Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Non-Gaussianity of quantum fields during inflation

Kazuya Koyama

TL;DR

The paper addresses how inflation generates non-Gaussianity in cosmological perturbations by computing the bispectrum of the curvature perturbation using the in-in formalism and delta-N formalism. It develops the cubic action in two gauges, analyzes both k-inflation and slow-roll inflation, and translates quantum-field bispectra into the curvature bispectrum, revealing distinct shapes: local from super-horizon nonlinearities and equilateral from horizon-scale derivative interactions. The work provides explicit amplitude and shape expressions and cross-checks gauge-based calculations, highlighting how observational templates can distinguish between models such as DBI/k-inflation and standard slow-roll. It underlines the significance for CMB and LSS analyses and the potential of upcoming data to constrain or reveal primordial non-Gaussianity, with implications for early-universe physics and model-building.

Abstract

In this review, we discuss how non-Gaussianity of cosmological perturbations arises from inflation. After introducing the in-in formalism to calculate the $n$-point correlation function of quantum fields, we present the computation of the bispectrum of the curvature perturbation generated in general single field inflation models. The shapes of the bispectrum are compared with the local-type non-Gaussianity that arises from non-linear dynamics on super-horizon scales.

Non-Gaussianity of quantum fields during inflation

TL;DR

The paper addresses how inflation generates non-Gaussianity in cosmological perturbations by computing the bispectrum of the curvature perturbation using the in-in formalism and delta-N formalism. It develops the cubic action in two gauges, analyzes both k-inflation and slow-roll inflation, and translates quantum-field bispectra into the curvature bispectrum, revealing distinct shapes: local from super-horizon nonlinearities and equilateral from horizon-scale derivative interactions. The work provides explicit amplitude and shape expressions and cross-checks gauge-based calculations, highlighting how observational templates can distinguish between models such as DBI/k-inflation and standard slow-roll. It underlines the significance for CMB and LSS analyses and the potential of upcoming data to constrain or reveal primordial non-Gaussianity, with implications for early-universe physics and model-building.

Abstract

In this review, we discuss how non-Gaussianity of cosmological perturbations arises from inflation. After introducing the in-in formalism to calculate the -point correlation function of quantum fields, we present the computation of the bispectrum of the curvature perturbation generated in general single field inflation models. The shapes of the bispectrum are compared with the local-type non-Gaussianity that arises from non-linear dynamics on super-horizon scales.

Paper Structure

This paper contains 15 sections, 81 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quantum correlations in the in-in formalism
  3. Non-linear cosmological perturbations
  4. Inflation models
  5. Effective action for higher order perturbations
  6. Non-linear perturbations in the comoving gauge
  7. Non-linear perturbations in the uniform curvature gauge
  8. Relation between gauges
  9. Bispectrum of curvature perturbation
  10. Bispectrum of quantum fields in k-inflation
  11. Bispectrum of quantum fields in slow-roll inflation
  12. Bispectrum of curvature perturbation
  13. Computation in comoving gauge
  14. Shapes of Bispectrum
  15. Conclusion

Figures (2)

  • Figure 1: Left: Plot of the function $F(1,\, k_2/k_1, \, k_3/k_1) (k_2/k_1)^2 (k_3/k_1)^2$ predicted by the DBI models Alishahiha:2004eh. Right: Difference between the above plot and the analogous one (top of fig. \ref{['fig:shapes']}) for the factorizable equilateral shape used in the analysis. From Creminelli:2005hu.
  • Figure 2: Plot of the function $F(1,\, k_2/k_1, \, k_3/k_1) (k_2/k_1)^2 (k_3/k_1)^2$ for the equilateral shape used in the analysis (left) and for the local shape (right). The functions are both normalized to unity for equilateral configurations $\frac{k_2}{k_1}= \frac{k_3}{k_1}=1$. Since $F(k_1,k_2,k_3)$ is symmetric in its three arguments, it is sufficient to specify it for $k_1\ge k_2\ge k_3$, so $\frac{k_3}{k_1} \le \frac{k_2}{k_1} \le 1$ above. Moreover, the triangle inequality says that no side can be longer than the sum of the other two, so we only plot $F$ in the triangular region $1-\frac{k_2}{k_1}\leq \frac{k_3}{k_1} \leq\frac{k_2}{k_1} \le 1$ above, setting it to zero elsewhere. From Creminelli:2005hu.