Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states

TL;DR

This work presents a nonperturbative, real-time study of interacting quantum fields in curved spacetime using tensor-network methods applied to λφ^4 theory and the Schwinger model in 1+1 dimensions under a homogeneous FLRW-like expansion. By formulating lattice Hamiltonians valid in curved backgrounds and evolving them from the asymptotic past, the authors validate free-field limits and demonstrate that self-interactions suppress gravitational particle production, as shown through two-point correlators and occupation numbers. They also explore entanglement dynamics, finding that λφ^4 reduces entanglement growth while the Schwinger model exhibits a nuanced balance between decreased production and enhanced inter-particle correlations due to cosine interactions. This work provides a concrete nonperturbative framework for real-time quantum dynamics in curved spacetime and points toward extensions to higher dimensions, de Sitter backgrounds, and backreaction effects.

Abstract

Understanding real-time dynamics of interacting quantum fields in curved spacetime remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar $λφ^4$ theory and the Schwinger model, i.e. a Dirac fermion coupled to a $U(1)$ gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the $λφ^4$ theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.

Figures (13)

• Figure 1: Scale factor as a function of time, given by Eq. (\ref{['eq:omega_profile']}). In this work, we fix $A=2$, $B=1$, and vary $\rho$ and $t_0$ depending on the model analyzed and its parameters. The parameters presented here correspond to our studies in the Schwinger model (except when exploring the effects of $\rho$ variation). The shaded region helps visualize the expansion rate, with the shading intensity proportional to $\partial_t \Omega^2$.
• Figure 2: Left: two-point charge density correlator ${\cal Q}_2^{\rm lat.}(n,t)$, given by Eq. (\ref{['eq:Q2_lat']}), in the massless Schwinger model with $M_1 = 0.25$, as a function of distance $x=2an$ for several fixed values of time $t$. Different markers correspond to different choices of lattice spacing; physical volume is fixed. Right: same for the two-point field correlator ${\cal C}_2^{\rm lat.}(n,t)$, given by Eq. (\ref{['eq:C2_lat']}), calculated in the $\lambda\phi^4$ theory with $\lambda=0$ and $m=1$; $x=an$ in this case. In both panels, black curves show the corresponding analytical continuum results for a free scalar theory, computed as described in App. \ref{['app:free_2pt']}. Solid curve and filled markers correspond to the positive value of the correlator; dashed curve and empty markers - to the negative one.
• Figure 3: Left: two-point charge density correlator ${\cal Q}_2^{\rm lat.}(n,t)$, given by Eq. (\ref{['eq:Q2_lat']}), in the Schwinger model, as a function of time for a fixed value of spatial separation $x=2an=6$. Fermion mass-to-coupling ratio is varied, while the lightest meson mass is fixed, $M_1 = 0.25$. Lattice parameters are $N=100, a=0.3$. Shaded region indicates when the expansion quench happens, with the shading intensity proportional to $\partial_t\Omega^2$. Right: same for the two-point field correlator ${\cal C}_2^{\rm lat.}(n,t)$, given by Eq. (\ref{['eq:C2_lat']}), calculated in the $\lambda\phi^4$ theory with $m=1$; $x=an=3$ in this case. Lattice parameters are $N=100, a=0.25$. In both panels, black dashed lines show the analytical continuum results for a free scalar theory of the corresponding mass, computed as described in App. \ref{['app:free_2pt']}.
• Figure 4: Comparison of the amount of excitations in a system for different values of the expansion rate $\rho$. Left: Excitation probability in the Schwinger model with parameters $g_f =0.5, m_f=0.5$, corresponding to $M_1 = 1.22$; $N=40, a=1$. Right: integrated occupation number, defined in Sec. \ref{['subsec:occupation']}, in the $\lambda\phi^4$ theory with parameters $m=1$, $\lambda=1$, $N=100$, $a=1$.
• Figure 5: Excitation probability at late time as a function of the interaction strength. Left: Schwinger model with $N=40, a=1$; $m_f$ and $g_f$ are adjusted so that the lightest meson mass $M_1=0.25$. The ratio $m_f/g_f$ controls the strength of cosine interaction in the bosonized form. Right: $\lambda\phi^4$ theory with $N=100, a=0.25$, and $m=1$.