Inflation with the standard and Randall-Sundrum model in the Two-time Physics

We propose a scalar inflationary potential as $V(\phi)=M^4\phi^{2n-2}(\phi^{2n}+m^{2n})^{1/n-1}$. This potential is similar to the shaft inflation one. However, they satisfy the $Z_2$ symmetry for all $n$. The potential may come from the Higgs-dilaton potential in the two-time (2T) physics. The slow-roll scenario is recomputed in the 4-dimension (4D) and Randall-Sundrum II (RSII) frameworks. The tensor-to-scalar ratio in the RSII model is always higher than in the 4D model and is in good agreement with the experimental data of BICEP2 and Planck. Comparing this with Planck data, we estimate $M_5$ to be around $[1-2]\times 10^{16}$ GeV. Furthermore, the potential allows much lower scalar field exponents than other potentials, which results in high agreement with experimental data. Moreover, the results also reinforce the models that have the extra dimensions, should be focused. The inflation data can be used to test for the existence of the extra dimensions.