Tachyon constant-roll inflation

The constant-roll inflation is studied where the inflaton is taken as a tachyon field. Based on this approach, the second slow-roll parameter is taken as a constant which leads to a differential equation for the Hubble parameter. Finding an exact solution for the Hubble parameter is difficult and leads us to a numerical solution for the Hubble parameter. On the other hand, since in this formalism the slow-roll parameter $\eta$ is constant and could not be assumed to be necessarily small, the perturbation parameters should be reconsidered again which, in turn, results in new terms appearing in the amplitude of scalar perturbations and the scalar spectral index. Utilizing the numerical solution for the Hubble parameter, we estimate the perturbation parameter at the horizon exit time and compare it with observational data. The results show that, for specific values of the constant parameter $\eta$, we could have an almost scale-invariant amplitude of scalar perturbations. Finally, the attractor behavior for the solution of the model is presented, and we determine that the feature could be properly satisfied.

Figure 1

The Hubble parameter versus the tachyon field.

Figure 2

The behavior of the slow-roll parameters $\epsilon$ and $\delta$ during the inflationary times versus tachyon field.

Figure 3

The tachyon field potential versus the field in the inflationary times.

Figure 4

The time derivative of the tachyon field versus the field is plotted during the inflation.

Figure 5

The slow-roll parameters $\epsilon$ versus tachyon field during inflation.

Figure 6

The behavior of (a) scalar spectral index and (b) tensor-to-scalar ratio versus the tachyon field during the inflationary times.

Figure 7

The $r-n_s$ diagram.

Figure 8

(a) The Hubble parameter and (b) the potential versus tachyon field during inflation.

Figure 9

(a) The time derivative of tachyon field, and (b) the behavior of the slow-roll parameter $\epsilon$ are plotted versus the field during the inflation.

Figure 10

The behavior of the parameter $\eta$ are plotted versus the field during the inflation.

Figure 11

(a) The scalar spectral index, and (b) the tensor-to-scalar ratio versus the tachyon field during the inflationary times.

Figure 12

The $r-n_s$ diagram of the model.

Figure 13

(a) The Hubble parameter, and (b) the potential of scalar field are plotted versus the field during the inflation.

Figure 14

Behavior of the integrand, $\frac{9}{2}\frac{H^3(T)}{H^{\prime }(T)}$, in terms of tachyon field during inflation for (a) first case related to Sec. 4; (b) second case related to Sec. 5.

Figure 15

For the first case: (a) The equation of state parameter and (b) acceleration of the Universe versus scalar field. Figures (c) and (d) show, respectively, the same parameters for the second case.