Thermal inflation with a thermal waterfall scalar field coupled to a light spectator scalar field

A new model of thermal inflation is introduced, in which the mass of the thermal waterfall field is dependent on a light spectator scalar field. Using the $\delta N$ formalism, the “end of inflation” scenario is investigated in order to ascertain whether this model is able to produce the dominant contribution to the primordial curvature perturbation. A multitude of constraints are considered so as to explore the parameter space, with particular emphasis on key observational signatures. For natural values of the parameters, the model is found to yield a sharp prediction for the scalar spectral index and its running, well within the current observational bounds.

Figure 1

The potential given by Eq. (2.5).

Figure 2

Values of $N_{*}$ and $N_{\mathrm{TI}}$ in our model, with ${\mathrm{\Gamma }}_{\phi }\ll H_{\mathrm{TI}}$ and $g$, ${\mathrm{\Gamma }}_{\phi }$ and $\lambda$ values from Table 1. [Plots of Eqs. (3.16) and (4.3), with $m=m_0$.] The blue solid line depicts $N_{*}$ and the red dashed line depicts $N_{\mathrm{TI}}$, such that $N_{*}+N_{\mathrm{TI}}=52$. The vertical dotted line depicts values for $m_0=10^3\mathrm{GeV}$.

Figure 3

Prediction of the model for $n_s$ with primordial inflation being quadratic chaotic inflation ${\mathrm{\Gamma }}_{\phi }\ll H_{\mathrm{TI}}$, $m_{\psi }={10}^{-2}\mathrm{GeV}$ and the parameter values from Table 1. [A plot of Eq. (4.73), irrespective of the value of ${\varphi }_{*}$, with $m=m_0$ and $\mathrm{\Gamma }=g^2{m}_0$.] The blue and red lines are the central value and lower/upper bounds of $n_s$, respectively, as obtained by the Planck mission [2].

Figure 4

Prediction of the model for $n_s^{\prime }$ with primordial inflation being quadratic chaotic inflation, with ${\mathrm{\Gamma }}_{\phi }\ll H_{\mathrm{TI}}$, $m_{\psi }={10}^{-2}\mathrm{GeV}$ and the parameter values from Table 1. [A plot of Eq. (4.76), irrespective of the value of ${\varphi }_{*}$, with $m=m_0$ and $\mathrm{\Gamma }=g^2{m}_0$.] The blue line is the central value of $n_s^{\prime }$ as obtained by the Planck mission [2], with the lower and upper bounds being outside the displayed range of $n_s^{\prime }$.