Strongly Coupled Sectors in Inflation: Gapped Theories of Unparticles

TL;DR

This work investigates a strongly coupled spectator sector during inflation realized as a five-dimensional CFT on $ ext{dS}_4\times S^1_R$ whose KK reduction produces gapped unparticles with gap $M_{ ext{Gap}}\sim 1/R$. By dimensional reduction and in-in computations, the authors derive the collapsed-limit trispectrum for conformally coupled scalars exchanging gapped unparticles, encoding the signal in a master function $F^{(\mu)}(u,v)$ with envelope controlled by the 5D scaling dimension $\Delta$ and oscillation frequency set by the 4D mass parameter $\mu=p/(HR)$. They highlight a clear strategy to distinguish gapped unparticles from heavy scalars, including interference patterns when multiple KK modes share a universal coupling, and discuss holographic duals and future directions such as analytic templates, holographic implementations, and observational constraints. The results reveal novel oscillatory features in cosmological correlators arising from gapped, highly anomalous sectors, providing a calculable framework to probe extra-dimensional unparticle dynamics during inflation. Overall, the study advances the understanding of how strongly coupled, gapped sectors leave imprints on primordial density perturbations and offers avenues for extracting their parameters from cosmological data.

Abstract

We consider a novel scenario for a strongly coupled spectator sector during inflation, that of a higher dimensional conformal field theory with large anomalous dimensions -- ``unparticles" -- and compactify the extra dimensions. More specifically, we take generalized free fields in five dimensions, where the extra dimension is compactified to a circle. Due to the usual Kaluza-Klein mechanism, the resulting excitations carry properties of both particles and unparticles, so we dub this scenario ``gapped unparticles". We derive a two-point function of the gapped unparticles by performing dimensional reduction. We then compute, in the collapsed limit, the four-point correlation function of conformally coupled scalars exchanging a gapped unparticle, which are used as seed functions to obtain the correlation function of primordial density perturbations. The phenomenology of the resulting correlators presents some novel features, such as oscillations with an envelope controlled by the anomalous dimension, rather than the usual value of 3/2. Depending on the value of the five-dimensional scaling dimension and effective mass of the gapped unparticles, we find a clear strategy to distinguish gapped unparticles from heavy massive scalars. If we assume the interactions are localized on a brane, gapped unparticles with different effective masses will share a universal coupling, and their exchanges produce an interesting interference pattern.

Figures (8)

• Figure 1:
• Figure 2: Behaviors in the collapsed limit when we fix $\Delta$ to be 1.8. In order to visually enhance the magnitudes for comparison, we rescaled $F^{(\mu)}(u,u)$ by $u^{-\Delta}$, and we set the absolute value of maxima/minima to be 1.
• Figure 3: Interfering behaviors in the collapsed limit, when we fix $\Delta$ to $2.7$, and effective mass to $\mu=n/2\pi$. The $n$'s in the legend denote the highest level of excitation in the KK tower we are considering. The zero mode is not included. In order to visually enhance the magnitudes for comparison, we rescaled $F^{(\mu)}(u,u)$ by $u^{-\Delta}$, and we rescaled the minima to $-1$.
• Figure 4: Behaviors in the collapsed limit with $\Delta=2.7$ and effective mass $\mu=n/100$. The $n$'s in the legend denote the highest level of excitation in the KK tower we are considering. The zero mode is not included. In order to visually enhance the magnitudes for comparison, we rescaled $F^{(\mu)}(u,u)$ by $u^{-\Delta}$.
• Figure 5: Behaviors in the collapsed limit with $\Delta=2.7$ and effective mass $\mu=n/2\pi$. We fix the highest level of excitation in the KK tower to $n=3$. The zero mode is not included. In order to visually enhance the magnitudes for comparison, we rescaled $F^{(\mu)}(u,u)$ by $u^{-\Delta}$, and we rescaled the minima to $-1$.