arXiv subjects

Julien Grain

Publications and source records attributed to Julien Grain.

At least 19 recordsLinked to original sources

arXiv2026

Universal CMB Phase Coherence from Single-Field Inflation

The phase coherence of primordial perturbations shapes the acoustic peaks of the CMB and is regarded as a key signature of inflation. Inflationary scenarios at different energy scales, thus with different durations, are commonly expected to leave different levels of coherence. We show this expectation fails: because the curvature perturbation is conserved on super-Hubble scales, the coherence at recombination inherits a value fixed by the observed primordial spectrum alone. This holds irrespective of the inflationary energy scale and the subsequent expansion history.

astro-ph.CO↗

arXiv2026

Explicit gauge-invariant variables in multifield inflation beyond linear order and Hamiltonian dynamics

General relativity coupled to multiple scalar fields is a diffeomorphism-invariant constrained system. Consequently, a naive counting of the perturbative degrees of freedom unavoidably overestimates the true number of physical modes propagating in the theory, as gauge redundancies and constraint equations remove non-dynamical ones. While this problem has been solved for linear fluctuations, this work presents the first explicit calculation of all large-scale gauge-invariant phase-space variables in multifield inflation and at second order in perturbation theory, in a Hamiltonian language. Building upon the well-known Sasaki-Mukhanov variables, we show how to construct a finite-dimensional basis of quadratic corrections which are invariant under gauge transformations. Although our procedure is generic to any number of fields and at any scale, we restrict to super-Hubble scales for their explicit solution, which we deliver. Henceforth, we prove that it is possible to recover the usual flat-gauge and comoving-gauge fluctuations as large-scale gauge-invariant combinations, making for a robust consistency check of the gauge-fixed procedure to connect theoretical predictions above the horizon to observations. We derive the quadratic and cubic Hamiltonian of multifield inflation in a gauge independent manner, then we gauge fix our theory by going into the flat gauge, and we show perfect agreement with the literature on this topic, usually based on a Lagrangian approach. After these concrete steps, we propose a more formal proof of the existence of gauge-invariant variables at quadratic order, and we provide a sketch of the procedure that should allow to go to higher orders in perturbation theory.

astro-ph.CO↗

arXiv2026

Large deviations for halos and voids: beyond perturbative non-gaussianities

The excursion-set formalism provides a key connection between primordial density fluctuations and the abundance of cosmic structures such as dark matter halos and voids, traditionally assuming Gaussian random walks. In this work, we extend this framework to fluctuations whose distribution presents strongly non-Gaussian tails. Such tails are beyond the reach of perturbative approaches to primordial non-Gaussianity based on moment expansion. We address the problem with rigorous, analytical derivations relying on the large deviation principle, suited for the study of rare fluctuations. We derive new first-passage time distributions for random walks with non-Gaussian statistics and obtain updated predictions for the halo mass function. We also study the two-barrier problem relevant to cosmic void formation, leading to a new analytical prediction for the void size function, with improved accuracy on large scales. Our results demonstrate the potential of large deviation techniques as a bridge between inflationary scenarios, often leading to strongly non-Gaussian tails, and late-Universe observables.

astro-ph.CO↗

arXiv2025

Recoherence, adiabaticity, and Markovianity in Gaussian maps

Motivated by the recent discovery of situations where cosmological fluctuations recohere during inflation, we investigate the relationship between quantum recoherence (late-time purification after a transient phase of decoherence), adiabaticity, and Markovianity. To that end, we study a simple setup of two linearly-coupled harmonic oscillators, and compute the purity of one oscillator when the interaction is switched off. We find that there exists a critical value for the coupling strength below which the purity oscillates and above which it decays exponentially. This decay cannot be captured by perturbation theory; hence, decoherence is always a non-perturbative phenomenon. When the interaction is turned off, the purity either freezes to its value prior to the turn-off, or it smoothly goes back to a value very close to one (recoherence). This depends on the rate at which the turn-off occurs. We thus develop a new adiabatic-expansion scheme and find complete recoherence at any finite order in the inverse turn-off time. Therefore, decoherence is always a non-adiabatic effect. The critical value of the turn-off time above which recoherence takes place is then expressed in terms of the other time scales of the problem. Finally, we show that the dynamics of the system is never Markovian, even when decoherence takes place. We introduce a new measure of Markovianity dubbed the Bures velocity and use it to optimise Markovian approximations.

