Observational test of holographic inflation

Abstract

Observational consequences of inflationary cosmology in the holographic dual of the Randall-Sundrum type II braneworld scenario, as motivated by the anti-de Sitter/conformal field theory correspondence, are investigated. High energy corrections to the standard four-dimensional Friedmann equation induce a corresponding modification to the form of the single-field inflationary consistency equation based on Einstein gravity. The degree of departure from the standard expression is determined by the ratio, $r$, of the primordial tensor and scalar perturbation amplitudes and the coefficient, $c$, of the conformal anomaly in the dual gauge theory. It is found that a necessary condition for detecting such a correction with the next generation of cosmic microwave background (CMB) polarization experiments is that $r\ensuremath{\ge}0.06$. The bound is tightened to $r>0.3$ for values of the central charge that are compatible with known compactifications of type IIB string theory as parametrized in terms of $F$-theory compactification on Calabi-Yau four-folds. This is close to the present upper bounds inferred from combined observations of the CMB anisotropy power spectrum and high redshift surveys. We conclude that if such modifications to the inflationary consistency equation are to be observable, the gravitational wave background should be detected in the near future. A further consequence of the nonstandard dynamics at high energies is that the initial state of the universe is a quiescent singularity with a finite density and pressure.