We give a full nonlinear numerical treatment of time-dependent 5D braneworld geometry, which is determined self-consistently by potentials for the scalar field in the bulk and at two orbifold branes, supplemented by boundary conditions at the branes. We describe the BRANECODE, an algorithm which we designed to solve the dynamical equations numerically. We apply the BRANECODE to braneworld models and find several novel phenomena of the brane dynamics. Starting with static warped geometry with de Sitter branes, we find numerically that this configuration is often unstable due to a tachyonic mass of the radion during inflation. If the model admits other static configurations with lower values of de Sitter curvature, this effect causes a violent restructuring towards them, flattening the branes, which appears as a lowering of the 4D effective cosmological constant. Braneworld dynamics can often lead to brane collisions. We find that, in the presence of the bulk scalar field, the 5D geometry between colliding branes approaches a universal, homogeneous, anisotropic strong gravity Kasner-like asymptotic, irrespective of the bulk or brane potentials. The Kasner indices of the brane directions are equal to each other but different from that of the extra dimension.

Braneworld models in extra dimensions can be tested in laboratory by the coupling of the radion to the standard model fields. The identification of the radion as a canonically normalized field involves a careful general relativity treatment: if a bulk scalar is responsible for the stabilization of the system, its fluctuations are entangled with the perturbations of the metric and they also have to be taken into account (similarly to the well-developed theory of scalar metric perturbations in 4D cosmology with a scalar field). Extracting a proper dynamical variable in a warped geometry/scalar setting is a nontrivial task, performed so far only in the limit of negligible backreaction of the scalar field on the background geometry. We perform the general calculation, diagonalizing the action up to second order in the perturbations and identifying the physical eigenmodes of the system for any amplitude of the bulk scalar. This computation allows us to derive a very simple expression for the exact coupling of the eigenmodes to the standard model fields on the brane, valid for an arbitrary background configuration. As an application, we discuss the Goldberger-Wise mechanism for the stabilization of the radion in the Randall-Sundrum-type models. The existing studies, limited to small amplitude of the bulk scalar field, are characterized by a radion mass which is significantly below the physical scale at the observable brane. We extend them beyond the small backreaction regime. For intermediate amplitudes, the radion mass approaches the electroweak scale, while its coupling to the observable brane remains nearly constant. At very high amplitudes, the radion mass instead decreases, while the coupling sharply increases. Severe experimental constraints are expected in this regime.

Abstract. Kaluza-Klein compactifications with four-dimensional inflationary geometry combine the attractive idea of higher dimensional models with an attempt to incorporate four-dimensional early-time or late-time cosmology. We analyze the mass spectrum of cosmological perturbations around such compactifications, including the scalar, vector and tensor sector. Whereas scalar perturbations were discussed before, the spectrum of vector and tensor perturbations is a new result of this paper. Moreover, the complete analysis shows that possible instabilities of such compactifications are restricted to the scalar sector. The mass squares of the vector and tensor perturbations are all non-negative. We discuss form fields with a non-trivial background flux in the extra space as matter degrees of freedom. They provide a source of scalar and vector perturbations in the effective four-dimensional theory. We analyze the perturbations in Freund-Rubin compactifications. Although it can only be considered as a toy model, we expect the results to qualitatively generalize to similar configurations. We find that there are two possible channels of instabilities in the scalar sector of perturbations, whose stabilization has to be addressed in any cosmological model that incorporates extra dimensions and form fields. One of the instabilities is associated with the perturbations of the form field.

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