# The function qz as a consistency check for cosmological parameters - General Relativity and Quantum Cosmology

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Abstract: In the Friedmann cosmology the deceleration of the expansion q plays afundamental role. We derive the deceleration as a function of redshift $qz$in two scenarios: $\Lambda$ CDM model and modified Chaplygin gas MCG model,without assuming spatial flatness. The expression relating the transitionredshift from decelerated to accelerated expansion $z t$ to the cosmologicalparameters is obtained; it is seen that the curvature parameter does not appearin this expression. Of course the numerical value of $z t$ depends on$\Omega k$, since $\Omega L + \Omega M + \Omega k = 1$. The exact function$qz$ allows the calculation of an infection point at $z \approx 0.1$ for theflat $\Lambda$ CDM model. This inflection point is visible in Fig.5 of the workof Daly and Djorgovski, Ap.J. 612,652 2004, where the deceleration wasplotted directly from observational data. We also consider the possibility of asmall contribution of the curvature, namely, $\Omega k = - 0.1 \Omega L $, andcalculate the transition redshift to be $z t = 0.56$, which falls inside theinterval $0.46 \pm 0.13$ obtained by Riess et al., Ap.J. 607, 665 2004. Thecalculated transition redshift for the MCG model is considerably lower $z t\approx 0.2$, but the observational data do not exclude a pure Chaplygin gas.

Author: ** M.L.Bedran**

Source: https://arxiv.org/