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

TL;DR

This paper explores higher derivative gravity in brane-world cosmology within AdS/CFT, revealing conditions for inflationary and hyperbolic brane universes, and highlights quantum effects' role in universe creation.

Contribution

It analyzes brane-world cosmology in higher derivative gravity, especially in the context of AdS/CFT duality, including quantum effects and their impact on universe evolution.

Findings

Inflationary brane universe does not occur for SG dual in classical theory.

Hyperbolic brane universe can occur in higher derivative gravity.

Quantum effects can induce inflationary or hyperbolic brane universes even for SG dual.

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.