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 natural beginning and natural ending. Inflation is driven by a cosine-form potential, $V(ϕ)= Λ^4 (1-\cos(ϕ/f))$, which begins at $ϕ\lesssim πf$ and ends at $ϕ=ϕ_{\text{end}} \lesssim 5 f/3$. The distance traversed by the inflaton field $ϕ$ is sub-Planckian. The Gauss-Bonnet term ${\cal R}^2$ arising as leading curvature corrections in the action $S = \int d^5{x} \sqrt{-g_{5}} M^3 (- 6λM^2 + R + αM^{-2} {\cal R}^2)+ \int d^{4}x \sqrt{-g_{4}} (\dotϕ^2/2 - V(ϕ)- σ+{\cal L}_{\text{matter}})$ (where $α$ and $λ$ 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 results from Planck and BICEP2. For example, for $N_*= 50-60$ and $n_s\sim 0.960\pm 0.005$, the model predicts that $M\sim 5.64\times 10^{16}\,{\text{GeV}}$ and $r\sim (0.14-0.21)$ [$N_*$ is the number of {\it e}--folds of inflation and $n_s$ ($n_{t}$) is the scalar (tensor) spectrum spectral index]. The ratio $-n_t/r$ is (13% -- 24%) less than its value in 4D Einstein gravity, $-n_t/r=1/8$. The upper bound on the energy scale of inflation $V^{1/4}=2.37\times 10^{16}\,{\text{GeV}}$ ($r<0.27$) implies that $(-λα) \gtrsim 75 \times 10^{-5}$ and $Λ<2.17\times 10^{16}\,{\text{GeV}}$, which thereby rule out the case $α=0$ (Randall-Sundrum model). The true nature of gravity is holographic as implied by braneworld realization of string and M theory. The model correctly predicts a late epoch cosmic acceleration with the dark energy equation of state ${\text w}_{\text{DE}}\approx -1$.