The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation

Abstract

Focusing on the local type primordial non-Gaussianities, we study the bispectrum and trispectrum during a non-minimal slow-roll inflation. We use the so-called $\delta N$ formalism to investigate the super-horizon evolution of the primordial perturbations in this setup. Firstly we obtain the main equations of the model and introduce the framework of the $\delta N$ formalism for this case. Then we give analytical expressions for the nonlinear parameters describing the non-Gaussianity in the slow-roll approximation. We analyze the bispectrum by its non-linear parameter, $f_{NL}$. Furthermore, we calculate ${\tau }_{NL}$ and $g_{NL}$ which are non-linear parameters characterizing the amplitude of trispectrum. Finally, by adopting a quadratic form for both the potential and non-minimal coupling (NMC) function, we test our setup in the light of Planck2015 data and constrain the model parameters space. Although the non-Gaussianity parameters are so small in this setup, this model is consistent with recent observation. We extend our analysis to see the situation in the Einstein frame and compare the results in these two frames.

arXiv comment22 two column pages, 18 figures, title changed, extension to the Einstein frame is added, major revision with new references

References in corpus (63)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Non-Gaussianity from Inflation: Theory and Observations
• DBI in the Sky
• Acoustic Signatures in the Primary Microwave Background Bispectrum
• Inflation Dynamics and Reheating
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• A new approach to the evolution of cosmological perturbations on large scales
• Reconstructing the Inflaton Potential --- an Overview
• A general proof of the conservation of the curvature perturbation
• The inflationary prediction for primordial non-gaussianity
• A new mechanism for generating density perturbations from inflation
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• Non-Gaussianity of the primordial perturbation in the curvaton model
• Limits on non-Gaussianities from WMAP data
• Large-scale structure, the cosmic microwave background, and primordial non-gaussianity
• Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation
• On non-gaussianities in single-field inflation
• Gravitational waves from inflation on the brane
• The Angular Trispectrum of the CMB
• Primordial trispectrum from inflation
• Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe
• Generating the curvature perturbation at the end of inflation
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• The Cosmic Microwave Background Bispectrum and Inflation
• The Angular Trispectra of CMB Temperature and Polarization
• Evolution of second-order cosmological perturbations
• Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function
• Conformal Transformations with Multiple Scalar Fields
• Inflationary models inducing non-Gaussian metric fluctuations
• Evidence for non-Gaussianity in the COBE DMR Four Year Sky Maps
• Primordial Bispectrum from Multifield Inflation with Nonminimal Couplings
• Non-Gaussianity from Preheating
• CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation
• Improved Primordial Non-Gaussianity Constraints from Measurements of Galaxy Clustering and the Integrated Sachs-Wolfe Effect
• Estimating non-gaussianity in the microwave background
• Nongaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation
• Constraints on primordial non-Gaussianity from 800,000 photometric quasars
• Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies
• Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity
• Signature of primordial non-Gaussianity of phi^3-type in the mass function and bias of dark matter haloes
• Lattice calculation of non-Gaussianity from preheating
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
• Very Large Primordial Non-Gaussianity from multi-field: Application to Massless Preheating
• Non-Gaussianity of quantum fields during inflation
• On the generation of density perturbations at the end of inflation
• Non-Gaussianity from massless preheating
• Some Aspects of Tachyon Field Cosmology
• Constraints on f_nl and g_nl from the analysis of the N-pdf of the CMB large scale anisotropies
• Optimal Trispectrum Estimators and WMAP Constraints
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum
• Use of delta N formalism - Difficulties in generating large local-type non-Gaussianity during inflation -
• Limits on Second-Order Non-Gaussianity from Minkowski Functionals of WMAP Data
• Braneworld non-minimal inflation with induced gravity
• DBI inflation with a non-minimally coupled Gauss-Bonnet term
• Optimal analysis of the CMB trispectrum
• The Separate Universe Approach to Soft Limits
• Large Non-Gaussianity in Non-Minimally Coupled Derivative Inflation with Gauss-Bonnet Correction
• Planck Trispectrum Constraints on Primordial Non-Gaussianity at Cubic Order
• Non-Minimal Braneworld Inflation after the Planck
• Non-Gaussianity constrains hybrid inflation