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, $V(\phi)= \Lambda^4 (1-\cos(\phi/f))$, which begins at $\phi \lesssim \pi f$ and ends at $\phi =\phi_{ \text{ end}} \lesssim 5 f/3$. The distance traversed by the inflaton field $\phi$ is sub-Planckian. The Gauss-Bonnet term ${ \cal R}^2$ arising as leading curvature corrections in the action $S = \int d^5{ x} \sqrt{ -g_{ 5}} M^3 (- 6\lambda M^2 + R + \alpha M^{ -2} { \cal R}^2)+ \int d^{ 4}x \sqrt{ -g_{ 4}} (\dot{ \phi}^2/2 - V(\phi)- \sigma +{ \cal L}_{ \text{ matter}})$ (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 $N_*= 50-60$ 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 $(-\lambda \alpha) \gtrsim 75 \times 10^{ -5}$ 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 ${ \text w}_{ \text{ DE}}\approx -1$.
Categories: astro-ph.CO gr-qc hep-ph hep-th