[Paper Review] Preheating in FRW Universes

D. Boyanovsky, D. Cormier+4 more|ArXiv.org|Sep 30, 1996

Cosmology and Gravitation Theories4 references9 citations

TL;DR

This paper investigates preheating—explosive particle production via spinodal instabilities or parametric resonance—in a radiation-dominated Friedmann-Robertson-Walker (FRW) universe using the O(N) model with large N. It demonstrates that preheating persists when cosmic expansion is included, though particle production is reduced compared to Minkowski space, and identifies a sum rule governing late-time behavior that implies the existence of Goldstone bosons in the final state due to spontaneous symmetry breaking.

ABSTRACT

The nonlinear time evolution of the quantum fields is studied in the O(N) model for large N in a radiation dominated FRW universe, with a view towards the phenomenon of explosive particle production due to either spinodal instabilities or parametric amplification, i.e. preheating. Quantum backreaction effects due to the produced particles are included consistently within the large N approximation. We find that preheating persists when the expansion is included, although the amount of particle production is reduced compared to the values found in Minkowski space. We also see that the behavior of the evolving zero mode is very different from that in Minkowski space, though the late time behavior in all cases is determined by a sum rule that implies the existence of Goldstone bosons in the final state.

Motivation & Objective

• To understand how preheating—driven by spinodal instabilities or parametric resonance—persists in an expanding FRW universe.
• To analyze the nonlinear time evolution of quantum fields in a radiation-dominated FRW background.
• To include quantum backreaction effects consistently within the large N approximation.
• To determine whether the late-time behavior of the zero mode and final particle spectrum differ from Minkowski space, particularly regarding Goldstone modes.
• To establish whether sum rules govern the final state, implying the existence of Goldstone bosons after symmetry breaking.

Proposed method

• The study employs the O(N) model in the large N limit to simplify the dynamics of interacting quantum fields.
• The FRW metric is used to model a radiation-dominated expanding universe, with time-dependent background fields.
• Nonlinear equations of motion for the quantum fields are solved numerically, including backreaction from produced particles.
• The large N approximation allows consistent inclusion of quantum corrections from particle production on the background evolution.
• The zero mode evolution is tracked to study the dynamics of the order parameter and symmetry breaking.
• A sum rule is derived and applied to analyze the late-time behavior of the system, linking it to the presence of Goldstone bosons.

Experimental results

Research questions

• RQ1 Does preheating survive in the presence of cosmic expansion in a radiation-dominated FRW universe?
• RQ2 How does the inclusion of quantum backreaction affect the efficiency of particle production during preheating?
• RQ3 How does the time evolution of the zero mode differ in FRW space compared to Minkowski space?
• RQ4 What is the role of the sum rule in determining the final state of the system after preheating?
• RQ5 Does the final state necessarily contain Goldstone bosons, and how is this implied by the sum rule?

Key findings

• Preheating persists in the FRW universe, though the total amount of particle production is reduced compared to the Minkowski space case.
• The behavior of the zero mode in FRW space differs significantly from that in Minkowski space due to the expansion.
• A sum rule governs the late-time dynamics, ensuring the existence of Goldstone bosons in the final state after spontaneous symmetry breaking.
• The sum rule is robust and holds regardless of the initial conditions, implying a universal feature of the final state.
• Quantum backreaction effects are consistently included and found to suppress particle production, but do not eliminate preheating.
• The final state contains a finite number of Goldstone bosons, consistent with the expectation from the Goldstone theorem in the context of broken global symmetry.