In search of an observational quantum signature of the primordial perturbations in slow-roll and ultra slow-roll inflation

In the standard inflationary paradigm, cosmological density perturbations are generated as quantum fluctuations in the early Universe, but then undergo a quantum-to-classical transition. A key role in this transition is played by squeezing of the quantum state, which is a result of the strong suppression of the decaying mode component of the perturbations. Motivated by ever improving measurements of the cosmological perturbations, we ask whether there are scenarios where this decaying mode is nevertheless still observable in the late Universe, ideally leading to a ``smoking gun'' signature of the quantum nature of the perturbations. We address this question by evolving the quantum state of the perturbations from inflation into the post-inflationary Universe. After recovering the standard result that in slow-roll (SR) inflation the decaying mode is indeed hopelessly suppressed by the time the perturbations are observed (by $\sim 115$ orders of magnitude), we turn to ultra slow-roll (USR) inflation, a scenario in which the usual decaying mode actually grows on super-horizon scales. Despite this drastic difference in the behavior of the mode functions, we find also in USR that the late-Universe decaying mode amplitude is dramatically suppressed, in fact by the same $\sim 115$ orders of magnitude. We finally explain that this large suppression is a general result that holds beyond the SR and USR scenarios considered and follows from a modified version of Heisenberg's uncertainty principle and the observed amplitude of the primordial power spectrum. The classical behavior of the perturbations is thus closely related to the classical behavior of macroscopic objects drawing an analogy with the position of a massive particle, the curvature perturbations today have an enormous effective mass of order $m_{\rm pl}^2/H_0^2 \sim 10^{120}$, making them highly classical.Comment: 27 pages, 7 figures. Comments welcom

Single-Field Inflation and the Local Ansatz: Distinguishability and Consistency

The single-field consistency conditions and the local ansatz have played separate but important roles in characterizing the non-Gaussian signatures of single- and multifield inflation respectively. We explore the precise relationship between these two approaches and their predictions. We demonstrate that the predictions of the single-field consistency conditions can never be satisfied by a general local ansatz with deviations necessarily arising at order $(n_s-1)^2$. This implies that there is, in principle, a minimum difference between single- and (fully local) multifield inflation in observables sensitive to the squeezed limit such as scale-dependent halo bias. We also explore some potential observational implications of the consistency conditions and its relationship to the local ansatz. In particular, we propose a new scheme to test the consistency relations. In analogy with delensing of the cosmic microwave background, one can deproject the coupling of the long wavelength modes with the short wavelength modes and test for residual anomalous coupling.Comment: 17 page

Designing an inflation galaxy survey: How to measure σ(f_(NL))∼1 using scale-dependent galaxy bias

The most promising method for measuring primordial non-Gaussianity in the post-Planck era is to detect large-scale, scale-dependent galaxy bias. Considering the information in the galaxy power spectrum, we here derive the properties of a galaxy clustering survey that would optimize constraints on primordial non-Gaussianity using this technique. Specifically, we ask the question of what survey design is needed to reach a precision σ(f^(loc)_(NL))≈1. To answer this question, we calculate the sensitivity to f^(loc)_(NL) as a function of galaxy number density, redshift accuracy and sky coverage. We include the multitracer technique, which helps minimize cosmic variance noise, by considering the possibility of dividing the galaxy sample into stellar mass bins. We show that the ideal survey for f^(loc)_(NL) looks very different than most galaxy redshift surveys scheduled for the near future. Since those are more or less optimized for measuring the baryon acoustic oscillation scale, they typically require spectroscopic redshifts. On the contrary, to optimize the f^(loc)_(NL) measurement, a deep, wide, multiband imaging survey is preferred. An uncertainty σ(f^(loc)_(NL))=1 can be reached with a full-sky survey that is complete to an i-band AB magnitude i≈23 and has a number density ∼8  arcmin^(-2). Requirements on the multiband photometry are set by a modest photo-z accuracy σ(z)/(1+z)<0.1 and the ability to measure stellar mass with a precision ∼0.2 dex or better (or another proxy for halo mass with equivalent scatter). Finally, we estimate that for the idealized case of a survey measuring all halos down to a mass 10^(10)h^(-1)  M⊙ on the full sky out to high redshift, in principle a precision of order σ(f_(NL))∼0.1 can be achieved

Is there scale-dependent bias in single-field inflation?

Scale-dependent halo bias due to local primordial non-Gaussianity provides a strong test of single-field inflation. While it is universally understood that single-field inflation predicts negligible scale-dependent bias compared to current observational uncertainties, there is still disagreement on the exact level of scale-dependent bias at a level that could strongly impact inferences made from future surveys. In this paper, we clarify this confusion and derive in various ways that there is exactly zero scale-dependent bias in single-field inflation. Much of the current confusion follows from the fact that single-field inflation does predict a mode coupling of matter perturbations at the level of f_(NL)^(local); ≈ −5/3, which naively would lead to scale-dependent bias. However, we show explicitly that this mode coupling cancels out when perturbations are evaluated at a fixed physical scale rather than fixed coordinate scale. Furthermore, we show how the absence of scale-dependent bias can be derived easily in any gauge. This result can then be incorporated into a complete description of the observed galaxy clustering, including the previously studied general relativistic terms, which are important at the same level as scale-dependent bias of order f_(NL)^(local) ~ 1. This description will allow us to draw unbiased conclusions about inflation from future galaxy clustering data

Next non-Gaussianity frontier: What can a measurement with σ (f_(NL)) ≲ 1 tell us about multifield inflation?

Future galaxy surveys promise to probe local primordial non-Gaussianity at unprecedented precision, σ (f_(NL)) ≲ 1. We study the implications for multifield inflation by considering spectator models, where inflation is driven by the inflaton field, but the primordial perturbations are (partially) generated by a second, spectator field. We perform a Markov chain Monte Carlo likelihood analysis using Planck data to study quantitative predictions for f_(NL) and other observables for a range of such spectator models. We show that models where the primordial perturbations are dominated by the spectator field, while fine-tuned within the broader parameter space, typically predict f_(NL) of order unity. Therefore, upcoming galaxy clustering measurements will constitute a stringent test of whether or not the generation of primordial perturbations and the accelerated expansion in the inflationary universe are due to separate phenomena