Observational constraints on dark energy cosmological model parameters

TL;DR

This paper reviews and constrains various dark energy cosmological models, including ΛCDM, XCDM, and φCDM, using observational data like H(z), supernovae, and BAO to understand the universe's accelerated expansion.

Contribution

It provides observational constraints on dark energy models with and without spatial curvature, extending previous analyses to include non-flat geometries and multiple data sets.

Findings

Constraints on model parameters from H(z), supernova, and BAO data.

Determination of the deceleration-acceleration transition redshift.

Observational limits on spatial curvature in dark energy models.

Abstract

The expansion rate of the Universe changes with time, initially slowing (decelerating) when the universe was matter dominated, because of the mutual gravitational attraction of all the matter in it, and more recently speeding up (accelerating). A number of cosmological observations now strongly support the idea that the Universe is spatially flat (provided the dark energy density is at least approximately time independent) and is currently undergoing an accelerated cosmological expansion. A majority of cosmologists consider "dark energy" to be the cause of this observed accelerated cosmological expansion. The "standard" model of cosmology is the spatially-flat {\Lambda}CDM model. Although most predictions of the {\Lambda}CDM model are reasonably consistent with measurements, the {\Lambda}CDM model has some curious features. To overcome these difficulties, different Dark Energy models have been proposed. Two of these models, the XCDM parametrization and the slow rolling scalar field model $\phi$CDM, along with "standard" {\Lambda}CDM, with the generalization of XCDM and $\phi$CDM in non-flat spatial geometries are considered here and observational data are used to constrain their parameter sets. In this thesis, we start with a overview of the general theory of relativity, Friedmann's equations, and distance measures in cosmology. In the following chapters we explain how we can constrain the three above mentioned cosmological models using three data sets: measurements of the Hubble parameter $H(z)$, Supernova apparent magnitudes, and the BAO peak length scale, as functions of redshift $z$. We then discuss constraints on the deceleration-acceleration transition redshift $z_{\rm da}$ using unbinned and binned $H(z)$ data. Finally, we incorporate the spatial curvature in the XCDM and $\phi$CDM model and determine observational constraints on the parameters of these expanded models.