arXiv subjects

Leonardo Senatore

Publications and source records attributed to Leonardo Senatore.

At least 55 records · Page 3Linked to original sources

arXiv2017

An effective description of dark matter and dark energy in the mildly non-linear regime

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the information resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.

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arXiv2017

IR-safe and UV-safe integrands in the EFTofLSS with exact time dependence

Because large-scale structure surveys may very well be the next leading sources of cosmological information, it is important to have a precise understanding of the cosmological observables; for this reason, the Effective Field Theory of Large-Scale Structure (EFTofLSS) was developed. So far, most results in the EFTofLSS have used the so-called Einstein-de Sitter approximation, an approximation of the time dependence which is known to be accurate to better than one percent. However, in order to reach even higher accuracy, the full time dependence must be used. The computation with exact time dependence is sensitive to both infrared (IR) and ultraviolet (UV) effects in the loop integrands, and while these effects must cancel because of diffeomorphism invariance, they make numerical computation much less efficient. We provide a formulation of the one-loop, equal-time exact-time-dependence power spectrum of density perturbations which is manifestly free of these spurious IR and UV divergences at the level of the integrand. We extend our results to the total matter mode with clustering quintessence, show that IR and UV divergences cancel, and provide the associated IR- and UV-safe integrand. This also establishes that the consistency conditions are satisfied in this system. We then use our one-loop result to do an improved precision comparison of the two-loop dark-matter power spectrum with the Dark Sky N-body simulation.

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arXiv2017

The Effective Field Theory of Large-Scale Structure in the presence of Massive Neutrinos

We develop a formalism to analytically describe the clustering of matter in the mildly non-linear regime in the presence of massive neutrinos. Neutrinos, whose free streaming wavenumber ($k_{\rm fs}$) is typically longer than the non-linear scale ($k_{\rm NL}$) are described by a Boltzmann equation coupled to the effective fluid-like equations that describe dark matter. We solve the equations expanding in the neutrino density fraction $(f_ν)$ and in $k/ k_{\rm NL}$, and add suitable counterterms to renormalize the theory. This allows us to describe the contribution of short distances to long-distance observables. Equivalently, we construct an effective Boltzmann equation where we add additional terms whose coefficients renormalize the contribution from short-distance physics. We argue that neutrinos with $k_{\rm fs}\gtrsim k_{\rm NL}$ require an additional counterterm similar to the speed of sound ($c_s$) for dark matter. We compute the one-loop total-matter power spectrum, and find that it is roughly equal to $16f_ν$ times the dark matter one for $k$'s larger that the typical $k_{\rm fs}$. It is about half of that for smaller $k$'s. The leading contribution results from the back-reaction of the neutrinos on the dynamics of the dark matter. The counterterms contribute in a hierarchical way: the leading ones can either be computed in terms of $c_s$, or can be accounted for by shifting $c_s$ by an amount proportional to $f_ν$.

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arXiv2017

Efficient exploration of cosmology dependence in the EFT of LSS

The most effective use of data from current and upcoming large scale structure~(LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure (EFTofLSS) provides an instrument for performing analytical computations of LSS observables with the required precision in the mildly nonlinear regime. In this paper, we develop efficient implementations of these computations that allow for an exploration of their dependence on cosmological parameters. They are based on two ideas. First, once an observable has been computed with high precision for a reference cosmology, for a new cosmology the same can be easily obtained with comparable precision just by adding the difference in that observable, evaluated with much less precision. Second, most cosmologies of interest are sufficiently close to the Planck best-fit cosmology that observables can be obtained from a Taylor expansion around the reference cosmology. These ideas are implemented for the matter power spectrum at two loops and are released as public codes. When applied to cosmologies that are within 3$σ$ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1\% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision. The ideas and codes we present may easily be extended for other applications or higher-precision results.

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arXiv2017

Boost Breaking in the EFT of Inflation

If time-translations are spontaneously broken, so are boosts. This symmetry breaking pattern can be non-linearly realized by either just the Goldstone boson of time translations, or by four Goldstone bosons associated with time translations and boosts. In this paper we extend the Effective Field Theory of Multifield Inflation to consider the case in which the additional Goldstone bosons associated with boosts are light and coupled to the Goldstone boson of time translations. The symmetry breaking pattern forces a coupling to curvature so that the mass of the additional Goldstone bosons is predicted to be equal to $\sqrt{2}H$ in the vast majority of the parameter space where they are light. This pattern therefore offers a natural way of generating self-interacting particles with Hubble mass during inflation. After constructing the general effective Lagrangian, we study how these particles mix and interact with the curvature fluctuations, generating potentially detectable non-Gaussian signals.

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arXiv2016

Inhomogeneous Anisotropic Cosmology

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that $arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including toroidal) and "open" (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat" or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.

