Abstract
A natural extension of the standard cosmological model are models that include curvature as a free parameter. In this work we study in detail the observational constraints on the non-flat Lambda CDM model using the two main geometric tests: SNIa and Hubble parameter measurements. In general we show that the observational constraints on the parameters of the Lambda CDM model strongly depend on the curvature parameter. In particular, we study the constraints on the transition redshift (z_{t}) of a universe dominated by matter for a universe dominated by the cosmological constant. Using this observable we construct a new null test defining zeta = z_{t, flat}-z_{t, non flat}. This test depends only on the data of the Hubble parameter, the Hubble constant and the matter density parameter. However, it does not depend on derivative of an observable as generally many tests in the literature. To reconstruct this test, we use the Gaussian process method. When we use the best-fit parameters values of PLANCK/2018, we find no evidence of a disagreement between the data and the standard model (flat Lambda CDM), but if we use the value H_{0} from RIESS/2018 we found a disagreement with respect at the standard model. However, it is important to note that the Hubble parameter data has large errors for a solid statistical analysis.
Highlights
The standard cosmology model is the C D M model with flat spatial curvature
Using the concept of transition redshift, we propose a new null test, which for the non-flat C D M model explicitly depends on the Hubble parameter, the Hubble constant and the matter density parameter today
We investigate the observational constraints on the different combinations of cosmological parameters
Summary
The standard cosmology model is the C D M model with flat spatial curvature. From the theoretical point of view, this model is the simplest explanation of the accelerating expansion of the universe [1,2] and is the model that best fits the different types of observational data: SNIa, BAO, CMB, Hubble parameter measurements, etc [3,4,5,6,7]. The determination of the transition redshift including curvature as a free parameter has been little investigated, with the exception of references [48,49] where a detailed analysis of the transition redshift for different non-flat models. Motivated by all these recent results, in the present work, we study observational constraints on the transition redshift. We use observational data from the Hubble parameter to reconstruct the expression of this test In this we used as a statistical method the non-parametric method of Gaussian processes.
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