[Paper Review] Out of Equilibrium Fields in Self-consistent Inflationary Dynamics. Density Fluctuations

D. Boyanovsky, H. J. de Vega|arXiv (Cornell University)|Jun 30, 2000

Cosmology and Gravitation Theories4 citations

TL;DR

This paper develops a non-perturbative, self-consistent framework using large-N field theory to study out-of-equilibrium quantum dynamics during inflation. It shows that spinodal instabilities drive explosive particle production and large quantum fluctuations, which reorganize into an effective classical zero mode that drives inflationary expansion, leading to a red-tilted scalar density power spectrum as a robust feature of symmetry-breaking inflation models.

ABSTRACT

The physics during the inflationary stage of the universe is of quantum nature involving extremely high energy densities. Moreover, it is out of equilibrium on a fastly expanding dynamical geometry.We present in these lectures non-perturbative out of equilibrium field theoretical methods in cosmological universes. We then study the non-linear dynamics of quantum fields in matter and radiation dominated FRW and de Sitter universes. We investigate the explosive particle production due to spinodal instabilities and parametric amplification in FRW and deSitter universes with and without symmetry breaking. We show how the particle production is sensitive to the expansion of the universe.We present a complete renormalization scheme for the equation of motion and the energy momentum tensor in flat cosmologies. We then consider an O(N) inflaton model coupled self-consistently to gravity in the semiclassical approximation, with `new inflation' type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. A very specific combination of these large quantum fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. The metric perturbations during inflation are computed using this effective field and the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensorperturbations and find for these models that the spinodal instabilities are responsible for a `red' primordial spectrum.

Motivation & Objective

• To understand the non-equilibrium quantum dynamics of the inflaton field during inflation, particularly in high-energy-density, far-from-equilibrium conditions.
• To overcome the limitations of equilibrium and perturbative methods in describing large quantum fluctuations and backreaction effects.
• To provide a self-consistent, non-perturbative treatment of inflation that includes the dynamics of the scale factor and quantum backreaction.
• To identify the correct effective field variable that governs classical evolution and metric perturbations during inflation.
• To compute the spectrum of scalar and tensor perturbations in a gauge-invariant, covariantly conserved framework.

Proposed method

• Uses large-N expansion to non-perturbatively resum dominant quantum effects in O(N) scalar field models.
• Applies out-of-equilibrium quantum field theory techniques to solve the real-time dynamics of the inflaton field and its correlation functions.
• Implements a numerically accessible renormalization scheme for the equation of motion and energy-momentum tensor in flat FRW and de Sitter spacetimes.
• Tracks the evolution of the inflaton zero mode, large quantum fluctuations, and the equation of state in self-consistent dynamics.
• Identifies the reassembled effective field via zero-mode reassembly, which behaves classically and drives the scale factor evolution.
• Computes metric perturbations using the Bardeen variable and a gauge-invariant approach to extract the scalar and tensor power spectra.

Experimental results

Research questions

• RQ1 How do non-perturbative quantum fluctuations evolve in a dynamically expanding universe during inflation?
• RQ2 What is the role of spinodal instabilities and parametric amplification in driving particle production and ending inflation?
• RQ3 How can a consistent effective field be defined from large quantum fluctuations to describe classical inflationary dynamics?
• RQ4 What is the resulting spectrum of scalar and tensor perturbations, and does it exhibit a red tilt due to non-equilibrium dynamics?
• RQ5 How does the backreaction of quantum fluctuations affect the scale factor and the transition to the post-inflationary era?

Key findings

• Spinodal instabilities drive the non-perturbative growth of superhorizon quantum fluctuations, which contribute to the energy-momentum tensor and terminate inflation.
• The amplitude of quantum fluctuations decays as the inverse square of the scale factor in FRW cosmologies, while the order parameter approaches the minimum of the potential.
• Large quantum fluctuations reassemble into a new effective classical field that governs the slow-roll evolution of the scale factor.
• The effective field is identified as the true background field whose dynamics drive the metric perturbations, enabling a consistent interpretation of inflation.
• The scalar density perturbation spectrum exhibits a red tilt (n_s < 1) due to long-wavelength spinodal instabilities, a robust feature of symmetry-breaking inflation models.
• Tensor perturbations remain unaffected by these instabilities and retain a Harrison-Zeldovich spectrum with small amplitude.