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Four-point correlation functions in axion inflation

Hing-Tong Cho, Kin-Wang Ng

TL;DR

The authors address parity violation in the early universe by computing the inflaton four-point function within axion inflation using an open quantum system approach. They derive the influence action to fourth order, extract the connected 4PCF, and decompose it with isotropic basis functions to separate parity-even and parity-odd components. The leading parity-odd coefficient $\zeta_{234}$ is found to be nonzero in the large-$\xi$ regime, providing a concrete signature of parity violation, and the results are contrasted with galaxy-survey measurements to constrain model parameters. The analytic, parameter-space-friendly method offers a path to testing axion-inflation scenarios with current and future large-scale structure data.

Abstract

We study parity violation in the early universe by examining the four-point correlation function within the axion inflation model. Using an open quantum system formalism from our previous work, we calculate the influence functional to fourth order, from which we then derive the inflaton four-point correlation function. When we decompose this function using isotropic basis functions, the expansion coefficients $ζ_{\ell',\ell'',\ell'''}$ naturally split into parity-even and parity-odd components. In the large $ξ$ approximation, which enhances the production of right-handed photons in the model, the derivation of these coefficients simplifies. We work out the lowest-order nonvanishing parity-odd $ζ_{234}$ term which clearly indicates the presence of parity violation. Moreover, our derived values of the coefficients are consistent with recent observational data from galaxy surveys.

Four-point correlation functions in axion inflation

TL;DR

The authors address parity violation in the early universe by computing the inflaton four-point function within axion inflation using an open quantum system approach. They derive the influence action to fourth order, extract the connected 4PCF, and decompose it with isotropic basis functions to separate parity-even and parity-odd components. The leading parity-odd coefficient is found to be nonzero in the large- regime, providing a concrete signature of parity violation, and the results are contrasted with galaxy-survey measurements to constrain model parameters. The analytic, parameter-space-friendly method offers a path to testing axion-inflation scenarios with current and future large-scale structure data.

Abstract

We study parity violation in the early universe by examining the four-point correlation function within the axion inflation model. Using an open quantum system formalism from our previous work, we calculate the influence functional to fourth order, from which we then derive the inflaton four-point correlation function. When we decompose this function using isotropic basis functions, the expansion coefficients naturally split into parity-even and parity-odd components. In the large approximation, which enhances the production of right-handed photons in the model, the derivation of these coefficients simplifies. We work out the lowest-order nonvanishing parity-odd term which clearly indicates the presence of parity violation. Moreover, our derived values of the coefficients are consistent with recent observational data from galaxy surveys.

Paper Structure

This paper contains 14 sections, 107 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Influence action of axion inflation
  3. Four-point correlation functions
  4. Three-argument isotropic basis functions
  5. $\zeta_{111}$
  6. $\zeta_{122}$
  7. $\zeta_{234}$
  8. Observational constraints on parity violation
  9. Conclusions and discussions
  10. Evaluation of the terms in the influence action
  11. Derivation of the four-point correlation function in Eq. (\ref{['4ptcf1']})
  12. Wigner-3j symbols
  13. Functions ${\cal R}_{l_{1}\cdots l_{6}}$ and ${\cal E}_{l_{1}m_{1}\cdots l_{6}m_{6}}$
  14. A toy inflation model

Figures (4)

  • Figure 1: Inflaton potential $V(\varphi)$ with $\mu_1=1.74 \times 10^{-10}$, $\mu_2=8.7 \times 10^{-10}$, $C=1000$, $A=7.55 \times 10^{-10}$, $s=100$, and $d=6.775$. Here and in the following figures, we have set the reduced Planck mass $M_{P}=1$.
  • Figure 2: Evolution of $\varphi$ (dashed line) and $\xi$ (solid line), with $\varphi_0=7.3754$, $(d\varphi/dt)_0=-1.3095 \times 10^{-6}$, $H_0=1.9429 \times 10^{-5}$, and $\alpha=18.5$. Inflation lasts for $60.29$ e-foldings.
  • Figure 3: Evolution of $n_s$ (dotted line), $r$ (dashed line), and $dn_s/d\ln k$ (solid line). The right panel zooms in on the first $7$ e-foldings, drawn with $|dn_s/d\ln k|$.
  • Figure 4: Density power spectrum.