Natural braneworld inflation in light of recent results from Planck and BICEP2

In this paper we report on a major theoretical observation in cosmology. We present a concrete cosmological model for which inflation has a natural beginning and natural ending. Inflation is driven by a cosine-form potential, V(phi) = A(4)(1 - cos(phi/f)), which begins at phi less than or similar to pi f and ends at phi = phi(end) less than or similar to 5f/3. The distance traversed by the inflaton field phi is sub-Planckian. The Gauss-Bonnet term R-2 arising as leading curvature corrections in the action S = integral d(5)x root-g(5)M(3) (-6 lambda M-2 + R + alpha(M-2R2)) + integral d(4)x root-g(4)(phi(2)/2 - V(phi) - sigma + L-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 Planck and BICEP2 data. For example, for N-* = 50-60 and n(s) similar to 0.960 +/- 0.005, the model predicts that M similar to 5.64 x 10(16) GeV and r similar to (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 x 10(16) GeV (r < 0.27) implies that (-lambda alpha) greater than or similar to 75 x 10(-5) and Lambda < 2.17 x 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(DE) approximate to -1.