arXiv subjects

Enrico Pajer

Publications and source records attributed to Enrico Pajer.

At least 55 records · Page 3Linked to original sources

arXiv2019

Systematics of Adiabatic Modes: Flat Universes

Adiabatic modes are cosmological perturbations that are locally indistinguishable from a (large) change of coordinates. At the classical level, they provide model independent solutions. At the quantum level, they lead to soft theorems for cosmological correlators. We present a systematic derivation of adiabatic modes in spatially-flat cosmological backgrounds with asymptotically-perfect fluids. We find several new adiabatic modes including vector, time-dependent tensor and time-dependent scalar modes. The new vector and tensor modes decay with time in standard cosmologies but are the leading modes in contracting universes. We present a preliminary derivation of the related soft theorems. In passing, we discuss a distinction between classical and quantum adiabatic modes, we clarify the subtle nature of Weinberg second adiabatic mode and point out that the adiabatic nature of a perturbation is a gauge dependent statement.

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arXiv2018

Spectral distortion anisotropies from single-field inflation

Distortions of the Cosmic Microwave Background energy spectrum of the $μ$ type are sensitive to the primordial power spectrum through the dissipation of curvature perturbations on scales $k\simeq 50$ - $10^4\,\mathrm{Mpc}^{-1}$. Their angular correlation with large-scale temperature anisotropies is then sensitive to the squeezed limit of the primordial bispectrum. For inflationary models obeying the single-field consistency relation, we show that the observed $μT$ angular correlation that would correspond to the local shape vanishes exactly. All leading non-primordial contributions, including all non-linear production and projection effects, are of the "equilateral shape", namely suppressed by $k^2/{\cal H}_f^2$, where ${\cal H}_f\simeq 10^{-1}\,{\rm Mpc}^{-1}$ is the Hubble radius at the end of the $μ$-era. Therefore, these non-primordial contributions are orthogonal to a potential local primordial signal (e.g. from multi-field inflation). Moreover, they are very small in amplitude. Our results strengthen the position of $μ$ distortions as the ultimate probe of local primordial non-Gaussianity.

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arXiv2018

Imprints of Oscillatory Bispectra on Galaxy Clustering

Long-short mode coupling during inflation, encoded in the squeezed bispectrum of curvature perturbations, induces a dependence of the local, small-scale power spectrum on long-wavelength perturbations, leading to a scale-dependent halo bias. While this scale dependence is absent in the large-scale limit for single-field inflation models that satisfy the consistency relation, certain models such as resonant non-Gaussianity show a peculiar behavior on intermediate scales. We reconsider the predictions for the halo bias in this model by working in Conformal Fermi Coordinates, which isolate the physical effects of long-wavelength perturbations on short-scale physics. We find that the bias oscillates with scale with an envelope similar to that of equilateral non-Gaussianity. Moreover, the bias shows a peculiar modulation with the halo mass. Unfortunately, we find that upcoming surveys will be unable to detect the signal because of its very small amplitude. We also discuss non-Gaussianity due to interactions between the inflaton and massive fields: our results for the bias agree with those in the literature.

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arXiv2018

Divergence of Perturbation Theory in Large Scale Structures

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White, and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

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arXiv2018

Soft Theorems For Shift-Symmetric Cosmologies

We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift-symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for Ultra-slow-roll inflation, a particular shift-symmetric, non-attractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.

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arXiv2018

The Effective Theory of Shift-Symmetric Cosmologies

A shift symmetry is a ubiquitous ingredient in inflationary models, both in effective constructions and in UV-finite embeddings such as string theory. It has also been proposed to play a key role in certain Dark Energy and Dark Matter models. Despite the crucial role it plays in cosmology, the observable, model independent consequences of a shift symmetry are yet unknown. Here, assuming an exact shift symmetry, we derive these consequences for single-clock cosmologies within the framework of the Effective Field Theory of Inflation. We find an infinite set of relations among the otherwise arbitrary effective coefficients, which relate non-Gaussianity to their time dependence. For example, to leading order in derivatives, these relations reduce the infinitely many free functions in the theory to just a single one. Our Effective Theory of shift-symmetric cosmologies describes, among other systems, perfect and imperfect superfluids coupled to gravity and driven superfluids in the decoupling limit. Our results are the first step to determine observationally whether a shift symmetry is at play in the laws of nature and whether it is broken by quantum gravity effects.

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arXiv2017

Hunting high and low: Disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function (PDF) and the two-point clustering of spherically-averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high and low density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale-dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured nonlinear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from $f_{\rm NL}=-100$ to $+100$ they are found to agree within 2\% or better for densities $ρ\in[0.5,3]$ in spheres of radius 15 Mpc$/h$ down to $z=0.35$. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the nonlinear variance $σ_8$ and primordial skewness $f_{\rm NL}$ are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.

