Non-Gaussianity and large-scale structure in a two-field inflationary model

TL;DR

This work analyzes a two-field inflationary scenario in which both the inflaton and a curvaton contribute to the primordial perturbations, producing a local-type, yet stochastic, non-Gaussian signature. It introduces two key parameters, $\tilde{f}_{\rm NL}$ and $\xi$, re-expressed as $x_1$ and $x_2$, to describe the nonlinear coupling and the inflaton-curvaton power mix, and derives their imprints on the CMB bispectrum and on the large-scale galaxy distribution via peak-background-split bias. The study shows that the CMB bispectrum alone cannot break the degeneracy between these parameters, but joint constraints from WMAP and SDSS reveal how LSS data can break it and predict large-scale stochasticity as a unique signal of multi-field contributions. A detected local $f_{NL}$ in the CMB would further constrain the inflaton's share of the perturbations, enabling a quantitative separation of inflaton and curvaton roles. The results highlight stochasticity as a crucial diagnostic for multi-field inflation and outline observational paths for future CMB and LSS surveys.

Abstract

Single field inflationary models predict nearly Gaussian initial conditions and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter $\tilde f_{\rm NL}$ and the ratio $ξ$ of the amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and SDSS data.

Figures (3)

• Figure 1: The allowed range ($2\sigma$) of $\tilde{f}_{\rm NL}$ as a function of $x_2$ derived from the WMAP data Komatsu08. As discussed in the text, $\tilde{f}_{NL}$ becomes unconstrained as $x_2 \rightarrow 0$ because in this case the statistics describing the density distribution is dominated by the inflaton field and is nearly Gaussian.
• Figure 2: The bias and stochasticity of galaxies at $z=1$ in a model with $x_1=30$ and $x_2=0.5$ ($\tilde{f}_{\rm NL}=120$). The solid lines show a tracer with $b=2$ and the dashed lines a tracer with $b=3$. The background cosmology and power spectrum are those of WMAP5.
• Figure 3: Constraints in the $(x_1,x_2)$ plane, including both the CMB bispectrum and the galaxy power spectrum.