Constraining Red-shift Parametrization Parameters in Brans-Dicke Theory: Evolution of Open Confidence Contours

Abstract

In Brans Dicke theory of gravity, from the nature of the scalar field-potential considered, the dark energy, dark matter, radiation densities predicted by different observations and the closedness of the universe considered, we can fix our $ω_{BD}$, the Brans Dicke parameter, keeping only the thing in mind that from different solar system constrains it must be greater than $5\times 10^{5}$. Once we have a value, satisfying the required lower boundary, in our hand we proceed for setting unknown parameters of the different dark energy models' EoS parameter. In this paper we work with three well known red shift parametrizations of dark energy EoS. To constrain their free parameters for Brans Dicke theory of gravity we take twelve point red shift vs Hubble's parameter data and perform $χ^{2}$ test. We present the observational data analysis mechanism for Stern, Stern+BAO and Stern+BAO+CMB observations. Minimising $χ^2$, we obtain the best fit values and draw different confidence contours. We analyze the contours physically. Also we examine the best fit of distance modulus for our theoretical models and the Supernovae Type Ia Union2 sample. For Brans Dicke theory of gravity the difference from the mainstream confidence contouring method of data analysis id that the confidence contours evolved are not at all closed contours like a circle or a ellipse. Rather they are found to be open contours allowing the free parameters to float inside a infinite region of parameter space. However, negative EoSs are likely to evolve from the best fit values.