Fitting Cosmological Data to the Function q(z) from GR Theory: Modified Chaplygin Gas

Abstract

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: CDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ 2 . We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q 0 = −0.65 ± 0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q 0 = −0.67 ± 0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: X0 = 0.81 ± 0.03 for the Union2 dataset and X0 = 0.83 ± 0.03 using the Constitution dataset.

Phase space analysis of some interacting Chaplygin gas models

“…(1) the case of A = 0 recovers generalized Chaplygin gas EoS, and A = 0 together α = 1 recovers the original Chaplygin gas EoS. The best fitted parameters are found to be A = 0.085 and α = 1.724, while Constitution + CMB + BAO and Union + CMB + BAO results are A = 0.061 ± 0.079, α = 0.053 ± 0.089, and A = 0.110 ± 0.097, α = 0.089 ± 0.099 respectively [20], [21]. Other observational constraints on modified Chaplygin gas model using Markov Chain Monte Carlo approach found that A = 0.00189 +0.00583 −0.00756 , α = 0.1079 +0.3397 −0.2539 at 1σ level and A = 0.00189 +0.00660 −0.00915 with α = 0.1079 +0.4678 −0.2911 at 2σ level [22].…”

Observational constraints on the non-flat $$\Lambda CDM$$ model and a null test using the transition redshift

“…where we can observe that the transition redshift for a non-flat universe C DM is a analytical function of the parameters of relative densities [55]. Using Eqs.…”

“…Thus, using the definition of H (z) and the condition for the transition redshift q(z t ) = 0. We can determine that [55],…”

Interacting extended Chaplygin gas cosmology in Lyra manifold

“…The best fitted parameters are found to be A = 0.085 and α = 1.724, while Constitution + CMB + BAO and Union + CMB + BAO results are A = 0.061 ± 0.079, α = 0.053 ± 0.089, and A = 0.110 ± 0.097, α = 0.089 ± 0.099 respectively [17], [18]. Other observational constraints on modified Chaplygin gas model using Markov Chain Monte Carlo approach found that A = 0.00189 −0.2911 at 2σ level [19].…”