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

A universal differentiability set in Banach spaces with separable dual

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fr\'echet differentiable somewhere in S.Comment: 41 pages, 1 figur

Dissecting the high-z interstellar medium through intensity mapping cross-correlations

We explore the detection, with upcoming spectroscopic surveys, of three-dimensional power spectra of emission line fluctuations produced in different phases of the Interstellar Medium (ISM) by ionized carbon, ionized nitrogen and neutral oxygen at redshift z>4. The emission line [CII] from ionized carbon at 157.7 micron, and multiple emission lines from carbon monoxide, are the main targets of planned ground-based surveys, and an important foreground for future space-based surveys like the Primordial Inflation Explorer (PIXIE). However, the oxygen [OI] (145.5 micron) line, and the nitrogen [NII] (121.9 micron and 205.2 micron) lines, might be detected in correlation with [CII] with reasonable signal-to-noise ratio (SNR). These lines are important coolants of both the neutral and the ionized medium, and probe multiple phases of the ISM. We compute predictions of the three-dimensional power spectra for two surveys designed to target the [CII] line, showing that they have the required sensitivity to detect cross-power spectra with the [OI] line, and the [NII] lines with sufficient SNR. The importance of cross-correlating multiple lines is twofold. On the one hand, we will have multiple probes of the different phases of the ISM, which is key to understand the interplay between energetic sources, the gas and dust at high redshift. This kind of studies will be useful for a next-generation space observatory such as the NASA Far-IR Surveyor. On the other end, emission lines from external galaxies are an important foreground when measuring spectral distortions of the Cosmic Microwave Background spectrum with future space-based experiments like PIXIE; measuring fluctuations in the intensity mapping regime will help constraining the mean amplitude of these lines, and will allow us to better handle this important foreground.Comment: 13 pages, 2 table, 7 figures, Accepted for publication in Ap

Do baryons trace dark matter in the early universe?

Baryon-density perturbations of large amplitude may exist if they are compensated by dark-matter perturbations so that the total density remains unchanged. Big-bang nucleosynthesis and galaxy clusters allow the amplitudes of these compensated isocurvature perturbations (CIPs) to be as large as $\sim10$. CIPs will modulate the power spectrum of cosmic microwave background (CMB) fluctuations---those due to the usual adiabatic perturbations---as a function of position on the sky. This leads to correlations between different spherical-harmonic coefficients of the temperature/polarization map, and it induces B modes in the CMB polarization. Here, the magnitude of these effects is calculated and techniques to measure them are introduced. While a CIP of this amplitude can be probed on the largest scales with WMAP, forthcoming CMB experiments should improve the sensitivity to CIPs by at least an order of magnitude.Comment: 4 pages, 3 figures, updated with version published in Phys. Rev. Lett. Results unchanged. Added expanded discussion of how to disentangle compensated isocurvature perturbations from weak lensing of the CMB. Expanded discussion of early universe motivation for compensated isocurvature perturbation