quant-ph↗

arXiv2025

Separate universe in multifield inflation: a phase-space approach

In this article we extend a study of the validity conditions of the separate-universe approach of cosmological perturbations to models of inflation with multiple fields. The separate-universe approach consists in describing the universe as a collection of homogeneous and isotropic patches, giving us an effective description of perturbation theory at large scales through phase-space reduction. This approximation is a necessary step in stochastic inflation, an effective theory of coarse-grained, super-Hubble, scalar fields fluctuations. One needs a stochastic inflation description in the context of primordial black hole productions since it needs enhancements of the curvature power spectrum. It easily achievable in multifield inflation models but necessarily comes with strong diffusive effects. We study and compare cosmological perturbation theory and the separate-universe approach in said non-linear sigma models as a typical framework of multifield inflation and employing the Hamiltonian formalism to keep track of the complete phase space (or the reduced isotropic phase space in the separate-universe approach). We find that the separate-universe approach adequately describes the cosmological perturbation theory provided the wavelength of the modes considered is greater that several lower bounds that depend on the cosmological horizon and the inverse of the effective Hamiltonian masses of the fields; the latter being fixed by the coupling potential and the field-space geometry. We also compare gauge-invariant variables and several gauge fixing procedures in both approaches. For instance, we showed that the uniform-expansion gauge is nicely described by the separate-universe picture, hence qualifying its use in stochastic inflation as commonly done.

astro-ph.CO↗

arXiv2024

In-in formalism for the entropy of quantum fields in curved spacetimes

We show how to compute the purity and entanglement entropy for quantum fields in a systematic perturbative expansion. To that end, we generalize the in-in formalism to non-unitary dynamics (i.e. accounting for the presence of an environment) and to the calculation of quantum information measures, which are not observables in the usual sense. This allows us to reduce the problem to one involving standard correlation functions, and to organize their computation in a diagrammatic expansion for which we construct the corresponding Feynman rules. As an illustration, we apply the formalism to a cosmological setting inspired by the effective field theory of inflation. We find that at late times, non-linear loop corrections share the same time behavior as the linear contribution, and only yield a slight redressing of the purity. In particular, when the environment is heavy compared to the Hubble scale, the phenomenon of recoherence previously encountered is robust to the class of non-linear extensions considered. Bridging the gap between perturbative quantum field theory and open quantum systems paves the way to a better understanding of renormalization and resummation in open effective field theories. It also enables a more systematic exploration of quantum information properties in field theoretic settings.

hep-th↗

arXiv2023

Hamiltonian formalism for cosmological perturbations: fixing the gauge

Cosmological perturbation theory is an example of a gauge theory, where gauge transformations correspond to changes in the space-time coordinate system. To determine physical quantities, one is free to introduce gauge conditions (\ie to work with specific space-time coordinates), and such conditions are often used to simplify technical aspects of the calculation or to facilitate the interpretation of the physical degrees of freedom. Some of the prescriptions introduced in the literature are known to fix the gauge only partially, but it is commonly assumed that the remaining gauge degrees of freedom can be fixed somehow. In this work, we show that this is not necessarily the case, and that some of these gauges are indeed pathological. We derive a systematic procedure to determine whether a gauge is pathological or not, and to complete partially-fixed gauges into healthy gauges when this is possible. In this approach, the Lagrange multipliers (\ie the perturbed lapse and shift in the ADM formalism) cannot appear in the off-shell definition of the gauges, they necessarily arise as on-shell consequences of the gauge conditions. As illustrative applications, we propose an alternative, non-pathological formulation of the synchronous gauge, and we show that the uniform-expansion gauge (as well as any gauge ensuring vanishing lapse perturbations) can hardly be made healthy. Our methodology also allows us to construct all gauge-invariant variables. We further show that our non-pathological criterion for gauges is also the one that ensures Dirac brackets to be properly defined. This allows cosmological perturbations to be quantised in a gauge-fixed way. We finally discuss possible generalisations of our formalism.

