Parametrizations of dark energy models in the background of general non-canonical scalar field in D-dimensional fractal universe

Ujjal Debnath,Kazuharu Bamba

doi:10.1140/epjc/s10052-019-7172-y

Abstract

We have explored non-canonical scalar field model in the background of non-flat D-dimensional fractal Universe on the condition that the matter and scalar field are separately conserved. The potential V, scalar field phi , function f, densities, Hubble parameter and deceleration parameter can be expressed in terms of the redshift z and these depend on the equation of state parameter w_{phi }. We have also investigated the cosmological analysis of four kinds of well known parametrization models. In graphically, we have analyzed the natures of potential, scalar field, function f, densities, the Hubble parameter and deceleration parameter. As a result, the best fitted values of the unknown parameters (w_{0},w_{1}) of the parametrization models due to the joint data analysis (SNIa+BAO+CMB+Hubble) have been found. Furthermore, the minimum values of chi ^{2} function have been obtained. Also we have plotted the graphs for different confidence levels 66%, 90% and 99% contours for (w_{0},~w_{1}) by fixing the other parameters.

Highlights

Motivated by high energy physics, the scalar field models play an significant role to explain the nature of dark energy (DE) due to its simple dynamics [52,53]
Model I (Linear): For this model, using SNIa+baryonic acoustic oscillations (BAO)+ Cosmic Microwave Background (CMB)+Hubble joint analysis, we found the minimum value of χT2ot = 7.104 and the best fit values of the parameters w0 = −0.738 and w1 = 0.174 where we have fixed the other parameters β = −0.5, D = 5, wm = −0.3, ω = 0.2, v0 = 0.5, f0 = 2, n = 3, m0 = 0.3, k0 = 0.05 and H0 = 72 km s−1 MPc−1
We have studied non-canonical scalar field model in the non-flat D-dimensional fractal Universe on the condition that the matter and scalar field are separately conserved

Summary

Introduction

Motivated by high energy physics, the scalar field models play an significant role to explain the nature of DE due to its simple dynamics [52,53]. We will consider noncanonical scalar field model with general form of k-essence Lagrangian [58,59,60,61,62,63,64]. We consider the non-canonical scalar field model in the background of effective fractal spacetime. In the general form of non-canonical scalar field model, the Lagrangian density can be expressed as [58,63]. For f (φ) = 1, it reduces to particular form of general non-canonical scalar field model [55]. From Eq (20), we obtain the potential function as sider different well known parameterization forms of wφ(z) and investigate the natures of Hubble parameter, deceleration parameter, scalar field and its potential in different models

Model I : linear parameterization

Model IV

Data fittings and numerical results

Discussions and concluding remarks