Imprints of Massive Primordial Fields on Large-Scale Structure

TL;DR

This work examines how massive isocurvature fields with $m\sim H$ during quasi-single-field inflation imprint tensor fluctuations into higher-point correlators. Using the in-in formalism, it computes tensor-scalar-scalar (tss) and scalar-tensor-tensor (stt) bispectra in the squeezed limit, finding that stt can violate consistency conditions while tss does not in the minimal model. The mass dependence enters through the parameter $\nu=\sqrt{9/4-m^{2}/H^{2}}$, shaping the squeezed-limit signals and their angular structure, with a local-type tss signature that could emerge in non-minimal, isotropy-broken realizations. Overall, the results clarify when single-clock consistency conditions hold and how extra fields could yield observable quadrupolar or anisotropic imprints in CMB and large-scale structure, offering a complementary angle to cosmological collider physics.

Abstract

Attention has focussed recently on models of inflation that involve a second or more fields with a mass near the inflationary Hubble parameter $H$, as may occur in supersymmetric theories if the supersymmetry-breaking scale is not far from $H$. Quasi-single-field (QsF) inflation is a relatively simple family of phenomenological models that serve as a proxy for theories with additional fields with masses $m\sim H$. Since QsF inflation involves fields in addition to the inflaton, the consistency conditions (ccs) between correlations that arise in single-clock inflation are not necessarily satisfied. As a result, correlation functions in the squeezed limit may be larger than in single-field inflation. Scalar non-Gaussianities mediated by the massive isocurvature field in QsF have been shown to be potentially observable. These are especially interesting since they would convey information about the mass of the isocurvature field. Here we consider non-Gaussian correlators involving tensor modes and their observational signatures. A physical correlation between a (long-wavelength) tensor mode and two scalar modes (tss), for instance, may give rise to local departures from statistical isotropy or, in other words, a non-trivial four-point function. The presence of the tensor mode may moreover be inferred geometrically from the shape dependence of the four-point function. We compute tss and stt (one soft curvature mode and two hard tensors) bispectra in QsF inflation, identifying the conditions necessary for these to "violate" the ccs. We find that while ccs are violated by stt correlations, they are preserved by the tss in the minimal QsF model. Our study of primordial correlators which include gravitons in seeking imprints of additional fields with masses $m\sim H$ during inflation can be seen as complementary to the recent "cosmological collider physics" proposal.

Figures (6)

• Figure 1: (a) Standard power spectrum of $\zeta$. (b) Correction to the power spectrum of $\zeta$ from interactions with $\sigma$. (c) Bispectrum of $\zeta$ from self-interactions. (d) Bispectrum of $\zeta$ from interactions with $\sigma$. Dashed line are associated with $\sigma$, continuous ones with $\zeta$.
• Figure 2: (e) Representation of a graviton-exchange diagram in the four-point function (which we mimic in the soft $K\ll k_i$ limit). Note the black shaded area stands for a generic type of interaction. (f) A pictorial representation of the momenta configuration of the non-trivial four-point function we are effectively probing in Eq. (\ref{['vara']}).
• Figure 3: (g) Tensor-scalar-scalar correlation from usual coupling between $\gamma$ and $\zeta$. (h,i) Leading order tensor-scalar-scalar correlator mediated by $\sigma$. Dashed line are associated with $\sigma$, wiggly lines with $\gamma$ and solid lines with $\zeta$.
• Figure 4: Plot of numerical values of the coefficient $w(\nu)$ introduced in Eq. (\ref{['res11']}) for $\nu$ ranging from $0.06$ up to $0.4$.
• Figure 5: Example of loop diagram contribution to the tss bispectrum. In QsF inflation any diagram that invoves a correlation between one tensor mode and one isocurvature mode is equal to zero for symmetry reasons.