Modified Friedmann Equation and Inflation in Warped Codimension-two Braneworld

TL;DR

This paper investigates the modified Friedmann equations in warped codimension-two braneworlds, revealing new static solutions, stability conditions, and implications for inflationary cosmology, including potential deviations from standard inflation predictions.

Contribution

It introduces new static solutions and stability analysis for warped codimension-two braneworlds, and explores their impact on inflationary predictions and cosmological constraints.

Findings

Two static solutions exist for 1<α<5, merging at a maximum Hubble rate.

The higher H branch is unstable, even with radion stabilization.

For α>5, the model is stable and can produce nonstandard inflationary predictions.

Abstract

We study the Friedmann equation for the warped codimension-two braneworld background which most closely resembles the Randall-Sundrum model. Extra matter on the (Planck) 4-brane, with equation of state p_\theta=(\alpha-1)\rho for the azimuthal pressure, is required to satisfy the junction conditions. For 1 < \alpha < 5, we show that there are two static solutions to the Einstein equations for given values of the brane stress-energies. Close to the static solutions, the relation between Hubble expansion rate H and brane tension reproduces the standard 4D result for small H, but exhibits unusual deviations when H is of order the AdS curvature scale. The two static branches for 1 <\alpha < 5 are shown to come together smoothly at a maximum value of H; however the radion is shown to be unstable in the branch with higher H. This remains true even with a mechanism for stabilization of the radion, i.e., the Goldberger-Wise (GW) mechanism, since large enough H overcomes the force of stabilization. Even in the unstabilized case, cosmological constraints on the time and spatial variation of Newton's constant are typically satisfied; only fifth force constraints require the stabilization. For \alpha > 5 the model is intrinsically stable, without the need for a GW field, and in this case we show that inflationary predictions can be modified by the nonstandard Friedmann equation; in particular it is possible to get an upper limit on the spectral index, large deviations from the consistency condition between the tensor spectrum and ratio r, and large running of the spectral index even though the slow roll parameters remain small.