Correlating features in the primordial spectra

Abstract

Heavy fields coupled to the inflaton reduce the speed of sound in the effective theory of the adiabatic mode each time the background inflationary trajectory deviates from a geodesic. This can result in features in the primordial spectra. We compute the corresponding bispectrum and show that if a varying speed of sound induces features in the power spectrum, the change in the bispectrum is given by a simple formula involving the change in the power spectrum and its derivatives. In this manner, we provide a uniquely discriminable signature of a varying sound speed for the adiabatic mode during inflation that indicates the influence of heavy fields. We find that features in the bispectrum peak in the equilateral limit and, in particular, in the squeezed limit we find considerable enhancement entirely consistent with the single field consistency relation. From the perspective of the underlying effective theory, our results generalize to a wide variety of inflationary models where features are sourced by the time variation of background quantities. A positive detection of such correlated features would be unambiguous proof of the inflaton's nature as a single light scalar degree of freedom embedded in a theory that is UV completable.Although no significant evidence for features in the primordial power spectrum has been observed to date [1], a 10% modulation of power remains entirely consistent with direct reconstruction [2] of that region of the power spectrum accessible to present cosmic microwave background (CMB) observations [3]. Further improvement in our knowledge of the matter spectrum beyond the CMB scales from future large scale structure surveys [4] ought to furnish far superior statistics that may yet allow us to determine if there are any other scales present in the primordial power spectrum other than that which sets its amplitude [5].Inflationary models that generate features have been considered in the literature for various theoretical motivations. Examples include explaining outliers to the best fit ΛCDM models in the CMB [6] (see however [7]), probing and constraining couplings of the inflaton to other fields through particle production [8], probing modified vacuum structure [9], interrupted slow-roll [10] and perhaps even signatures of inflation's embedding in a UV complete theory [11].The perspective of this article is informed by recent findings that features induced by reduced and varying speeds of sound c s of the adiabatic mode might be an inevitable consequence of field excursions during inflation [12][13][14][15][16][17], and the surprisingly large role played by heavy fields in the dynamics of light fields (first noticed in [18], additionally elaborated upon in [19]). Specifically, heavy fields with masses much larger than the Hubble scale can influence the dynamics of the adiabatic mode in a manner that is entirely consistent with the persistence of slow-roll [13,14], the validity of an effectively single field description and the decoupling of the true high and low energy modes of the sys...

Probing primordial features with future galaxy surveys

“…Some of these mechanisms are based on a temporary violation of the slow-roll regime for the inflaton field and include punctuated inflation [7], a short inflationary stage preceded by a kinetic stage [8] or by a bounce from a contracting stage [9], a string theory-motivated climbing phase prior to inflation [10], a sharp edge in the first derivative of the inflaton potential [11], a step in the inflaton potential [12,13], a variation in the effective speed of sound [14][15][16], or a burst of particle production during inflation [17,18]. Resonant models instead include periodic oscillations in the potential and therefore super-imposed periodic features to the PPS [19] (see [20] for a review on primordial features).…”

Planck2015 results

“…For the simplest models there is a predicted relationship between the power spectrum and bispectrum amplitude (e.g., see also Achucarro et al 2013 for a two-field model). We note that typically the power spectrum has larger signal-to-noise at low frequency (i.e., below ω 1000) while the bispectrum dominates at higher frequency.…”

Correlating correlation functions of primordial perturbations

“…For example, M 4 3 =M 4 2 ¼ 3ð1 − c −2 s Þ=2 for Dirac-BornInfeld inflation [22] and 3ð1 − c −2 s Þ=4 when a single heavy degree of freedom is integrated out [3]. The source g B can be explicitly connected to P R for specific cases [5].…”

“…Heavy field effects which are justifiably described in effective field theories are shown to be capable of leaving observable imprints in a cosmological background by reducing the effective speed of sound for the curvature perturbation [2,3]. Inflationary dynamics involving heavy degrees of freedom can lead to oscillatory features in the power spectrum and a resonantly enhanced bispectrum [4,5] (see also [6]). The outliers in the power spectrum of the cosmic microwave background [7] and hints of primordial oscillatory signals in the bispectrum [8] could well be echoing the effects of heavy fields during inflation.…”