^{1}

^{1}

^{3}.

In this letter, we explore a generalized model based on two scenarios including the Randall-Sundrum model and gravity model

According to the standard model of cosmology, the Planck Era refers to a time starting from the creation of the universe (about 14 billion years ago) until

Kaluza (1921) and Klein (1926) proposed the unified field theory of gravitation and electromagnetism, which needs an extra spatial dimension that is a function of the Planck length [

Randall and Sundrum [

In this model, the torsional metric in the five-dimensional space-time is defined according to the following:

Given the abovementioned explanations, we first study the Randall-Sundrum standard model. Then, we obtain the equations of the model by generalizing this model by adding a function

The equations of the gravitational field in general relativity are based on the interaction between the curvature of space-time and the energy density content of the universe. Other models have been proposed for gravity [

In the following, a brief overview of the abovementioned model is presented. We assume Planck constant, Boltzmann constant, and the speed of light as

In this subsection, we need to explain the compression mechanism of the Kaluza-Klein [

In the simplest case, assume a gravitational function in the form of

Considering the solution of vacuum equations in a five-dimensional space-time and (RS) type (II) model, which has only one mass within a five-dimensional bulk with positive energy density, it is concluded that the five-dimensional space-time is an anti-desitter (AdS) space. In the following, according to Randall model type II [

Another example of the generalized model based on the

An important feature of this model is the effect of geometry and the universe content through space-time torsion and trace of momentum-energy tensors, where

First, we transfer the five-dimensional space-time in which the gravity model is related to the scalar field and coupled with the additional dimension of space, into a four-dimensional space-time in a brane with a flat metric FLRW using the compression mechanism of the Kaluza-Klein. We have already investigated that in the gravity model

The universe scale factor for the inflation period (where

The equation of state

It is shown that inflation or the dark energy-dominated stage can be realized only by the effect of the torsion and trace energy-momentum tensor without the curvature. As a result, it can be interpreted that these models may be equivalent to the Kaluza-Klein and RS models without gravitational effects of the curvature but just due to those of the torsion and trace energy-momentum tensor in teleparallelism. Indeed, this is the new work on the concrete cosmological solutions to describe the cosmic accelerated expansion of the KK and RS models in

In this paper, a generalized gravity model was proposed based on the time-space torsion and interaction with the universe content. The study of this gravity model in a five-dimensional space according to the Randall-Sundrum approach included a four-dimensional brane in a five-dimensional bulk. In this regard, the Kaluza-Klein theory was used to compress the fifth dimension of space in this gravity model. Then, in accordance with the inflation period of the standard cosmological model, the new critical value for the energy density of the brane, the Hubble parameter, and the scale factor were obtained. Finally, it has been illustrated that, in

No data were used to support this study.

The authors declare that they have no conflicts of interest.