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arXiv2016

Biased Tracers in Redshift Space in the EFT of Large-Scale Structure

The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a novel formalism that is able to accurately predict the clustering of large-scale structure (LSS) in the mildly non-linear regime. Here we provide the first computation of the power spectrum of biased tracers in redshift space at one loop order, and we make the associated code publicly available. We compare the multipoles $\ell=0,2$ of the redshift-space halo power spectrum, together with the real-space matter and halo power spectra, with data from numerical simulations at $z=0.67$. For the samples we compare to, which have a number density of $\bar n=3.8 \cdot 10^{-2}(h \ {\rm Mpc}^{-1})^3$ and $\bar n=3.9 \cdot 10^{-4}(h \ {\rm Mpc}^{-1})^3$, we find that the calculation at one-loop order matches numerical measurements to within a few percent up to $k\simeq 0.43 \ h \ {\rm Mpc}^{-1}$, a significant improvement with respect to former techniques. By performing the so-called IR-resummation, we find that the Baryon Acoustic Oscillation peak is accurately reproduced. Based on the results presented here, long-wavelength statistics that are routinely observed in LSS surveys can be finally computed in the EFTofLSS. This formalism thus is ready to start to be compared directly to observational data.

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arXiv2016

The Supersymmetric Effective Field Theory of Inflation

We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable Stückelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplifying the analysis in this regime. We study the phenomenology of this Lagrangian. The Goldstino can have a non-relativistic dispersion relation. Gravitino and Goldstino affect the primordial curvature perturbations at loop level. The UV modes running in the loops generate three-point functions which are degenerate with the ones coming from operators already present in the absence of supersymmetry. Their size is potentially as large as corresponding to $f_{\rm NL}^{\rm equil.,\,orthog.}\sim 1$ or, for particular operators, even $\gg 1$. The non-degenerate contribution from modes of order $H$ is estimated to be very small.

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arXiv2016

Very Massive Tracers and Higher Derivative Biases

Most of the upcoming cosmological information will come from analyzing the clustering of the Large Scale Structures (LSS) of the universe through LSS or CMB observations. It is therefore essential to be able to understand their behavior with exquisite precision. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a consistent framework to make predictions for LSS observables in the mildly non-linear regime. In this paper we focus on biased tracers. We argue that in calculations at a given order in the dark matter perturbations, highly biased tracers will underperform because of their larger higher derivative biases. A natural prediction of the EFTofLSS is therefore that by simply adding higher derivative biases, all tracers should perform comparably well. We implement this prediction for the halo-halo and the halo-matter power spectra at one loop, and the halo-halo-halo, halo-halo-matter, and halo-matter-matter bispectra at tree-level, and compare with simulations. We find good agreement with the prediction: for all tracers, we are able to match the bispectra up to $k\simeq0.17\,h/$Mpc at $z=0$ and the power spectra to a higher wavenumber.

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arXiv2016

Lectures on Inflation

Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.

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arXiv2016

Beginning inflation in an inhomogeneous universe

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

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arXiv2016

Precision Comparison of the Power Spectrum in the EFTofLSS with Simulations

We study the prediction of the dark matter power spectrum at two-loop order in the Effective Field Theory of Large Scale Structures (EFTofLSS) using high precision numerical simulations. In our universe, short distance non-linear perturbations, not under perturbative control, affect long distance fluctuations through an effective stress tensor that needs to be parametrized in terms of counterterms that are functions of the long distance fluctuating fields. We find that at two-loop order it is necessary to include three counterterms: a linear term in the over density, $δ$, a quadratic term, $δ^2$, and a higher derivative term, $\partial^2δ$. After the inclusion of these three terms, the EFTofLSS at two-loop order matches simulation data up to $k\simeq 0.34 \,h\, {\rm Mpc}^{-1}$ at redshift $z=0$, up to $k\simeq 0.55\,h\, {\rm Mpc}^{-1}$ at $z=1$, and up to $k\simeq 1.1\,h\, {\rm Mpc}^{-1}$ at $z=2$. At these wavenumbers, the cosmic variance of the simulation is at least as small as $10^{-3}$, providing a high precision comparison between theory and data. The actual reach of the theory is affected by theoretical uncertainties associated to not having included higher order terms in perturbation theory, for which we provide an estimate, and by potentially overfitting the data, which we also try to address. Since in the EFTofLSS the coupling constants associated with the counterterms are unknown functions of time, we show how a simple parametrization gives a sensible description of their time-dependence. Overall, the $k$-reach of the EFTofLSS is much larger than previous analytical techniques, showing that the amount of cosmological information amenable to high-precision analytical control might be much larger than previously believed.

