Gauss-Bonnet assisted braneworld inflation in light of BICEP2 and Planck data

Abstract

Motivated by the idea that quantum gravity corrections usually suppress the power of the scalar primordial spectrum (E-mode) more than the power of the tensor primordial spectrum (B-mode), in this paper we construct a concrete gravitational theory in five-dimensions for which $V(\ensuremath{\phi})\ensuremath{\propto}{\ensuremath{\phi}}^{n}$-type inflation ($n\ensuremath{\ge}1$) generates an appropriate tensor-to-scalar ratio that may be compatible with the BICEP2 and Planck data together. The true nature of gravity is five-dimensional and described by the action $S=\ensuremath{\int}{d}^{5}x\sqrt{|g|}{M}^{3}(\ensuremath{-}6\ensuremath{\lambda}{M}^{2}+R+\ensuremath{\alpha}{M}^{\ensuremath{-}2}{\mathcal{R}}^{2})$ where $M$ is the five-dimensional Planck mass and ${\mathcal{R}}^{2}={R}^{2}\ensuremath{-}4{R}_{ab}{R}^{ab}+{R}_{abcd}{R}^{abcd}$ is the Gauss-Bonnet (GB) term. The five-dimensional ``bulk'' spacetime is anti-de Sitter ($\ensuremath{\lambda}<0$) for which inflation ends naturally. The effects of ${\mathcal{R}}^{2}$ term on the magnitudes of scalar and tensor fluctuations and spectral indices are shown to be important at the energy scale of inflation. For GB-assisted ${m}^{2}{\ensuremath{\phi}}^{2}$-inflation, inflationary constraints from BICEP2 and Planck, such as, ${n}_{s}\ensuremath{\simeq}\phantom{\rule{0ex}{0ex}}0.9603(\ifmmode\pm\else\textpm\fi{}0.0073)$, $r=0.16(+0.06\ensuremath{-}0.05)$ and ${V}_{*}^{1/4}\ensuremath{\gtrsim}1.5\ifmmode\times\else\texttimes\fi{}1{0}^{16}\text{ }\text{ }\mathrm{GeV}$ are all satisfied for $(\ensuremath{-}\ensuremath{\lambda}\ensuremath{\alpha})\ensuremath{\simeq}\phantom{\rule{0ex}{0ex}}(3\ensuremath{-}300)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}5}$.