Hamilton-Jacobi formalism for tachyon inflation

Tachyon inflation is reconsidered by using the recent observational data obtained from Planck-2013 and BICEP2. The Hamilton-Jacobi formalism is picked out as a desirable approach in this work, which allows one to easily obtain the main parameters of the model. The Hubble parameter is supposed as a power-law and exponential function of the scalar field, and each case is considered separately. The constraints on the model, which come from observational data, are explained during the work. The results show a suitable value for the tensor spectral index and an appropriate form of the potential.

Figure 1

The potential for different values of the number of $e$-folds and scalar spectral index as $n_s=0.9528$ (solid line), 0.9541 (large-dashed line), and 0.9554 (dotted line). The vertical axis indicates the potential ($\times {10}^{-45}$), and the horizon axis denotes the scalar field ($\times {10}^{-4}$). (a) Potential for $\mathrm{N}=55$; (b) Potential for $\mathrm{N}=60$; (c) Potential for $\mathrm{N}=65$.

Figure 2

The potential for different values of the number of the scalar spectral index as $n_s=0.9528$ (solid line), 0.9611 (large-dashed line), and 0.9675 (dotted line). The vertical axis indicates the potential ($\times {10}^{-64}$), and the horizon axis denotes the scalar field ($\times {10}^{-14}$). (a) Potential for ${\mathcal{H}}_2^2={10}^{30}$; (b) Potential for ${\mathcal{H}}_2^2={10}^{31}$; (c) Potential for ${\mathcal{H}}_2^2={10}^{32}$.