Preheating after technicolor inflation

We investigate the particle production due to parametric resonances in a model of inflation where the lightest composite state stemming from the minimal walking technicolor theory plays the role of the inflaton. For this model of inflation, the effective theory couples nonminimally to gravity. Regarding the preheating, we study in detail a model of a composite inflaton field $\varphi$ coupled to another scalar field $\chi$ with the interaction term $g^2{\varphi }^2{\chi }^2$. Particularly, in Minkowski space, the stage of parametric resonances can be described by the Mathieu equation. Interestingly, we discover that broad resonances can be typically achieved and are potentially efficient in our model causing the particle number density in this process to exponentially increase.

Figure 1

The theoretical predictions in the $(r-n_s)$ plane for technicolor inflation with Planck 2015 results for TT, TE, EE, +lowP and assuming $\mathrm{\Lambda }\mathrm{CDM}+r$ [7] for different values of $e$-folds $40\le N\le 90$.

Figure 2

We plot the approximate solution of the field $\varphi (t)$ as given in Eq. (38). The value of the scalar field here is measured in units of $M_{\mathrm{P}}$ and time is measured in units of ${\mathcal{M}}^{-1}$.

Figure 3

By taking $k=5\mathcal{M}(=m_{\chi }),q\sim 10^2$, the upper plot shows the amplification of the real part of the eigenmode $Y_k(z)$. The exponents show the order of magnitude for each given mode of fluctuations. We also see for each oscillation of the field $\varphi (t)$ that the field $Y_k$ oscillates many times. The lower plot shows the logarithm of the comoving particle number density, $n_k(z)$, calculated with Eq. (46). The basic finding is that the number of particles grows exponentially, $\ln n_k\approx 2{\mu }_{k}z$. Here $z$ is measured in units of $2\pi /\mathcal{M}$.