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

Abstract

We propose a scalar inflationary potential as $V(φ)=M^4φ^{2n-2}(φ^{2n}+m^{2n})^{1/n-1}$. This potetial similar to the shaft inflation one. The potential may come from the Higgs-dilaton potential in the Two-time (2T) physics, especially in the case where $n=3$, this suggests an explanation for the inflationary potential. Therefore, we call it shaft-warm inflation potential for short. The slow-roll scenario is recomputed in the 4-dimension (4D) and Randall-Sundrum II (RSII) frameworks. The tensor-to-scalar ratio in RSII is always higher than in 4D and is in good agreement with the experimental data of BICEP2 and Planck. When compared 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.

Figures (8)

• Figure 1: The shaft-warm-like inflaton potential with $n=2,3,4,5$.
• Figure 2: The $\phi(t)$ field in the standard 4D spacetime model with $n=2,3,4,5$, $M\simeq 10^{15}$ GeV, $M_4\simeq 10^{19}$ GeV, $m\simeq 10^{18}$ GeV, and $\phi_i\equiv 2\times 10^{19}$ GeV.
• Figure 3: The $\phi(t)$ field in the RSII model with $n=2,3$, $M\simeq 10^{15}$ GeV, $M_4\simeq 10^{19}$ GeV, $m\simeq 10^{18}$ GeV, and $\phi_i\equiv 2\times 10^{19}$ GeV.
• Figure 4: $M_5$ in the RSII model depends on $n$ with $A_s=2\times 10^{-9}$.
• Figure 5: The $r$ function depends on $N$ in the 4D model. From top to bottom, the lines correspond to $n=2,3,4,6,8$, respectively.