astro-ph.CO↗

arXiv2016

The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures

Given the importance of future large scale structure surveys for delivering new cosmological information, it is crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbative scheme to compute the clustering of dark matter in the weakly nonlinear regime in an expansion in $k/k_{\rm NL}$, where $k$ is the wavenumber of interest and $k_{\rm NL}$ is the wavenumber associated to the nonlinear scale. It has been recently shown that the EFTofLSS matches to $1\%$ level the dark matter power spectrum at redshift zero up to $k\simeq 0.3 h\,$Mpc$^{-1}$ and $k\simeq 0.6 h\,$Mpc$^{-1}$ at one and two loops respectively, using only one counterterm that is fit to data. Similar results have been obtained for the momentum power spectrum at one loop. This is a remarkable improvement with respect to former analytical techniques. Here we study the prediction for the equal-time dark matter bispectrum at one loop. We find that at this order it is sufficient to consider the same counterterm that was measured in the power spectrum. Without any remaining free parameter, and in a cosmology for which $k_{\rm NL}$ is smaller than in the previously considered cases ($σ_8=0.9$), we find that the prediction from the EFTofLSS agrees very well with $N$-body simulations up to $k\simeq 0.25 h\,$Mpc$^{-1}$, given the accuracy of the measurements, which is of order a few percent at the highest $k$'s of interest. While the fit is very good on average up to $k\simeq 0.25 h\,$Mpc$^{-1}$, the fit performs slightly worse on equilateral configurations, in agreement with expectations that for a given maximum $k$, equilateral triangles are the most nonlinear.

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arXiv2016

Productive Interactions: heavy particles and non-Gaussianity

We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton $ϕ$. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale $\dot ϕ^{1/2}$, much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structure of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order $\lesssim 1$. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the {\it Planck} collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.

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arXiv2016

The EFT of Large Scale Structures at All Redshifts: Analytical Predictions for Lensing

We study the prediction of the Effective Field Theory of Large Scale Structures (EFTofLSS) for the matter power spectrum at different redshifts. In previous work, we found that the two-loop prediction can match the nonlinear power spectrum measured from $N$-body simulations at redshift zero within approximately 2% up to $k\sim 0.6\,h\, {\rm Mpc}^{-1}$ after fixing a single free parameter, the so-called "speed of sound". We determine the time evolution of this parameter by matching the EFTofLSS prediction to simulation output at different redshifts, and find that it is well-described by a fitting function that only includes one additional parameter. After the two free parameters are fixed, the prediction agrees with nonlinear data within approximately 2% up to at least $k\sim 1\,h\, {\rm Mpc}^{-1}$ at $z\geq 1$, and also within approximately 5% up to $k\sim 1.2\,h\, {\rm Mpc}^{-1}$ at $z=1$ and $k\sim 2.3\,h\, {\rm Mpc}^{-1}$ at $z=3$, a major improvement with respect to other perturbative techniques. We also develop an accurate way to estimate where the EFTofLSS predictions at different loop orders should fail, based on the sizes of the next-order terms that are neglected, and find agreement with the actual comparisons to data. Finally, we use our matter power spectrum results to perform analytical calculations of lensing potential power spectra corresponding to both CMB and galaxy lensing. This opens the door to future direct applications of the EFTofLSS to observations of gravitational clustering on cosmic scales.

astro-ph.CO↗

arXiv2016

On the Statistics of Biased Tracers in the Effective Field Theory of Large Scale Structures

With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial non-Gaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo three-point functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of $N$-body simulations. For the lowest mass bin, we find percent level agreement up to $k\simeq 0.3\,h\,{\rm Mpc}^{-1}$ for the one-loop two-point functions, and up to $k\simeq 0.15\,h\,{\rm Mpc}^{-1}$ for the tree-level three-point functions, with the $k$-reach decreasing with higher mass bins. This is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.

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arXiv2015

Linear response to long wavelength fluctuations using curvature simulations

We study the local response to long wavelength fluctuations in cosmological $N$-body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, most probably more precise, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naive derivation assuming a universal mass function by 18%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.

astro-ph.CO↗

arXiv2015

The cosmological Higgstory of the vacuum instability

The Standard Model Higgs potential becomes unstable at large field values. After clarifying the issue of gauge dependence of the effective potential, we study the cosmological evolution of the Higgs field in presence of this instability throughout inflation, reheating and the present epoch. We conclude that anti-de Sitter patches in which the Higgs field lies at its true vacuum are lethal for our universe. From this result, we derive upper bounds on the Hubble constant during inflation, which depend on the reheating temperature and on the Higgs coupling to the scalar curvature or to the inflaton. Finally we study how a speculative link between Higgs meta-stability and consistence of quantum gravity leads to a sharp prediction for the Higgs and top masses, which is consistent with measured values.

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