Matter creation in a nonsingular bouncing cosmology

We examine reheating in the two-field matter bounce cosmology. In this model, the Universe evolves from a matter-dominated phase of contraction to an Ekpyrotic phase of contraction before the nonsingular bounce. The Ekpyrotic phase frees the model from unwanted anisotropies, but leaves the Universe cold and empty of particles after the bounce. For this reason, we explore two particle production mechanisms which take place during the course of the cosmological evolution: Parker particle production where the matter field couples only to gravity and particle creation via interactions between the matter field and the bounce field. Although we show that both mechanisms can produce particles in this model, we find that Parker particle production is sufficient to reheat the Universe to high temperatures. Thus there is a priori no need to add an interaction term to the Lagrangian of the model. Still, particle creation via interactions can contribute to the formation of matter and radiation, but only if the coupling between the fields is tuned to be large.

Figure 1

Space-time sketch in the two-field matter bounce scenario. The comoving length and conformal time are labeled by $x$ and $\eta$, respectively. The solid blue curve shows ${\mathcal{H}}^{-1}$, the comoving Hubble radius. The different phase transition times are labeled on the vertical axis. The shaded areas show the regions of integration for the respective phases (the Ekpyrotic and bounce phases are shown). The comoving wavelengths of the fluctuating modes that we integrate originate in these shaded areas. The green line shows the comoving wavelength of such a fluctuating mode that forms in the Ekpyrotic phase of contraction. We see that this mode reenters the Hubble horizon at later times, after ${\eta }_{B+}$.

Figure 2

Plot of the ratio of the energy density of particle production to the background energy density as a function of the coupling constant. The slope of the Hubble parameter and the physical duration of the bounce are taken to be $\mathrm{\Upsilon }=5.5\times 10^{-7}{M}_p^2$ and $t_{B+}=2.1\times 10^3{M}_p^{-1}$, respectively. The blue curve shows the analytic upper bound found in Eq. (84) and the black curve was obtained by solving the EoM and the integral for the energy density numerically. The dashed red line is the contribution from Parker particle production that we found earlier [see Eq. (54)].