On Einstein equations with cosmological constant in braneworld models

Abstract

In this paper, we investigate the Einstein equations with cosmological constant for Randall-Sundrum (RS) and Dvali-Gabadadze-Porrati (DGP) models to determine the warp functions in the context of warp product spacetimes. In RS model, it is shown that Einstein's equation in the bulk is reduced into the brane as a vacuum equation, having vacuum solution, which is not affected by the cosmological constant in the bulk. In DGP model, it is shown that the Einstein's equation in the bulk is reduced into the brane and along the extra dimension, where both equations are affected by the cosmological constant in the bulk. We have solved these equations in DGP model, subject to vanishing cosmological constants on the brane and along extra dimension, and obtained exact solutions for the warp functions. The solutions depend on the typical values of cosmological constant in the bulk as well as the dimension of the brane. So, corresponding to the typical values, some solutions have exponential behaviours which may be set to represent warp inflation on the brane, and some other solutions have oscillating behaviours which may be set to represent warp waves or branes waves along the extra dimension.

Charged Taub-NUT-de Sitter spacetime in DGP braneworld and its thermodynamics*

“…In this chapter, we review the action and equations of motion associated with the DGP brane model. In the presence of sources, DGP gravitational action takes the form [9]…”

“…So far, we have shown that the resulting spacetime metric on the brane is simply a family of RNTNdS type solutions in Einstein-Maxwell theory with the cosmological constant. However, in the corresponding equation of motion (9), there is a second rank tensor , which originates from the projection of the five-dimensional Weyl…”

“…By assuming the existence of this second rank tensor , we can accept that the above metric and vector solution obey the Einstein equation, (9).…”

“…There are several braneworld gravity models in literature, for example, the Horava-Witten [6], Arkani Hamed-Dimopoulos-Dvali (ADD) [7], Randall-Sundrum (RS) [8], and Dvali-Gabadadze-Porrati (DGP) [9] models. The DGP model, which is the topic of investigation in this study, has several interesting properties in regards to astronomical observations.…”