BPS brane cosmology in 𝒩 = 2 supergravity

Abstract

We study the embedding of flat BPS 3-branes in five dimensional N = 2 supergravity theory.We derive the branes' dynamical equations as well as general expressions for the hypermultiplet fields then focus on a single brane and study its time evolution. It is shown that the brane's Hubble parameter correlates with the moduli of the underlying manifold's complex structure.For certain particular solutions, the moduli seem to exhibit an instability; being large valued at early times then rapidly decaying to either zero or some convergent constant value. The possibility of extending these results to the cosmology of our universe is implied and briefly discussed. Our results are in line with the production and decay of heavy moduli in the early universe, as is currently believed in the literature.

Brane-worlds and the Calabi–Yau complex structure moduli

“…In fact, it is unclear in the literature how an action can be constructed that will give ( 22) 2 , it follows that it is also unclear how to couple the density and pressure parameters ρ and p to the SUSY fermions. As such what we have here is a deformation of what is essentially a supersymmetric model in the case of the vacuous brane [8] and is thus not exactly supersymmetric. Fixing this problem requires the inclusion of the brane's matter content in the action of the theory and deriving a new set of variation equations with extra terms.…”

“…This metric may be interpreted as representing a single 3-brane located at y = 0 in the transverse space. Either way, we will focus, as was similarly done in [8], on the four dimensional (t, r, θ, φ) dynamics of a single brane, effectively evaluating the warp functions at a specific, but arbitrary, y value. This approach was shown to be a consistent one in [25], where the authors called it the 'thin brane' approximation (also see [26] and [27]); i.e.…”

“…As we will see, this norm is not positive-definite; in fact it has a negative value for all times in most of the cases considered. Analysis of the field equations ( 7), (9), and (10) (continuing from [8]) leads to the following results: For the dilaton:…”

Interpreting the cosmic history of the Universe through five-dimensional supergravity

“…We have explored this embedding in two earlier papers. In the first [18] an 'empty' brane-world was analytically studied, and a correlation between the dynamics of the brane, i.e. the time evolution of the scale factors, was found.…”

“…It is worth mentioning that in a previous work of one of us, a similar model has been explored but the brane was vacuous [18], so it was considered a toy model of our universe. In a further study [19] we investigated a brane filled with dust and radiation separately and only the inflation era of the universe has been considered.…”