Probing P and CP Violations on the Cosmological Collider

TL;DR

This paper develops a cosmological collider framework to probe P and CP violation in the early universe via the four-point correlation (trispectrum) of primordial fluctuations. By coupling an axion-like rolling field to a massive gauge sector and analyzing both perturbative and non-perturbative regimes, the authors demonstrate that CP violation produces a CP-odd, imaginary part of the trispectrum with a distinctive dihedral-angle dependence, and that observable signals arise from on-shell particle production rather than from local EFT operators in exact de Sitter space. They show that, within a realistic two-field model, leading-order results yield $ au_{NL}$ of order $10$, while partially non-perturbative effects can boost the signal to ${\rm Im}\,\tau_{NL} \sim 10^2$, subject to energy-density and perturbativity constraints. A key theoretical result is that CP-violating local four-field EFT operators in exact dS are unobservable, implying any detected signal would indicate non-local dynamics beyond single-field EFT and potentially point to new high-energy physics during inflation. The study thus establishes CP violation in the cosmological collider as a probe of on-shell dynamics and motivates UV-complete models and possible links to spontaneous baryogenesis.

Abstract

In direct analogy to the 4-body decay of a heavy scalar particle, the 4-point correlation function of primordial fluctuations carries P and CP information. The CP violation appears as a P-odd angular dependence in the imaginary part of the trispectrum in momentum space. We construct a model with axion-like couplings which leads to observably large CP-violating trispectrum for future surveys. Furthermore, we show the importance of on-shell particle production in observing P- and CP-violating signals. It is impossible to observe these signals from local 4-scalar EFT operators that respect dS isometries, and thus any such observation can rule out single-field EFT with sufficiently small slow-roll parameters. This calculation opens a new frontier of studying P and CP at very high energy scales.

Figures (10)

• Figure 1: The kinematics of $X\rightarrow VV\rightarrow 4f$.
• Figure 2: The induced CP-violating t-channel diagram. See the text for explanation of various lines. We adopted the diagrammatic notation in Chen:2017ryl.
• Figure 3: The leading-order CP-violating t-channel diagram.
• Figure 4: The perturbatively computed dimensionless trispectrum divided by couplings $\tilde{T}^{PT}\equiv T^{PT}/c(\frac{\rho_2}{H})^2(\frac{\rho_{1,Z}}{\dot{\phi}_0})^2$ as a function of $\phi$ with different momentum configurations. Left panel: $k_1=q_1=1,p=2,\theta_k=\theta_q=\pi/3$, middle panel: $k_1=1,q_1=\sqrt{2},p=2,\theta_k=\pi/3,\theta_q=\pi/4$, right panel: $k_1=1,q_1=p=2,\theta_k=\pi/3,\theta_q=\pi/4$. The masses are chosen as $\mu_h=0.3$, $\mu_Z=0.2$, which correspond to $m_h=1.53H, m_Z=0.54H$.
• Figure 5: The dimensionless trispectrum divided by couplings $\tilde{T}^\bot\equiv T^\bot/(\frac{\rho_2}{H})^2(\frac{\rho_{1,Z}}{\dot{\phi}_0})^2$ as a function of $\phi$ with different momentum configuration. Left panel: $k_1=q_1=1,p=2,\theta_k=\theta_q=\pi/3$, middle panel: $k_1=1,q_1=\sqrt{2},p=2,\theta_k=\pi/3,\theta_q=\pi/4$, right panel: $k_1=1,q_1=p=2,\theta_k=\pi/3,\theta_q=\pi/4$. Here we have taken $c=0.1$ (perturbative in $c$) for the first line and $c=0.6$ (non-perturbative in $c$, marginal in loops) for the second line. The masses are chosen as $\mu_h=0.3$, $\mu_Z=0.2$, which correspond to $m_h=1.53H, m_Z=0.54H$. In these cases, $\mathrm{Im}\,\tau_{NL}\sim \mathcal{O}(10^{2})$ if the couplings are all near $0.2$.

Theorems & Definitions (2)

• Theorem
• proof