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arXiv2016

How Gaussian can our Universe be?

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of $k_\ell^2/k_s^2$, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order $0.1\times(n_\mathrm{s}-1)$.

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arXiv2016

The Conformal Limit of Inflation in the Era of CMB Polarimetry

We argue that the non-detection of primordial tensor modes has taught us a great deal about the primordial universe. In single-field slow-roll inflation, the current upper bound on the tensor-to-scalar ratio, $r < 0.07$ $(95 \% ~CL)$, implies that the Hubble slow-roll parameters obey $\varepsilon \ll η$, and therefore establishes the existence of a new hierarchy. We dub this regime the conformal limit of (slow-roll) inflation, and show that it includes Starobinsky-like inflation as well as all viable single-field models with a sub-Planckian field excursion. In this limit, all primordial correlators are constrained by the full conformal group to leading non-trivial order in slow-roll. This fixes the power spectrum and the full bispectrum, and leads to the "conformal" shape of non-Gaussianity. The size of non-Gaussianity is related to the running of the spectral index by a consistency condition, and therefore it is expected to be small. In passing, we clarify the role of boundary terms in the $ζ$ action, the order to which constraint equations need to be solved, and re-derive our results using the Wheeler-deWitt formalism.

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arXiv2016

Inflation on a Slippery Slope

We study inflation in a random multifield potential, using techniques developed by Marsh et al. The potential is a function of a large number of fields, and we choose parameters so that inflation only occurs in regions where the potential is accidentally flat. Using an improved estimate for the dynamics of eigenvalue repulsion, we are able to describe the steepening of the potential as inflation progresses. We provide suggestive arguments, but not a proof, that the resulting scalar power spectrum generically disagrees with observations. We also point out two problematic aspects of the model: there is no well-defined probability distribution for the gradient of the potential, and the evolution of the potential over small distances in field space is unphysical.

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arXiv2016

Running the running

We use the recent observations of Cosmic Microwave Background temperature and polarization anisotropies provided by the Planck satellite experiment to place constraints on the running $α_\mathrm{s} = \mathrm{d}n_{\mathrm{s}} / \mathrm{d}\log k$ and the running of the running $β_{\mathrm{s}} = \mathrm{d}α_{\mathrm{s}} / \mathrm{d}\log k$ of the spectral index $n_{\mathrm{s}}$ of primordial scalar fluctuations. We find $α_\mathrm{s}=0.011\pm0.010$ and $β_\mathrm{s}=0.027\pm0.013$ at $68\%\,\mathrm{CL}$, suggesting the presence of a running of the running at the level of two standard deviations. We find no significant correlation between $β_{\mathrm{s}}$ and foregrounds parameters, with the exception of the point sources amplitude at $143\,\mathrm{GHz}$, $A^{PS}_{143}$, which shifts by half sigma when the running of the running is considered. We further study the cosmological implications of such preference for $α_\mathrm{s},β_\mathrm{s}\sim0.01$ by including in the analysis the lensing amplitude $A_L$, the curvature parameter $Ω_k$, and the sum of neutrino masses $\sum m_ν$. We find that when the running of the running is considered, Planck data are more compatible with the standard expectations of $A_L = 1$ and $Ω_k = 0$ but still hint at possible deviations. The indication for $β_\mathrm{s} > 0$ survives at two standard deviations when external datasets such as BAO and CFHTLenS are included in the analysis, and persists at $\sim 1.7$ standard deviations when CMB lensing is considered. We discuss the possibility of constraining $β_\mathrm{s}$ with current and future measurements of CMB spectral distortions, showing that an experiment like PIXIE could provide strong constraints on $α_\mathrm{s}$ and $β_\mathrm{s}$.

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arXiv2016

Lifting Primordial Non-Gaussianity Above the Noise

Primordial non-Gaussianity (PNG) in Large Scale Structures is obfuscated by the many additional sources of non-linearity. Within the Effective Field Theory approach to Standard Perturbation Theory, we show that matter non-linearities in the bispectrum can be modeled sufficiently well to strengthen current bounds with near future surveys, such as Euclid. We find that the EFT corrections are crucial to this improvement in sensitivity. Yet, our understanding of non-linearities is still insufficient to reach important theoretical benchmarks for equilateral PNG, while, for local PNG, our forecast is more optimistic. We consistently account for the theoretical error intrinsic to the perturbative approach and discuss the details of its implementation in Fisher forecasts.

