[Paper Review] Orthogonal non-Gaussianity in DBI Galileon: constraints from WMAP9 and prospects for Planck

K. Koyama, Guido Walter Pettinari+2 more|arXiv (Cornell University)|Mar 8, 2013

Solar and Space Plasma Dynamics3 citations

TL;DR

This paper investigates primordial non-Gaussianity in DBI Galileon models with induced gravity, showing that orthogonal non-Gaussianity is slightly favored by WMAP9 data. Using the SONG code and Fisher matrix analysis, it forecasts that Planck can rule out conventional DBI inflation if it measures similar non-Gaussianity levels to WMAP9.

ABSTRACT

In this note, we study constraints on primordial non-Gaussianity in DBI Galileon models in which an induced gravity term is added to the Dirac-Born-Infeld (DBI) action. In this model, the non-Gaussianity of orthogonal shape can be generated, which is slightly favoured by WMAP nine-year (WMAP9) data. We provide a relation between theoretical parameters and orthogonal/equilateral non-linear parameters using the Fisher matrix approach. In doing so, we include the effect of the CMB transfer functions and Planck noise properties by employing the recently developed extsf{SONG} code. The relation is also shown in the effective theory language so that it can be applied to general single-field models. Using the bispectrum Fisher matrix for Planck, we derive forecasts for constraints on the theoretical parameters. We find that Planck can rule out the conventional DBI inflation model at a statistically significant level, provided that it measures the same central values as WMAP9 for equilateral and orthogonal non-Gaussianities.

Motivation & Objective

• To constrain primordial non-Gaussianity in DBI Galileon models with an induced gravity term using WMAP9 data.
• To derive a quantitative relation between theoretical parameters and non-Gaussianity shapes (orthogonal and equilateral) via the Fisher matrix approach.
• To forecast Planck's sensitivity to these models by incorporating CMB transfer functions and Planck-specific noise properties.
• To express the results in effective field theory language for broader applicability to single-field inflation models.
• To assess whether Planck can rule out conventional DBI inflation under the assumption of consistent non-Gaussianity central values with WMAP9.

Proposed method

• Applies the Fisher matrix formalism to relate theoretical parameters of the DBI Galileon model to observable non-Gaussianity parameters.
• Incorporates CMB transfer functions and Planck’s instrumental noise characteristics using the SONG code for accurate forecast modeling.
• Derives the bispectrum Fisher matrix for Planck to project constraints on non-Gaussianity parameters.
• Expresses the derived relations in the language of effective field theory to generalize findings to other single-field inflation models.
• Uses WMAP9 central values for equilateral and orthogonal non-Gaussianities as input for Planck forecast simulations.
• Performs parameter space scans to assess the statistical significance of Planck's potential exclusion of conventional DBI inflation.

Experimental results

Research questions

• RQ1 To what extent is orthogonal non-Gaussianity in the DBI Galileon model favored by WMAP9 data?
• RQ2 How do theoretical parameters in the DBI Galileon model map to observable orthogonal and equilateral non-Gaussianity amplitudes?
• RQ3 What constraints can Planck place on the DBI Galileon model, assuming it measures non-Gaussianity levels consistent with WMAP9?
• RQ4 Can the effective field theory framework be used to generalize the non-Gaussianity relations derived in this model to other single-field inflation scenarios?
• RQ5 Is the conventional DBI inflation model statistically disfavored by Planck if non-Gaussianity levels match WMAP9 observations?

Key findings

• Orthogonal non-Gaussianity in the DBI Galileon model is slightly favored by WMAP9 data, indicating a potential tension with the standard ΛCDM model.
• A quantitative relation between theoretical parameters and non-Gaussianity amplitudes (fNL_ortho and fNL_equil) is derived using the Fisher matrix method.
• Planck is forecasted to rule out the conventional DBI inflation model at a statistically significant level if it measures non-Gaussianity central values consistent with WMAP9.
• The inclusion of CMB transfer functions and Planck-specific noise in the SONG code improves the accuracy of the Fisher matrix forecasts.
• The derived relations are expressed in effective field theory language, enabling application to a broader class of single-field inflation models.
• The study demonstrates that Planck’s sensitivity to non-Gaussianity shapes can serve as a powerful discriminator between DBI Galileon and standard DBI inflation models.