Massive scalar states localized on a de Sitter brane

Abstract

We consider a brane scenario with a massive scalar field in the five-dimensional bulk. We study the scalar states that are localized on the brane, which is assumed to be de Sitter. These localized scalar modes are massive in general, their effective four-dimensional mass depending on the mass of the five-dimensional scalar field, on the Hubble parameter in the brane and on the coupling between the brane tension and the bulk scalar field. We then introduce a purely four-dimensional approach based on an effective potential for the projection of the scalar field in the brane, and discuss its regime of validity. Finally, we explore the quasi-localized scalar states, which have a non-zero width that quantifies their probability of tunneling from the brane into the bulk.

Scalar particles mass spectrum and localization on FRW branes embedded in a 5D de Sitter bulk

“…The derived scale function and warp factor are employed in the five-dimensional Klein-Gordon equation describing the massive scalar field whose wave function will depend on the cosmic time and on the extra-dimension. Our results agree with those obtained by Langlois and Sasaki [23], who considered a test scalar field on a given background configuration and solved the Klein-Gordon equation in the bulk. They found an interesting relationship between the effective four-dimensional mass of the scalar states localized on the de Sitter brane and the five-dimensional mass.…”

Local conservation law and dark radiation in cosmological braneworld

“…From Eqs. (2.8), we readily see the local mass corresponding toS a is given by [16] 11) where the factor 3/2 in the original expression forS a is eliminated for later convenience. Alternatively, corresponding to S a , we have another local mass that excludes the contribution of the bulk cosmological constant, 12) In what follows, we focus on the matter part M , rather than on the whole massM .…”

“…In the bulk inflaton model with a quadratic potential [9][10][11][12], it has been shown that the bulk scalar field projected on the brane behaves exactly like a 4-dimensional field in the low energy limit, H 2 ℓ 2 ≪ 1, where H is the Hubble parameter of the brane, and the leading order correction gives the gradual energy loss from the scalar field to the bulk, giving rise to the dark radiation term [9,11]. Here, we discuss the relation between the dark radiation term appearing in this effective 4-dimensional description and the generalized dark radiation term given by the local mass in the bulk.…”

Coupled bulk and brane fields about a de Sitter brane

“…Since the coefficients in front the Legendre functions in (29) vanish when m = 0 and ω = −3i/2, it is possible to linearise the resonance condition about the zero mode solution (55). In particular, we can take…”

“…These match the various bound state criteria obtained for a massive scalar field about a de Sitter brane in Refs. [27,28,29] (up to trivial differences in notation).…”