Strongly Coupled Sectors in Inflation: Gapless Theories and Unparticles

TL;DR

This work investigates inflationary perturbations coupled to a gapless, strongly coupled spectator sector ('unparticles') and develops a framework to compute their cosmological signatures. The authors derive an analytic de Sitter four-point function for conformally coupled scalars with unparticle exchange using Mellin-Barnes methods, and then obtain inflationary bispectra and trispectra via weight-shifting and bootstrap differential equations that encode the unparticle symmetries. They extend the analysis to spinning unparticles, providing explicit results for spin-1 and spin-2 exchanges, and study the phenomenology of the resulting shape functions, identifying three characteristic bispectrum shapes and novel half-integer-dimension shapes. A key finding is that the squeezed limit alone cannot determine the presence of a light particle; full shapes of bispectra and trispectra are required to break degeneracies and extract unparticle physics, with implications for future cosmological probes and holographic modeling of strongly coupled sectors during inflation.

Abstract

We compute correlation functions of the primordial density perturbations when they couple to a gapless, strongly coupled sector of spectator fields -- ``unparticles" -- during inflation. We first derive a four-point function of conformally coupled scalars for all kinematic configurations in de Sitter, which exchanges an unparticle at tree-level, by performing direct integration using the Mellin-Barnes method. To obtain inflationary bispectra and trispectra, we apply weight-shifting operators to the conformally coupled scalar correlator. We show that the correlators solve differential equations determined by the additional symmetries enjoyed by the unparticle propagator. Based on these differential equations, we are able to discuss the spinning-unparticle exchanges, focusing on two possible cases where the currents or the stress tensor of unparticles are coupled to inflatons, with the help of spin-raising operators. Finally, we study the phenomenology of the resulting shape functions. Depending on the value of the unparticle scaling dimension, we classify three characteristic shapes for the inflationary bispectra, including near-equilateral, near-orthogonal, and a novel shape which appears when the scaling dimensions are close to half-integers. More generally, we find that the leading order squeezed limits are insufficient to conclusively determine the detection of a light particle or unparticle. Only the full shapes of bispectra and trispectra can break this degeneracy.

Figures (10)

• Figure 1: Holographic picture for $\text{M}_{\text{Gap}} \ll H$ scenario. The gravity dual of a gapless theory is pure $\text{AdS}$ with a $\text{dS}$ conformal boundary.
• Figure 2: Holographic picture for $\text{M}_{\text{Gap}} \gg H$ scenario. The lightest state in the spectrum is heavy in Hubble units, thus the resulting non-Gaussianities in this model will be equilateral-like.
• Figure 3: Holographic picture for $\text{M}_{\text{Gap}} \sim H$ scenario. Many resonances around the Hubble scale will be produced efficiently, interfering with each other and producing a novel shape of non-Gaussianity.
• Figure 4: Soft limit of trispectra
• Figure 5: Left panel: Example of massive scalar exchange, $u^{-1}\tilde{F}(u,0.5)$, for four-point function of conformally coupled scalars $\varphi$ and an internal particle with $\mu=3$Arkani-Hamed:2018kmz. Right panel: Example of scalar unparticle exchange $u^{-1}F(u,0.5)$, for four-point function of $\varphi$ and an internal unparticle with $\Delta=7/2$. Note that we rescaled the four-point functions by $u^{-1}$ in order to visually enhance the squeezed-limit behaviors. To illustrate the shape in the right panel, we also rescale the prefactor in \ref{['result:4pt']} which is supposed to significantly suppress the amplitude with the increase of $\Delta$.