Curvature Perturbations from Broken Symmetries

TL;DR

This work addresses how curvature perturbations can arise after slow-roll inflation in a multi-field setting with a broken global symmetry. It develops a general framework in which isocurvature fluctuations in the angular direction convert into curvature perturbations through inhomogeneous preheating, yielding $\zeta \approx \alpha \frac{\partial \ln(n_{\chi})}{\partial \phi_{\perp}} \delta\phi_{\perp}$ and a power spectrum $\mathcal{P}_{\zeta}(k)$ tied to the spectrum of $\delta\phi_{\perp}$. Applying the mechanism to a broken $U(1)$ potential with instant preheating, the authors derive explicit expressions for the preheating variables $|\phi_*|$ and $|\dot{\phi}_*|$, show how $\delta\theta_0$ modulates $n_{\chi}$, and obtain $\mathcal{P}_{\zeta}(k)$ with a nearly flat tilt $n-1 \approx 2\eta_1[1 - x\cos^2(\theta_0)]$, where $\eta_1 = m^2/(3H^2)$ and $x$ measures symmetry breaking. The results imply that broken-symmetry preheating can be a dominant source of curvature perturbations under certain conditions and provides a link between inflationary fluctuations and post-inflationary dynamics, akin to curvaton scenarios but without an external field.

Abstract

We present a new general mechanism to generate curvature perturbations after the end of the slow-roll phase of inflation. Our model is based on the simple assumption that the potential driving inflation is characterized by an underlying global symmetry which is slightly broken.

Figures (4)

• Figure 1: Two background trajectories arising from fluctuations in the initial conditions in the case in which the background field space is two dimensional. Also shown are the equipotential contours (units of $10^{-16} M_p^4$). The potential used in this figure is the one given in Eq. (\ref{['App:V']}) and further analyzed in Sec. \ref{['sect:Application']}, which is characterized by a global $U(1)$ broken symmetry. In this case, and for illustration purposes only, the symmetry breaking parameter has been arbitrarily set to $x=0.15$.
• Figure 2: Values of $f(\theta_0)$ obtained through numerical simulation and using the approximate expression given in Eq. (\ref{['App:deltanchinchi2']}) for a value of the symmetry breaking parameter of $x=0.05$ and for a coupling constant $g=0.01$.
• Figure 3: Values of $|\phi_*|/(|\phi_0|\pi x /2\sqrt{2})$ obtained through numerical simulation and using the above approximate expression Eq. (\ref{['Append:lapprox']}) for a value of the symmetry breaking parameter of $x=0.05$.
• Figure 4: Values of $|\dot{\phi}_*|/|\dot{\tilde{\phi}}_*|$ obtained through numerical simulation and using the approximate expression Eq. (\ref{['Append:m3']}) for a value of the symmetry breaking parameter of $x=0.05$.