(z)$ are proposed to describe the cosmic transition from deceleration to acceleration.
• The Hubble parameter $H(z)$ is derived for each $q(z)$ model by solving the Friedmann equation.
• Model parameters are constrained using combined observational datasets: $H(z)$, Pantheon SNIa, BAO, and CMB.
• Monte Carlo Markov Chain (MCMC) technique is employed to estimate best-fit parameter values.
• Cosmographic parameters—deceleration, jerk, and snap—are computed and plotted using best-fit parameters.
• Statefinder and $Om$ diagnostics are used to distinguish dark energy model behaviors and assess model viability.

Experimental results

Research questions

• RQ1 How do the four three-parameter $q(z)$ models compare in fitting observational data from $H(z)$, Pantheon SNIa, BAO, and CMB?
• RQ2 What are the best-fit values of the model parameters, and how do they affect the evolution of the deceleration, jerk, and snap parameters?
• RQ3 How do the statefinder and $Om$ diagnostics distinguish the proposed models from $\Lambda$CDM and from each other?
• RQ4 Which model shows the highest viability according to information criteria and comparison with $\Lambda$CDM?
• RQ5 What is the late-time behavior of the deceleration parameter in each model, particularly at $z = -1$?

Key findings

• Model 1 (M1) closely resembles $\Lambda$CDM at high and low redshifts, transitioning into a de Sitter phase with $q \to -1$.
• Model 2 (M2) shows systematic deviations from $\Lambda$CDM at all redshifts but also reaches a de Sitter phase, with $j(0) \approx 0.42$ and $s(0) \approx 0.9$.
• Model 3 (M3) matches $\Lambda$CDM at high redshift but exhibits a slower acceleration at low redshift, with $q(-1) \approx -0.7$ and $s(0) \approx 0.9$.
• Model 4 (M4) displays super-accelerated expansion at low redshift with $j(0) \approx 2.1$, significantly exceeding $\Lambda$CDM, and $s(0) \approx 0.7$.
• Statefinder diagnostics show M1 and M4 exhibit quintessence-like behavior ($r<1, s>0$) and cross into $\Lambda$CDM’s region ($r<1, s<0$), while M3 starts with Chaplygin gas-like behavior ($r>1, s>0$).
• The $Om$ diagnostic indicates M1 and M4 show phantom-like behavior, while M2 and M3 remain in the quintessence region with positive $Om$ values throughout, supporting normal dark energy.