Energy from the Bulk through Parametric Resonance

We demonstrate that energy can be transferred very rapidly from the bulk to the brane through parametric resonance. In a simple realization, we consider a massless bulk field that interacts only with fields localized on the brane. We assume an initial field configuration that has the form of a wave-packet moving towards the brane. During the reflection of the wave-packet by the brane the localized fields can be excited through parametric resonance. The mechanism is also applicable to bulk fields with a potential. The rapid energy transfer can have important cosmological and astrophysical implications. PACS numbers: 11.10.Kk, 04.50, 98.80.Cq Introduction: The idea that our Universe is a defect embedded in a higher-dimensional bulk space is old [1]. The Randall-Sundrum model [2] provides a realization of this idea. The defect is a four-dimensional hypersurface (a 3-brane) in a five-dimensional bulk with negative cosmological constant (AdS space). The geometry is non-trivial (warped) along the fourth spatial dimension, so that an effective localization of low-energy gravity takes place near the brane. The matter is assumed to be concentrated only on the brane. For low matter densities the cosmological evolution on the brane becomes typical of a Friedmann-Robertson-Walker Universe [3, 4]. Of particular interest in the scenario of a brane Universe is the possibility of exchange of energy between the defect and the bulk space. For this to occur the bulk must contain some matter component in addition to the negative cosmological constant. The presence of matter in the bulk affects the expansion on the brane. For an observer on the brane the modification can be attributed to “mirage” matter components [5]. The energy exchange can modify the cosmological evolution as well [6]. In particular, the energy transfer from the bulk to the brane can lead to periods of accelerated expansion on the brane [7]. In this letter we concentrate on the mechanism that can lead to a rapid energy transfer from the bulk to the brane. We omit the gravitational effects and study a simplified system that consists of a flat five-dimensional bulk space with a four-dimensional brane as its boundary. In the bulk we assume the presence of a field that interacts only with fields localized on the brane. Our aim is to demonstrate that energy can be transferred very efficiently from the bulk to the brane fields through a process that resembles very strongly the parametric resonance [8, 9]. The incorporation of gravitational effects is technically complicated and will be left for a future publication. The model: We consider a massless bulk field φ that interacts with a field χ localized on the brane. We neglect gravitational effects and assume that the system is described by the action S = ∫