Curvaton Dynamics

TL;DR

This work analyzes the full dynamical evolution of a curvaton field, including Hubble-induced mass terms, higher-order nonrenormalizable contributions, and thermal corrections. By deriving analytic solutions for σ(t) and ρ_σ across inflation and post-inflation epochs, the authors map out when the curvaton can dominate or nearly dominate the energy density and how its perturbations propagate via the transfer coefficient q. A key result is that, in most regimes, ρ_σ/ρ declines after inflation, so curvaton domination requires the soft mass m to take over before decay, and thermal corrections must be suppressed to avoid premature thermalization; an attractor constraint for higher-order terms also emerges, threatening the preservation of the primordial spectrum. The paper also presents a concrete example showing that, for c ≈ 1 after inflation, viable curvaton parameter space is severely restricted, thereby reinforcing models with suppressed post-inflation c, such as pseudo-Nambu-Goldstone boson curvatons. Overall, the analysis provides analytic criteria and bounds (on r, q, m, g, and decay rates) to assess curvaton viability in a broad class of potentials and cosmological histories.

Abstract

In contrast to the inflaton's case, the curvature perturbations due to the curvaton field depend strongly on the evolution of the curvaton before its decay. We study in detail the dynamics of the curvaton evolution during and after inflation. We consider that the flatness of the curvaton potential may be affected by supergravity corrections, which introduce an effective mass proportional to the Hubble parameter. We also consider that the curvaton potential may be dominated by a quartic or by a non-renormalizable term. We find analytic solutions for the curvaton's evolution for all these possibilities. In particular, we show that, in all the above cases, the curvaton's density ratio with respect to the background density of the Universe decreases. Therefore, it is necessary that the curvaton decays only after its potential becomes dominated by the quadratic term, which results in (Hubble damped) sinusoidal oscillations. In the case when a non-renormalizable term dominates the potential, we find a possible non-oscillatory attractor solution that threatens to erase the curvature perturbation spectrum. Finally, we study the effects of thermal corrections to the curvaton's potential and show that, if they ever dominate the effective mass, they lead to premature thermalization of the curvaton condensate. To avoid this danger, a stringent bound has to be imposed on the coupling of the curvaton to the thermal bath.

Figures (3)

• Figure 1: Illustration of the scaling solution in the quasi-quadratic case, where $m_{\rm eff}\sim\sqrt{c}H(t)$. For $t_1<t_2<t_3$, the curvaton field $\sigma$ rolls down a potential which changes in time so that the field's value gradually reduces towards $\sigma_{\rm min}$.
• Figure 2: Illustration (log-log plot) of the different scalings of the various contributions to $V"$ assuming a given background barotropic parameter $w$. The solid line corresponds to the higher--order case, where $V"\sim m_{\rm eff}^2\sim\sigma^{n+2}/M^n$. The dashed line corresponds to the quasi-quadratic case, where $V"\sim cH^2$. The thin dot-dashed lines correspond to $(gT)^2$ for different values of $g$ growing as the thick dot-dashed arrow shows. It is depicted that the quasi-quadratic contribution to the effective mass decreases faster than the higher--order one and they both decrease faster than the temperature induced mass. From the figure, it is evident that, if $(gT)^2$ is subdominant when the soft mass--squared $m^2$ takes over, then this is enough to ensure that the temperature contribution to the effective mass is always subdominant, both before and after the moment when $m^2$ takes over.
• Figure 3: Illustration (log-log plot) of the parameter space (solid line) for a successful curvaton in the case when $c=c_*\sim 10^{-3}$, with model parameters given by Eq. (\ref{['parameters']}). The upper bound $g\leq 10^{-9}$ is determined by the requirement of Eq. (\ref{['gboundqq']}), which ensures that $(gT)^2$ never dominates the effective mass. For $g<10^{-12}$, the curvaton decays predominantly through gravitational couplings.