Effects of Nonlinear Dispersion Relations on Non-Gaussianities

Abstract

We investigate the effect of non-linear dispersion relations on the bispectrum. In particular, we study the case were the modified relations do not violate the WKB condition at early times, focusing on a particular example which is exactly solvable: the Jacobson-Corley dispersion relation with quartic correction with positive coefficient to the squared linear relation. We find that the corrections to the standard result for the bispectrum are suppressed by a factor $\frac{H^2}{p_c^2}$ where $p_c$ is the scale where the modification to the dispersion relation becomes relevant. The modification is {\it mildly} configuration-dependent and equilateral configurations are more suppressed with respect to the local ones, by a factor of one percent. There is no configuration leading to enhancements. We then analyze the results in the framework of particle creation using the approximate gluing method of Brandenberger and Martin, which relates more directly to the modeling of the trans-Planckian physics via modifications of the vacuum at a certain cutoff scale. We show that the gluing method overestimates the leading order correction to the spectrum and bispectrum by one and two orders, respectively, in $\frac{H}{p_c}$. We discuss the various approximation and conclude that for dispersion relations not violating WKB at early times the particle creation is small and does not lead to enhanced contributions to the bispectrum. We also show that in many cases enhancements do not occur when modeling the trans-Planckian physics via modifications of the vacuum at a certain cutoff scale. Most notably they are only of order O(1) when the Bogolyubov coefficients accounting for particle creation are determined by the Wronskian condition and the minimization of the uncertainty between the field and its conjugate momentum.

v1: 11 pages, 2 figures; v2: references updated

References in corpus (8)

• Quantum Gravity at a Lifshitz Point
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Enhanced Non-Gaussianity from Excited Initial States
• Equilateral Non-Gaussianity and New Physics on the Horizon
• Minimum Length Cutoff in Inflation and Uniqueness of the Action
• A Note on Calm Excited States of Inflation
• On the Tensor/Scalar Ratio in Inflation with UV Cutoff

Cited by in corpus (35)

• Features and New Physical Scales in Primordial Observables: Theory and Observation
• EFT Compatible PBHs: Effective Spawning of the Seeds for Primordial Black Holes during Inflation
• Effective field theory of weakly coupled inflationary models
• On (in)stabilities of perturbations in mimetic models with higher derivatives
• Galilean Creation of the Inflationary Universe
• Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound
• Inflationary cosmology with nonlinear dispersion relations
• Extended Effective Field Theory of Inflation
• Testing quantum gravity effects with latest CMB observations
• Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame
• Phenomenological implications of modified loop cosmologies: an overview
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Inflationary spectra with inverse-volume corrections in loop quantum cosmology and their observational constraints from Planck 2015 data
• High-order Primordial Perturbations with Quantum Gravitational Effects
• Scalar and tensor perturbations in loop quantum cosmology: High-order corrections
• Detecting quantum gravitational effects of loop quantum cosmology in the early universe?
• Enhanced CMBR non-Gaussianities from Lorentz violation
• Getting Super-Excited with Modified Dispersion Relations
• Primordial non-Gaussianities of gravitational waves beyond Horndeski
• Scalar-Induced Gravitational Waves from Ghost Inflation and Parity Violation
• Mimetic Inflation
• Non-Unitary Evolution in the General Extended EFT of Inflation & Excited Initial States
• No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics
• Correlation of supernova redshifts with temperature fluctuations of the Cosmic Microwave Background
• Inflationary perturbation spectrum in extended effective field theory of inflation
• Effect of intermediate Minkowskian evolution on CMB bispectrum
• Non-Gaussianities in the Extended EFT of Inflation
• Quantum Entanglement in Multi-field Inflation
• A resolution of the Trans-Planckian problem in the R_h=ct universe
• Aspects of Quantum Gravity in Cosmology
• Inflationary Cosmology with Quantum Gravitational Effects and the Swampland Conjectures
• Suppressing the primordial tensor amplitude without changing the scalar sector in quadratic curvature gravity
• No smooth spacetime: Exploring primordial perturbations in Lorentzian quantum cosmology
• Inflationary perturbations with Lifshitz scaling
• Stable initial conditions and analytical investigations of cosmological perturbations in a modified loop quantum cosmology