Numerical tiling-based simulations of decoherence in multifield models of inflation

TL;DR

The paper develops a numerically efficient framework to study decoherence effects on primordial perturbations during inflation in multifield setups by embedding open-quantum-system corrections via the Lindblad equation into a fast-slow scale separation of mode dynamics. It introduces a tile-based decoherence scheme across $N$ e-folds and $k$-space, and extends the covariance-matrix (Gaussian-state) formalism to multiple fields with cross-field correlations. A Cholesky-based coloring transformation is implemented to evolve the covariance efficiently while preserving the determinant, enabling stable exploration of complex decoherence sequences. The results show that controlled decoherence events can generate, modulate, or erase features in the primordial power spectrum and induce cross-correlations between adiabatic and isocurvature modes, while providing initial-condition realizations for nonlinear reheating studies, thereby offering a versatile tool for connecting open-quantum dynamics to observable inflationary phenomenology.

Abstract

In previous work, we developed a method for computing two-point correlators by decomposing the mode degrees of freedom into fast and slow components. Building on this framework, we present a numerical implementation to study the evolution of primordial scalar perturbations under controlled state deformations induced by the simplest environment corrections from the Lindblad equation. Our approach generalizes to an arbitrary number of degrees of freedom and does not rely on the slow-roll approximation. The computational routine is numerically efficient and allows users to configure arbitrary sequences of decoherence events, with full control over their duration, shape, amplitude and effective wavelength range. The resulting outputs are compatible with nonlinear numerical codes, enabling studies of how decoherence effects propagate during reheating.

Figures (13)

• Figure 1: Map of initial conditions for the potential $V(\phi)=\lambda\phi^4/4$ with $\lambda=10^{-14}$. In this case, background trajectories converge to the attractor exponentially fast. The green dashed curves mark the boundaries where $\epsilon=1$. Under the slow-roll approximation, the allowed region of background field configurations is restricted to the wedge shaded with green lines.
• Figure 2: Evolution scheme for perturbation modes during cosmic inflation. The x-axis shows the number of e-folds, while the y-axis tracks the evolution of physical length scales $(\ell)$, including the horizon $1/H$ (red curve). Approximate time-translational symmetry permits choosing initial conditions on a surface of large constant physical wavelength $k_{\rm phys}$. Lateral insets illustrate the deformation of the Wigner ellipse at different times, shown in dimensionless units. The evolution reflects the squeezing of the ellipse as modes cross the horizon.
• Figure 3: Example of an arbitrary configuration of decoherence events ("accidents") in a portion of the $(N,\ln\ell)$ plane. These accidents are arranged as "tiles" within a region bounded above by the horizon and below by a surface of constant $k_{\rm phys}$. The source term can either increase or reduce the determinant of the covariance matrix. This setup enables the evaluation of an arbitrary time-dependent power spectrum of the environment.
• Figure 4: Implementation of a random distribution of accidents spanning different wavenumber ranges and durations. We use the same color convention as in Figure \ref{['fig:scheme_acc_sf']} to denote accidents with positive $\alpha_\Gamma$ in different tones of brown, and yellow in the cases with $\alpha_{\Gamma}<0$. Panel (a): Distribution of accidents together with the mode injection scheme. Several modes are selected to evaluate their evolution, their contribution to the power spectrum, and the resulting gain or loss in state availability. Panel (b): Power spectrum of primordial curvature fluctuations. The red curve corresponds to the spectrum in the presence of accidents, while the black dotted curve shows the spectrum free of decoherence events. Panel (c): Evolution of the curvature spectrum at fixed wavenumber. Dotted lines depict the evolution with no accidents highlighting how accidents alter the mode dynamics. The inset on the left depicts the reduction of amplitude caused by negative changes in the determinant. Panel (d): Changes in the area of the Wigner ellipse for several modes. The label "no accidents" refers to the conservation of the determinant in the accident-free scenarios. In contrast, decoherence events with finite duration modify the determinant during their action but leave it unchanged once they switch off.
• Figure 5: Implementation of a distribution of decoherence events that leave the primordial power spectrum unaltered. The same color convention as in Figures \ref{['fig:scheme_acc_sf']} and \ref{['fig:imp_rndm_acc_sf']} is adopted: accidents with positive $\alpha_\Gamma$ are shown in different tones of brown, while those with $\alpha_{\Gamma}<0$ are shown in yellow. Panel (a): Mode injection scheme and distribution of accidents $(\rm A)$, together with their corresponding anti-accidents $(\bar{\rm A})$ that cancel effects in mode evolution. We use the source term parameterization proposed in Eq. \ref{['eq:tiling_source_mod']} to confine the effects to specific bands of wavelengths. Panel (b): Power spectrum of primordial curvature fluctuations in the presence of accidents (black dotted line) and after including accident/anti-accident pairs. The compensation mechanism restores the spectrum, leaving it unchanged. Panels (c1) and (c2): Evolution of the deformations in the squeezing parameters $\Delta r_k\equiv r_k-r^{(0)}_k$ and $\Delta \varphi_k\equiv \varphi_k-\varphi^{(0)}_k$, measured relative to the accident-free scenario. The insets show that the final state is represented by a Wigner ellipse with unit area (approx.) and almost negligible eccentricity, which rotates until crossing the horizon. Panel (d): Evolution of the Wigner ellipse area for several modes. After passing through an accident/anti-accident pair, the area relaxes back to unity. The label "no $(\bar{\mathrm{A}})$" indicates cases without anti-accidents, where the enlarged (or reduced) area persists without reversal.