Features and New Physical Scales in Primordial Observables: Theory and Observation

TL;DR

This review addresses how features and new physical scales in primordial observables can illuminate the UV completion of inflation. It combines perturbation theory, the Mukhanov–Sasaki formalism, and the effective field theory of the adiabatic mode to show how transient variations in the speed of sound, background modulations, heavy-field dynamics, and pre-inflationary history imprint characteristic scales in the power spectrum ${P}_{ m R}(k)$ and, via consistency relations, in higher-point correlators like the bispectrum ${B}_{ m R}(k_1,k_2,k_3)$. It then connects these theoretical signatures to a broad array of observables, including CMB temperature and polarization anisotropies, 3D matter clustering, 21 cm probes, and especially CMB spectral distortions, which can access small scales inaccessible to traditional anisotropy measurements. The review also discusses statistical frameworks for feature searches, contrasting frequentist and Bayesian approaches, and surveys reconstruction versus top-down feature tests. Overall, the work outlines how current and upcoming data can perform coarse-grained spectroscopy of inflation, potentially revealing the presence and properties of heavy fields, initial-state effects, and pre-inflationary dynamics, thereby constraining the parent theory behind the cosmological standard model.

Abstract

All cosmological observations to date are consistent with adiabatic, Gaussian and nearly scale invariant initial conditions. These findings provide strong evidence for a particular symmetry breaking pattern in the very early universe (with a close to vanishing order parameter, $ε$), widely accepted as conforming to the predictions of the simplest realizations of the inflationary paradigm. However, given that our observations are only privy to perturbations, in inferring something about the background that gave rise to them, it should be clear that many different underlying constructions project onto the same set of cosmological observables. Features in the primordial correlation functions, if present, would offer a unique and discriminating window onto the parent theory in which the mechanism that generated the initial conditions is embedded. In certain contexts, simple linear response theory allows us to infer new characteristic scales from the presence of features that can break the aforementioned degeneracies among different background models, and in some cases can even offer a limited spectroscopy of the heavier degrees of freedom that couple to the inflaton. In this review, we offer a pedagogical survey of the diverse, theoretically well grounded mechanisms which can imprint features into primordial correlation functions in addition to reviewing the techniques one can employ to probe observations. These observations include cosmic microwave background anisotropies and spectral distortions as well as the matter two and three point functions as inferred from large-scale structure and potentially, 21 cm surveys.

Figures (29)

• Figure 1: Relaxation to the attractor with $W(\tau) = \lambda e^{-(\tau-\tau_0)\mu}$, with $\lambda = 5\times 10^{-5}/(4\pi^4), \tau_0 = -10^4$ and with $\mu$ running from $2,1,0.5$ and $0.35$ in the upper left, upper right, lower left and lower right panels, respectively. The fiducial attractor has spectral index $n_s = 0.965$.
• Figure 2: Transient drop in $c_s$, modelled by $w(\tau) = \lambda \tau^2e^{-(\tau-\tau_0)^2\mu}$, with $\lambda = 2\times 10^{-4}/(4\pi^4), \tau_0 = -30$ and with $\mu$ running from $0.01,0.1,1$ and $5$ in the upper left, upper right, lower left and lower right panels, respectively. The fiducial attractor has spectral index $n_s = 0.965$.
• Figure 3: Transient drop in $c_s$, modelling a so called 'ultra-slow turn', represented by $w(\tau) = \lambda \tau^2 ({\rm Tanh}[(\tau-\tau_i)\mu] - {\rm Tanh}[(\tau-\tau_f)\mu])$, with $\lambda = 5\times 10^{-5}/(4\pi^4), \tau_i = -75, \tau_f = -60$ and with $\mu$ running from $0.001, 0.005, 0.05$ and $0.1$ in the upper left, upper right, lower left and lower right panels, respectively. The fiducial attractor has spectral index $n_s = 0.965$.
• Figure 4: $f_{\rm NL}/\Delta_{\rm max}$ (Black lines) vs $\frac{\Delta {\@fontswitch{}{\mathcal{}} P}}{{\@fontswitch{}{\mathcal{}} P}}/\Delta_{\rm max}$ (Blue lines) for the equilateral (right), folded (middle) and squeezed shapes (left) for $\tau_0 k_* = -11$, $c =0.8$ (top) and $\tau_0 k_* = -11$, $c =1.5$ (bottom) respectively for the 'cosh' drop in the speed of sound, given by $c_s^{2} =1 -\frac{\Delta_{\rm max}}{{\rm cosh}[c(\tau - \tau_0)]}$.
• Figure 5: $m^2_\psi = M^2\left(1 - {\rm Sech}^2[\phi/\mu]\right)$