Brane-World Cosmology in Higher Derivative Gravity or Warped Compactification in the Next-to-leading Order of AdS/CFT Correspondence

TL;DR

This work investigates brane-world cosmologies within five-dimensional higher-derivative gravity with an AdS$_5$ bulk, examining how boundary geometry choices ($S^4$, $H^4$, or $R^4$) and surface counterterms constrain viable brane solutions. A key insight is that next-to-leading order AdS/CFT corrections, exemplified by the SG dual of a $\ obreakspace\mathcal{N}=2$ $Sp(N)$ SCFT, can qualitatively alter classical results: spherical branes may be forbidden while hyperbolic branes become possible, and quantum brane matter as captured by the anomaly-induced action can induce inflationary or hyperbolic branes even when classical analysis forbids them. The analysis blends direct HD gravity dynamics with holographic RG interpretations, showing that conformal anomalies on the brane can dynamically generate warped compactifications and small-rate inflation in a controlled AdS/CFT framework. The findings highlight the crucial role of brane quantum matter and next-to-leading order effects in shaping brane-world cosmologies and offer a platform for exploring graviton trapping, dilatonic extensions, and more general bulk geometries.

Abstract

The general model of higher derivative (HD) gravity is considered. The search of brane-world cosmology in such theory is presented when bulk is d5 AdS and boundary is spherical, hyperbolic or flat (single) brane. It is found the wide range of theory parameters where such cosmology may be realized. Special attention is paid to the version of HD theory representing SG dual of ${\cal N}=2$ $Sp(N)$ SCFT (in next-to-leading order of large $N$ expansion). In particular, it is shown that inflationary brane Universe does not occur for SG dual while hyperbolic brane occurs (which was not possible in leading order). The quantum effects of CFT living on the brane (via the corresponding conformal anomaly induced effective action) may qualitatively change the results of classical analysis. There appears inflationary (or hyperbolic) brane Universe induced by only quantum effects. In AdS/CFT correspondence (next-to-leading order) the addition of such CFT effective action (in some energy region) is naturally explained in terms of holographic renormalization group. It results in the possibility of quantum creation of inflationary brane Universe (with small rate) even for SG dual.