  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 ${\text
w}_{\text{DE}}\approx -1$.
