Holographic RG and Cosmology in Theories with Quasi-Localized Gravity

TL;DR

This paper develops a holographic renormalization group framework to analyze brane-worlds with quasi-localized gravity (GRS-type models). It shows that at intermediate scales gravity is effectively 4D due to a graviton resonance, while at very large scales it becomes 5D with a radion-driven scalar anti-gravity; the large-distance theory is holographically dual to the DGP model with a tensionless brane and an induced $R^{(4)}$ term. The radion on the tensionless brane is ghost-like, canceling extra graviton polarizations at intermediate scales but driving scalar anti-gravity at long distances, signaling potential instabilities. The analysis yields explicit propagator results, clarifies the intermediate-scale crossover to DGP, and discusses cosmological implications, albeit with limitations due to radion-induced instabilities. Overall, holographic RG provides a practical tool to connect GRS-type quasi-localized gravity to DGP-like IR physics and to explore deviations from standard FRW cosmology on the largest scales.

Abstract

We study the long distance behaviour of brane theories with quasi-localized gravity. The 5D effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar anti-gravity. The holographic description shows that at large distances the GRS model is equivalent to the model recently proposed by Dvali, Gabadadze and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghost-like field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic RG can be used as a practical tool for calculations.

Figures (2)

• Figure 1: (a) The GRS brane set-up and warp factor. (b) Brane translation associated with the holographic RG running.
• Figure 2: The holographic RG: the Planck brane is translated to $\tilde{y}$ and identified with the image brane at $-\tilde{y}$.