Probing two-field open inflation by resonant signals in correlation functions

Abstract

We derive oscillatory signals in correlation functions in two-field open inflation by means of the in-in formalism; such signatures are caused by resonances between oscillations in the tunnelling field and fluctuations in the inflaton during the curvature dominated, intermediate and subsequent inflationary regime. While amplitudes are model-dependent, we find distinct oscillations in the power and bi-spectrum that can act as a direct probe of the curvature dominated phase and thus, indirectly, strengthen the claim of the string landscape if they were observed. We comment on the prospects of detecting these tell-tale signs in current experiments, which is challenging, but not impossible.At the technical level, we pay special attention to the applicability conditions for truncation fluctuations to the light (inflaton) field and derive upper limits on the oscillation amplitude of the heavy field. A violation of these bounds requires a multi-field analysis at the perturbed level.1 In the original treatment by Coleman and De Luccia (CdL), the bubble expands almost at the speed of light after it has nucleated; the inner edge of its wall traces out hyperbolic surfaces in the surrounding Minkowski space (in the bubble interior) which are asymptotic to the light cone at the origin of the bubble. These surfaces of constant (negative) spatial curvature are precisely where the field is constant. They subsequently correspond to surfaces of constant CMB temperature, which is our definition of constant cosmic time. Thus, the whole of the observable (infinite) universe today fits in the space-time interior of the finite bubble. In the two-field model that we consider the universe inside the bubble is actually finite [6], which is sometimes referred to as quasi-open inflation.2 This line of reasoning is hampered by the measure problem [44,45] (see [46] for a review or proposed measures). The earliest attempt at making quantitative predictions for Ω k in open inflation can be found in [47], and for quasi-open inflation [6] in [48].

Planck2015 results

“…On the other hand, sharp features or corners in an inflationary potential can temporarily drive the inflaton away from slow-roll; these large changes in the field and derivatives can create evenly-spaced oscillations, to be discussed in the next subsection. However, in multifield models residual oscillations after corner-turning can also lead to logspaced oscillations, just as in the resonance models (Chen 2011;Achúcarro et al 2011;Battefeld et al 2013;Chen et al 2015). A preliminary search for bispectrum resonance signals was performed in the first Planck analysis (Planck Collaboration XXIV 2014) and our purpose here is to substantially increase the frequency range and number of models investigated.…”

Features and new physical scales in primordial observables: Theory and observation

“…Resonant non-Gaussianity, first observed in [199] and subsequently in the context brane [200] and axion monodromy inflation [201,202] is in fact a general feature of any model where a smooth slow-rolling potential is modulated by sinusoidal oscillations (cf. [203] for a general study of signatures of discrete shift symmetries during inflation, and [204] for studies of resonance in a multi-field context). As was first noticed in [205], the equation of motion for the mode functions of R that follow from (4)…”

A universal bound on excitations of heavy fields during inflation

“…Such a truncation can be justified if ε 1, so that the excitation amplitude after the transition is not too big. As shown in [55], a necessary (but not sufficient) conditions is (2.38), the above condition is satisfied for ε 0.01. Since corrections to the power-spectrum computed in Sec.…”