Multifaceted Schwinger effect in de Sitter space

We investigate particle production à la the Schwinger mechanism in an expanding, flat de Sitter patch as is relevant for the inflationary epoch of our Universe. Defining states and particle content in curved spacetime is certainly not a unique process. There being different prescriptions on how that can be done, we have used the Schrödinger formalism to define instantaneous particle content of the state, etc. This allows us to go past the adiabatic regime to which the effect has been restricted in the previous studies and bring out its multifaceted nature in different settings. Each of these settings gives rise to contrasting features and behavior as per the effect of the electric field and expansion rate on the instantaneous mean particle number. We also quantify the degree of classicality of the process during its evolution using a “classicality parameter” constructed out of parameters of the Wigner function to obtain information about the quantum to classical transition in this case.

Figure 1

Facets of Schwinger effect in de Sitter space. The color shading of the Schwinger-de Sitter cube gives the mean particle number, $⟨n_{\mathbf{k}}⟩$, as a function of the electric field strength, $L$; mass of the field, $M$; and $x=aH/k$ with $x=1$ (dashed line) is where the modes exit the comoving Hubble radius. We have $L=1$ for the $M-x$ plot, while the rest are according to the faces of the cube. We see the particle creation is enhanced for $x>1$, a weak electric field, and low mass of the scalar field.

Figure 2

Evolution of adiabaticity parameter $\epsilon$ with the scale factor for different $L$ and $M$ specifying field strength and mass, taking $k=k_z=1$. The system can have nonadiabatic evolution as in plots (a), (b), and (c) where the in-out prescription fails.

Figure 3

Evolution of the excitation parameter, $z_k$; the mean number density, $⟨n_k⟩$; and the classicality parameter, $C_k$. The evolution is with respect to $x=aH/k$ such that $x<1$ is a sub-Hubble (dotted lines) period and $x=1$ specifies the point at which modes exit the comoving Hubble radius to become super-Hubble for $x>1$ (regular lines).