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arXiv2016

$μ$-Distortions or Running: A Guaranteed Discovery from CMB Spectrometry

We discuss the implications of a PIXIE-like experiment, which would measure $μ$-type spectral distortions of the CMB at a level of $σ_μ=(1/n)\times 10^{-8}$, with $n\geq1$ representing an improved sensitivity (e.g. $n=10$ corresponds to PRISM). Using Planck data and considering the six-parameter $Λ$CDM model, we compute the posterior for $μ_8\equivμ\times 10^{8}$ and find $μ_8=1.57^{+0.11}_{-0.13}$ ($68\%\,\mathrm{CL}$). This becomes $μ_{8} = 1.28^{+0.30}_{-0.52}$ ($68\%\,\mathrm{CL}$) when the running $α_\mathrm{s}$ of the spectral index is included. We point out that a sensitivity of about $3\times$ PIXIE implies a guaranteed discovery: $μ$-distortion is detected or $α_\mathrm{s}\geq 0$ is excluded (both at $95\%\,\mathrm{CL}$ or higher). This threshold sensitivity sets a clear benchmark for CMB spectrometry. For a combined analysis of PIXIE and current Planck data, we discuss the improvement on measurements of the tilt $n_\mathrm{s}$ and the running $α_\mathrm{s}$ and the dependence on the choice of the pivot. A fiducial running of $α_\mathrm{s}=-0.01$ (close to the Planck best-fit) leads to a detection of negative running at $2σ$ for $5\times$ PIXIE. A fiducial running of $α_\mathrm{s}=-0.02$, still compatible with Planck, requires $3\times$ PIXIE to rule out $α_\mathrm{s} = 0$ (at $95\%\,\mathrm{CL}$). We propose a convenient and compact visualization of the improving constraints on the tilt, running and tensor-to-scalar ratio.

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arXiv2015

Systematic Renormalization of the Effective Theory of Large Scale Structure

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast $δ$ and momentum density $\mathbfπ(\mathbf k)$ scale as $k^2$ and $k$, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of $ δ$ is indeed valid to all orders.

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arXiv2015

Effective Theory of Large-Scale Structure with Primordial Non-Gaussianity

We develop the effective theory of large-scale structure for non-Gaussian initial conditions. The effective stress tensor in the dark matter equations of motion contains new operators, which originate from the squeezed limit of the primordial bispectrum. Parameterizing the squeezed limit by a scaling and an angular dependence, captures large classes of primordial non-Gaussianity. Within this parameterization, we classify the possible contributions to the effective theory. We show explicitly how all terms consistent with the symmetries arise from coarse graining the dark matter equations of motion and its initial conditions. We also demonstrate that the system is closed under renormalization and that the basis of correction terms is therefore complete. The relevant corrections to the matter power spectrum and bispectrum are computed numerically and their relative importance is discussed.

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arXiv2015

On the Three Primordial Numbers

Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: $ 1-n_{s} $, $ N $ and $\lnΔ_R^2$. Although each of the three numbers individually carries limited information about the physics of inflation, one may hope to extract non-trivial information from relations among them. Invoking minimality, namely the absence of ad hoc large numbers, we find two viable and mutually exclusive inflationary scenarios. The first is the well-known inverse relation between $1- n_{s} $ and $ N $. The second implies a new relation between $ 1-n_{s} $ and $\lnΔ_R^2$, which might provide us with a handle on the beginning of inflation and predicts the intriguing $\textit{lower}$ bound on the tensor-to-scalar ratio $ r> 0.006 $ ($ 95\% $ CL).

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arXiv2015

On Separate Universes

(abridged version) The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in $Λ$CDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity $f_{\rm NL}^{\rm loc}$, and hence does not contribute to a scale-dependent galaxy bias $Δb \propto k^{-2}$ on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent $f_{\rm NL}^{\rm loc}$-type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of $f_{\rm NL}^{\rm loc}$ beyond these projection effects signals a departure from standard single-clock inflation.

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arXiv2015

The Bispectrum in the Effective Field Theory of Large Scale Structure

We study the bispectrum in the Effective Field Theory of Large Scale Structure, consistently accounting for the effects of short-scale dynamics. We begin by proving that, as long as the theory is perturbative, it can be formulated to arbitrary order using only operators that are local in time. We then derive all the new operators required to cancel the UV-divergences and obtain a physically meaningful prediction for the one-loop bispectrum. In addition to new, subleading stochastic noises and the viscosity term needed for the one-loop power spectrum, we find three new effective operators. The three new parameters can be constrained by comparing with N-body simulations. The best fit is precisely what is suggested by the structure of UV-divergences, hence justifying a formula for the EFTofLSS bispectrum whose only fitting parameter is already fixed by the power spectrum. This result predicts the bispectrum of N-body simulations up to $k \approx 0.22\, h\, \text{Mpc}^{-1}$ at $z=0$, an improvement by nearly a factor of two as compared to one-loop standard perturbation theory.

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