Abstract
Non-analyticity in co-moving momenta within the non-Gaussian bispectrum is a distinctive sign of on-shell particle production during inflation, presenting a unique opportunity for the “direct detection” of particles with masses as large as the inflationary Hubble scale (H). However, the strength of such non-analyticity ordinarily drops exponentially by a Boltzmann-like factor as masses exceed H. In this paper, we study an exception provided by a dimension-5 derivative coupling of the inflaton to heavy-particle currents, applying it specifically to the case of two real scalars. The operator has a “chemical potential” form, which harnesses the large kinetic energy scale of the inflaton, {overset{cdot }{phi}}_0^{1/2}approx 60H , to act as an efficient source of scalar particle production. Derivative couplings of inflaton ensure radiative stability of the slow-roll potential, which in turn maintains (approximate) scale-invariance of the inflationary correlations. We show that a signal not suffering Boltzmann suppression can be obtained in the bispectrum with strength fNL ∼ mathcal{O} (0.01–10) for an extended range of scalar masses lesssim {overset{cdot }{phi}}_0^{1/2} , potentially as high as 1015 GeV, within the sensitivity of upcoming LSS and more futuristic 21-cm experiments. The mechanism does not invoke any particular fine-tuning of parameters or breakdown of perturbation-theoretic control. The leading contribution appears at tree-level, which makes the calculation analytically tractable and removes the loop-suppression as compared to earlier chemical potential studies of non-zero spins. The steady particle production allows us to infer the effective mass of the heavy particles and the chemical potential from the variation in bispectrum oscillations as a function of co-moving momenta. Our analysis sets the stage for generalization to heavy bosons with non-zero spin.
Highlights
We compute the full analytic form of these contributions in appendix B, we show the same calculation using the stationary phase method, which is more transparent in terms of demonstrating particle production through chemical potential
We have shown that a derivative coupling of the inflaton to heavy scalar fields of “chemical potential” type can lead to unsuppressed production of heavy particles and leave observable imprints in primordial non-Gaussianities
The unsuppressed particle production above H draws on the large kinetic energy of the inflaton background, φ0 ∼ (60H)2
Summary
Let us start with the definitions and the notation that we will use throughout the paper. It is related to the proper time t through the relation dη = dt/a(t), where a(t) is the scale factor. This gives ηH = −e−Ht during inflation. It is customary to typify the strength of NG by a single number, fNL, at the “equilateral” configuration where all the momenta have the same magnitude, fNL This definition is consistent with the convention for local NG (fNloLcal) at the equilateral point. The reader may refer to [58] for a more comprehensive review Using this formalism, the expectation value of a Heisenberg operator OH at any single time t can be perturbatively computed using, Ω| OH (t) |Ω = 0|. The bispectrum is the 3-point correlation function evaluated at the end of inflation, i.e., O(t) → (ξk1ξk2ξk3)|η≈0 in eq (2.11)
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