[Paper Review] Primordial non-gaussianity from multiple curvaton decay

J. Väliviita, Hooshyar Assadullahi+1 more|ArXiv.org|Jun 3, 2008

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper extends the curvaton model to multiple curvatons, showing that non-Gaussianity (quantified by $f_{\rm{NL}}$) can be large even when curvatons dominate energy density at decay, provided the radiation from the first decay is diluted by a subsequent homogeneous curvaton decay. The key novel result is a mechanism for large $f_{\rm{NL}}$ in the dominant-curvaton regime, with $f_{\rm{NL}} \geq -5/4$ as a robust lower bound.

ABSTRACT

We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, and solve them in a sudden-decay approximation. We calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. Not surprisingly, we find large positive values of fNL if the energy densities of the curvatons are sub-dominant when they decay, as in the single curvaton case. But we also find a novel effect, which can be present only in multi-curvaton models: fNL becomes large even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case. Using (non-)Gaussianity observations, Planck can be able to distinguish between single-field inflation and curvaton model. Hence it is important to derive theoretical predictions for curvaton model. From particle physics point of view it is more natural to assume multiple scalar fields (rather than just one ``curvaton'' in addition to inflaton). Our work updates the theoretical predictions of curvaton model to this case.

Motivation & Objective

• To generalize the single-curvaton model to include multiple curvaton fields, motivated by the naturalness of multiple scalar fields in beyond-Standard-Model physics.
• To derive the primordial power spectrum and non-linearity parameter $f_{\rm{NL}}$ in a two-curvaton model with sequential decays.
• To identify new mechanisms for generating large $f_{\rm{NL}}$ beyond the standard subdominant-curvaton regime.
• To assess the distinguishability of multi-curvaton models from single-field inflation using Planck non-Gaussianity constraints.

Proposed method

• Formulates non-linear equations relating the primordial curvature perturbation $\zeta$ to curvaton field perturbations on super-Hubble scales.
• Uses a sudden-decay approximation to solve the evolution of curvature perturbations through two sequential curvaton decays.
• Derives the primordial power spectrum $P_\zeta$ as a function of decay efficiency parameters $f_{a1}$, $f_{b1}$, and $f_{b2}$, and the relative perturbation amplitude $\beta$.
• Computes the non-linearity parameter $f_{\rm{NL}}$ up to second order in perturbations, using the bispectrum normalization.
• Analyzes the dependence of $f_{\rm{NL}}$ on the energy density ratios at decay times and the relative perturbation amplitudes.
• Considers three limiting cases: $\beta \to \infty$ (nearly homogeneous curvaton $a$), $\beta = 1$ (equal perturbations), and $\beta = 0$ (homogeneous curvaton $b$).

Experimental results

Research questions

• RQ1 Can large primordial non-Gaussianity ($f_{\rm{NL}}$) arise in multi-curvaton models even when curvatons dominate the energy density at decay?
• RQ2 What is the role of radiation dilution from a second, nearly homogeneous curvaton decay in enabling large $f_{\rm{NL}}$ in the dominant-curvaton regime?
• RQ3 How does the inclusion of a second curvaton field modify the standard single-curvaton prediction for $f_{\rm{NL}}$?
• RQ4 What is the lower bound on $f_{\rm{NL}}$ in multi-curvaton models with Gaussian curvaton perturbations?

Key findings

• Large positive $f_{\rm{NL}}$ is generated when curvatons are subdominant at decay, consistent with the single-curvaton case.
• A novel mechanism allows large $f_{\rm{NL}}$ even when both curvatons are dominant at decay, provided the radiation from the first decay is diluted by a subsequent homogeneous curvaton decay.
• The minimum value of $f_{\rm{NL}}$ is $-5/4$, which is the same as in the single-curvaton model and appears to be a robust lower bound in Gaussian multi-curvaton models.
• The first-order power spectrum is given by $P_\zeta = \left[r_a^2 + \beta^2 r_b^2\right] P_{\zeta_a}$, with $r_a$ and $r_b$ depending on decay efficiency parameters and $\beta$.
• The result differs from previous work (e.g., Choi and Gong) due to the inclusion of the $f_{b1}$ term, which accounts for non-negligible curvaton $b$ density at the first decay.
• For $\beta = 0$ (homogeneous curvaton $b$), large $f_{\rm{NL}}$ is possible even in the regime $f_{a1} \sim 1$, $f_{b2} \sim 1$, demonstrating a new path to non-Gaussianity.