Defining perturbations on submanifolds

Abstract

We study the definition of perturbations in the presence of a submanifold, like e.g. a brane. In the standard theory of cosmological perturbations, one compares quantities at the same coordinate points in the non-perturbed and the perturbed manifolds, identified via a (non-unique) mapping between the two manifolds. In the presence of a physical submanifold one needs to modify this definition in order to evaluate perturbations of quantities at the submanifold location. As an application, we compute the perturbed metric and the extrinsic curvature tensors at the brane position in a general gauge.

9 pages, 2 figures, Revtex4

References in corpus (9)

• Cosmology and Brane Worlds: A Review
• Brane cosmology: an introduction
• On Brane World Cosmological Perturbations
• Cosmological perturbations in the bulk and on the brane
• Gravity waves from inflating brane or Mirrors moving in adS${}_5$
• Bulk Gravitational Field and Cosmological Perturbations on the Brane
• Cosmological Perturbations Through a General Relativistic Bounce
• Transdimensional physics and inflation
• (1+3) Covariant Dynamics of Scalar Perturbations in Braneworlds

Cited by in corpus (3)

• Scalar perturbations from brane-world inflation
• First and Second Order Perturbations of Hypersurfaces
• Models for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation