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, $V(\varphi )={\Lambda }^4(1-\cos (\varphi /f))$, which begins at $\varphi \lesssim \pi f$ and ends at $\varphi ={\varphi }_{\text{end}}\lesssim 5f/3$. The distance traversed by the inflaton field $\varphi$ is sub-Planckian. The Gauss-Bonnet term ${\mathcal{R}}^2$ arising as leading curvature corrections in the action $S=\int d^{5}x\sqrt{-g_5}{M}^3(-6\lambda M^2+R+\alpha M^{-2}{\mathcal{R}}^2)+\int d^{4}x\sqrt{-g_4}({\dot{\varphi }}^2/2-V(\varphi )-\sigma +{\mathcal{L}}_{\text{matter}})$ (where $\alpha$ and $\lambda$ 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 results from Planck and BICEP2. For example, for $N_{\ast }=50-60$ and $n_s\sim 0.960\pm 0.005$, the model predicts that $M\sim 5.64\times 10^{16}\text{GeV}$ and $r\sim (0.14-0.21)$ [$N_{\ast }$ 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 $(-\lambda \alpha )\gtrsim 75\times 10^{-5}$ and $\Lambda <2.17\times 10^{16}\text{GeV}$, which thereby rule out the case $\alpha =0$ (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 ${\text{w}}_{\text{DE}}\approx -1$.

Comments: 13 pages, 14 figures; v2: minor changes, published version