Abstract
Observations of the cosmic microwave background do not yet determine whether inflation was driven by a slowly-rolling scalar field or involved another physical mechanism. In this paper we discuss the prospects of using the power spectra of scalar and tensor modes to probe the nature of inflation. We focus on the leading modification to the slow-roll dynamics, which entails a sound speed cs for the scalar fluctuations. We derive analytically a lower bound on cs in terms of a given tensor-to-scalar ratio r, taking into account the difference in the freeze-out times between the scalar and tensor modes. We find that any detection of primordial B-modes with r > 0.01 implies a lower bound on cs that is stronger than the bound derived from the absence of non-Gaussianity in the Planck data. For r ≳ 0.1, the bound would be tantalizingly close to a critical value for the sound speed, (cs)⋆ = 0.47 (corresponding to (fNLequil)⋆ = -0.93), which we show serves as a threshold for non-trivial dynamics beyond slow-roll. We also discuss how an order-one level of equilateral non-Gaussianity is a natural observational target for other extensions of the canonical paradigm.
Highlights
One of the central goals of modern cosmology is to determine the nature of inflation
While measurements of the cosmic microwave background (CMB) and the large-scale structure (LSS) are consistent with the predictions of single-field slow-roll models [1], we should still ask to what degree observations require that inflation occurred in this way
For δ1 = 0, removing the low- data has the effect of allowing large values of ε1 which lower the bound on cs, combined with small values of ε2 to satisfy the constraint from the running
Summary
One of the central goals of modern cosmology is to determine the nature of inflation. The amplitude of the induced equilateral bispectrum is fNeqLuil ∝ c−s 2, and the absence of significant non-Gaussianity in the Planck data [7] puts a lower bound on the allowed value of the sound speed: cs > 0.02 (95%CL). The critical sound speed (1.1) corresponds to equilateral non-Gaussianity with (fNeqLuil) = −0.93, which is two orders of magnitude below the sensitivity of Planck [7] but two orders of magnitude above the slow-roll expectation This result is surprisingly robust, as similar thresholds, with |fNeqLuil| O(1), exist for other cubic Goldstone interactions even when cs = 1. The outline of the paper is as follows: In Section 2, we derive an analytic bound on the sound speed for a given value of the tensor-to-scalar ratio This result follows from the expression in (1.2) and relies on minimal input from the data.
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