Natural braneworld inflation in light of recent results from Planck and BICEP2

Abstract

In this paper we report on a major theoretical observation in cosmology. We present a concrete cosmological model for which inflation has a natural beginning and natural ending. Inflation is driven by a cosine-form potential, $V(\ensuremath{\phi})={\mathrm{\ensuremath{\Lambda}}}^{4}(1\ensuremath{-}\mathrm{cos}(\ensuremath{\phi}/f))$, which begins at $\ensuremath{\phi}\ensuremath{\lesssim}\ensuremath{\pi}f$ and ends at $\ensuremath{\phi}={\ensuremath{\phi}}_{\text{end}}\ensuremath{\lesssim}5f/3$. The distance traversed by the inflaton field $\ensuremath{\phi}$ is sub-Planckian. The Gauss-Bonnet term ${\mathcal{R}}^{2}$ arising as leading curvature corrections in the action $S=\ensuremath{\int}{d}^{5}x\sqrt{\ensuremath{-}{g}_{5}}{M}^{3}(\ensuremath{-}6\ensuremath{\lambda}{M}^{2}+R+\ensuremath{\alpha}{M}^{\ensuremath{-}2}{\mathcal{R}}^{2})+\ensuremath{\int}{d}^{4}x\sqrt{\ensuremath{-}{g}_{4}}({\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\phi}}}^{2}/2\ensuremath{-}V(\ensuremath{\phi})\ensuremath{-}\ensuremath{\sigma}+{\mathcal{L}}_{\text{matter}})$ (where $\ensuremath{\alpha}$ and $\ensuremath{\lambda}$ are constants and $M$ is the five-dimensional Planck mass) plays a key role to terminate inflation. The model generates appropriate tensor-to-scalar ratio $r$ and inflationary perturbations that are consistent with Planck and BICEP2 data. For example, for ${N}_{*}=50--60$ and ${n}_{s}\ensuremath{\sim}0.960\ifmmode\pm\else\textpm\fi{}0.005$, the model predicts that $M\ensuremath{\sim}5.64\ifmmode\times\else\texttimes\fi{}1{0}^{16}\text{ }\text{ }\mathrm{GeV}$ and $r\ensuremath{\sim}(0.14--0.21)$ [${N}_{*}$ is the number of $e$-folds of inflation and ${n}_{s}$ (${n}_{t}$) is the scalar (tensor) spectrum spectral index]. The ratio $\ensuremath{-}{n}_{t}/r$ is (13%--24%) less than its value in 4D Einstein gravity, $\ensuremath{-}{n}_{t}/r=1/8$. The upper bound on the energy scale of inflation ${V}^{1/4}=2.37\ifmmode\times\else\texttimes\fi{}1{0}^{16}\text{ }\text{ }\mathrm{GeV}$ ($r<0.27$) implies that $(\ensuremath{-}\ensuremath{\lambda}\ensuremath{\alpha})\ensuremath{\gtrsim}75\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}5}$ and $\mathrm{\ensuremath{\Lambda}}<2.17\ifmmode\times\else\texttimes\fi{}1{0}^{16}\text{ }\text{ }\mathrm{GeV}$, which thereby rule out the case $\ensuremath{\alpha}=0$ (Randall-Sundrum model). The true nature of gravity is holographic as implied by the braneworld realization of string and M theory. The model correctly predicts a late-epoch cosmic acceleration with the dark energy equation of state ${\mathrm{w}}_{\mathrm{D}E}\ensuremath{\approx}\ensuremath{-}1$.