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 } \left ( 1 - \cos ( \phi / f ) \right ) , which begins at \phi \lesssim \pi f and ends at \phi = \phi _ { 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 _ { \lower 2.0 pt \hbox { $ \scriptstyle 5 $ } } } M ^ { 3 } \left ( -6 % \lambda M ^ { 2 } + R + \alpha M ^ { -2 } { \cal R } ^ { 2 } \right ) + \int d ^ { 4 } x \sqrt { - g _ { \lower 2 % .0 pt \hbox { $ \scriptstyle 4 $ } } } \left ( \dot { \phi } ^ { 2 } / 2 - V ( \phi ) - \sigma + { \cal L } _ { % \text matter } \right ) ( 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 Planck and BICEP2 data .
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 } { GeV } and r \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 - 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 } { GeV } ( r < 0.27 ) implies that ( - \lambda \alpha ) \gtrsim 75 \times 10 ^ { -5 } and \Lambda < 2.17 \times 10 ^ { 16 } { GeV } , which thereby rule out the case \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 { w } _ { \lower 2.0 pt \hbox { $ \scriptstyle \text DE$ } } \approx - 1 .