Quantum quenches during inflation

We propose a new technique to study fast transitions during inflation, by studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in de Sitter spacetime. We compute the time evolution of the system using a nonperturbative large-$N$ limit approach. We derive the self-consistent mass equation for several physically relevant transitions of the parameters of the theory, in a slow motion approximation. Our computations reveal that the effective mass after the quench evolves in the direction of recovering its value before the quench, but stopping at a different asymptotic value, in which the mass squared is strictly positive. Furthermore, we tentatively find situations in which the effective mass squared can be temporarily negative, thus breaking the $O(N)$ symmetry of the system for a certain time, only to then come back to a positive value, restoring the symmetry. We argue the relevance of our new method in a cosmological scenario.

Figure 1

Evolution of ${\epsilon }_2(x)$ for transition 1 (dotted) as compared to the analytical result (solid) for $g_4^R=0.01$, varying ${\epsilon }_1$.

Figure 2

Evolution of ${\epsilon }_2(x)$ for transition 1 (dotted) as compared to the analytical result (solid) for ${\epsilon }_1=0.1$, varying $g_4^R$.

Figure 3

Numerical evolution of ${\epsilon }_2(x)$ for transition 2 (dotted), showing the asymptotic mass (dashed) for $g_4^R=0.01$, varying ${\mu }_R^2$ (shown in units of $H^2$).

Figure 4

Numerical evolution of ${\epsilon }_2(x)$ for transition 2 (dotted) as compared to both the corrected (solid) and uncorrected (dashed) analytical results, for $g_4^R=0.01$, varying ${\mu }_R^2$ and rescaled by ${\mu }_R^2$ (shown in units of $H^2$).

Figure 5

Numerical evolution of ${\epsilon }_2(x)$ for transition 2 (dotted) as compared to the corrected analytical results (solid) and showing the asymptotic mass (dashed), with ${\mu }_R^2/H^2=0.1$, varying $g_4^R$.

Figure 6

Numerical evolution of ${\epsilon }_2(x)$ for transition 3 (dotted) and showing the asymptotic mass (dashed) with ${\mu }_R^2/H^2=0.2$, $g_4^R=0.1$, varying ${\epsilon }_1$.

Figure 7

Numerical evolution of ${\epsilon }_2(x)$ for transition 3 (dotted) as compared to the corrected analytical results (solid) and showing the asymptotic mass (dashed), with ${\epsilon }_1=0.01$, $g_4^R=0.1$, varying ${\mu }_R^2$ (shown in units of $H^2$).

Figure 8

Numerical evolution of ${\epsilon }_2(x)$ for transition 3 (dotted) as compared to the corrected analytical results (solid) and showing the asymptotic mass (dashed), with ${\epsilon }_1=0.01$ (also shown as dot-dashed in the middle), ${\mu }_R^2/H^2=0.002$, varying $g_4^R$.

Figure 9

Numerical evolution of $|{\epsilon }_2(x)|$ for negative ${\mu }_R^2$ (dotted) as compared to the analytical results (solid) and showing the asymptotic mass (dashed). Initially ${\epsilon }_2(x)$ is negative, but evolves toward positive values after some time.

Figure 10

The spectral index (solid) as a function of scale $k$ for the transition with parameters ${\epsilon }_1=0.01$, $g_4^R=0.1$, ${\mu }_R^2=0.2$, shown at a time in which all scales have become super-horizon. Also shown is the value of $2{\epsilon }_2$ (dashed), representing the effective mass via ${\epsilon }_2\approx m^2/3H^2$ and evaluated at the time each scale exited the horizon, $\tau =k^{-1}$.