^{1}

^{2}

^{1}

^{2}

A review on spatially flat D-dimensional Friedmann-Robertson-Walker (FRW) model of the universe has been performed. Some standard parameterizations of the equation of state parameter of the dark energy models are proposed and the possibilities of finite time future singularities are investigated. It is found that certain types of these singularities may appear by tuning some parameters appropriately. Moreover, for a scalar field theoretic description of the model, it was found that the model undergoes bouncing solutions in some favorable cases.

In order to avoid the initial singularity problem [

On the other hand, various cosmological observations indicate the current cosmic acceleration ([

The reconstruction problem for dark energy is reviewed in [

The paper is organized as follows. In Section

We consider the D-dimensional spatially flat Friedmann-Robertson-Walker universe, given by [

where

Here

By considering scalar field

where

The scalar potential associated with the field is given by

In the next subsections, we will investigate the scalar field and its potential in different well-known parameterization models. A detailed review of different dark energy models can be found in [

Here we assume the linear equation of state [

Here

Then (

which on further integration gives rise to the scalar field as

where

We draw the variations of energy density

(a), (b), (c), (d), (e), and (f) show the variation of energy density

In the Chevallier-Polarski-Linder (CPL) parameterization model, the equation of state is given by [

We draw the variations of energy density

(a), (b), (c), (d), (e), and (f) show the variation of energy density

For the Jassal-Bagla-Padmanabhan (JBP) parameterization model, the equation of state changes to [

We draw the variations of energy density

(a), (b), (c), (d), (e), and (f) show the variation of energy density

In the Alam-Sahni-Saini-Starobinsky (ASSS) parameterization model, the equation of state parameter has the expression [

where,

We draw the variations of energy density

(a), (b), (c), (d), (e), and (f) show the variation of energy density

Here, in Efstathiou parametrization model, the equation of state takes the form [

We draw the variations of energy density

(a), (b), (c), (d), (e), and (f) show the variation of energy density

The future singularities can be classified in the following ways [

Type I (big rip): for

Type II (sudden): for

Type III:

Type IV: for

where

Table

Singularity/Model | Linear | CPL | JBP | ASSS | Efstathiou |
---|---|---|---|---|---|

Type I (Big Rip) | | | | No | |

Type II (Sudden) | No | No | No | No | No |

Type III | No | No | No | No | No |

Type IV | No | No | No | | No |

The initial singularity in the cosmological models can be avoided by introducing the nonsingular bouncing models. In these models, a universe undergoing a “bounce” stage attains a minimum after a collapsing phase and then subsequently expands. During the collapse, the scale factor

In the current study, the bouncing universe can be viewed in different parameterizing models from Figures

(a) and (b) (linear), (c) and (d) (CPL), (e) and (f) (JBP), (g) and (h) (ASSS), and (i) and (j) (Efstathiou) show the variation of scale factor

In this work, we have considered the D-dimensional flat FRW model of the universe in the background of some well-known parametrization of dark energy models like linear, CPL, JBP, ASSS, and Efstathiou. By considering the scalar field model as these parametrizations of dark energy, we found the energy density, pressure, scalar field, and corresponding potential in terms of the redshift

In model II (CPL), we have drawn the variations of energy density

In model III (JBP), we have drawn the variations of energy density

In model IV (ASSS), we have drawn the variations of energy density

In model V (Efstathiou), we have drawn the variations of energy density

Also the present work is designed to investigate the possibilities of finite time future singularities, that is, types I (big rip), II (sudden), III, and IV singularities. From Table

The data used to support the findings of this study are included within the article in the references and therein.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The authors are thankful to IUCAA, Pune, for their warm hospitality where most of the work has been done during a visit under the Associateship Programme.