Mixed inflaton and curvaton perturbations

TL;DR

This work investigates a mixed inflationary scenario in which primordial curvature perturbations receive comparable contributions from both the inflaton and a subdominant curvaton with a light effective mass during inflation. The authors derive the background and perturbation evolution, show that the final curvature perturbation can be written as $\Phi_{RD}=\Phi_* -\dfrac{f(\sigma_*)}{m_{ m P}}\delta\sigma_*$ after curvaton decay, and introduce the interpolating function $f(\sigma_*)$ that connects the standard curvaton and secondary-inflaton limits. They provide analytical results in limiting cases and numerical results for the general case, and compute the resulting power spectrum, spectral index, and tensor-to-scalar ratio, including a modified consistency relation $r = { -8 n_T }/{1 - {\tilde f}^2 n_T/2}$. Applying the formalism to a quartic inflaton potential $V(\phi)=\lambda\phi^4$, they show how curvaton mixing shifts $N_*$, $n_s$, and $r$, potentially reconciling otherwise disfavored models with observations and offering a way to break degeneracies in single-field inflation via the modified consistency relation. The results provide a generic framework for interpreting primordial perturbations when inflaton and curvaton perturbations are both significant, with implications for future probes of the early Universe.

Abstract

A recent variant of the inflationary paradigm is that the ``primordial'' curvature perturbations come from quantum fluctuations of a scalar field, subdominant and effectively massless during inflation, called the ``curvaton'', instead of the fluctuations of the inflaton field. We consider the situation where the primordial curvature perturbations generated by the quantum fluctuations of an inflaton and of a curvaton field are of the same order of magnitude. We compute the curvature perturbation and its spectrum in this case and we discuss the observational consequences.

Figures (5)

• Figure 1: The standard curvaton limit, for $\sigma_* = 0.3 m_{\rm P}$. Evolution of the curvaton, its energy density fraction $\Omega_\sigma\equiv \rho_\sigma/(\rho_\sigma+\rho_r)$ (upper part), and of the curvature perturbation $\Phi$ (lower part). The initial conditions for the perturbations are $\delta \sigma_* = m_{\rm P}$ and $\Phi_* =-2$.
• Figure 2: The secondary inflaton limit, for $\sigma_* = 3 m_{\rm P}$. Evolution of $\sigma$, its energy density fraction (upper part), and of the curvature perturbation (lower part). The initial conditions for the perturbations are $\delta \sigma_* = m_{\rm P}$ and $\Phi_* =-2$.
• Figure 3: The intermediate case, for $\sigma_* = m_{\rm P}$. Evolution of $\sigma$, its energy density fraction (upper part), and of the curvature perturbation (lower part) for two different initial conditions: $\Phi_*=0$ and for $\Phi_* =-2$ (both cases with $\delta \sigma_* = m_{\rm P}$).
• Figure 4: The function $f(\sigma_*)$, which characterizes the amplitude of the contribution of $\sigma$ to the curvature perturbation. For $\sigma_* \ll m_{\rm P}$ one recognizes the $\propto 1/\sigma_*$ contribution of the pure curvaton model. For $\sigma_* \gg m_{\rm P}$, one recognizes the contribution of a secondary inflaton, proportional to $\sigma_*$ .
• Figure 5: Two-dimensional likelihood contours at $68$% and $95$% confidence level of the WMAP data on the $(n_s,r)$-plane, as compared to the predictions of a pure inflationary model (solid $N$-trajectory), a mixed model with $f=1$ (upper dotted $N$-trajectory), corresponding to $\sigma_* \sim 0.5 m_{\rm P}$, and one with $f=3$ (lower dotted $N$-trajectory), corresponding to $\sigma_* \sim 0.1 m_{\rm P}$, respectively. The stars denote $N=64$ on the $N$-trajectories. The interval $60 \le N \le 64$ is represented by bold dots on the $N$-trajectories of the mixed models. The likelihood contours are from the analysis of S. Leach and A. Liddle Leach.