gr-qc↗

arXiv2022

Quantum recoherence in the early universe

Despite being created through a fundamentally quantum-mechanical process, cosmological structures have not yet revealed any sign of genuine quantum correlations. Among the obstructions to the direct detection of quantum signatures in cosmology, environmental-induced decoherence is arguably one of the most inevitable. Yet, we discover a mechanism of quantum recoherence for the adiabatic perturbations when they couple to an entropic sector. After a transient phase of decoherence, a turning point is reached, recoherence proceeds and adiabatic perturbations exhibit a large amount of self-coherence at late-time. This result is also understood by means of a non-Markovian master equation, which reduces to Wilsonian effective-field theory in the unitary limit. This allows us to critically assess the validity of open-quantum-system methods in cosmology and to highlight that re(de)coherence from linear interactions has no flat-space analogue.

gr-qc↗

arXiv2022

Benchmarking the cosmological master equations

Master equations are commonly employed in cosmology to model the effect of additional degrees of freedom, treated as an "environment", onto a given "system". However, they rely on assumptions that are not necessarily satisfied in cosmology, where the environment may be out of equilibrium and the background is dynamical. In this work, we apply the master-equation program to a model that is exactly solvable, and which consists of two linearly coupled scalar fields evolving on a cosmological background. The light field plays the role of the system and the heavy field is the environment. By comparing the exact solution to the output of the master equation, we can critically assess its performance. We find that the master equation exhibits a set of "spurious" terms that explicitly depend on the initial conditions, and which arise as a consequence of working on a dynamical background. Although they cancel out in the perturbative limit of the theory (i.e. at leading orders in the interaction strength), they spoil resummation. However, when those terms are removed, the master equation performs impressively well to reproduce the power spectra and the amount of the decoherence of the light field, even in the strongly decohered regime. We conclude that master equations are able to perform late-time resummation, even though the system is far from the Markovian limit, provided spurious contributions are suppressed.

hep-th↗

arXiv2021

Hamiltonian formalism for cosmological perturbations: the separate-universe approach

The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the phase space to homogeneous and isotropic degrees of freedom, it greatly simplifies the analysis of large-scale fluctuations. It is also a prerequisite for the stochastic-inflation formalism. In this work, we formulate the separate-universe approach in the Hamiltonian formalism, which allows us to analyse the full phase-space structure of the perturbations. Such a phase-space description is indeed required in dynamical regimes which do not benefit from a background attractor, as well as to investigate quantum properties of cosmological perturbations. We find that the separate-universe approach always succeeds in reproducing the same phase-space dynamics for homogeneous and isotropic degrees of freedom as the full cosmological perturbation theory, provided that the wavelength of the modes under consideration are larger than some lower bound that we derive. We also compare the separate-universe approach and cosmological perturbation theory at the level of the gauge-matching procedure, where the agreement is not always guaranteed and requires specific matching prescriptions that we present.

astro-ph.CO↗

arXiv2021

Four-mode squeezed states: two-field quantum systems and the symplectic group $\mathrm{Sp}(4,\mathbb{R})$

We construct the four-mode squeezed states and study their physical properties. These states describe two linearly-coupled quantum scalar fields, which makes them physically relevant in various contexts such as cosmology. They are shown to generalise the usual two-mode squeezed states of single-field systems, with additional transfers of quanta between the fields. To build them in the Fock space, we use the symplectic structure of the phase space. For this reason, we first present a pedagogical analysis of the symplectic group $\mathrm{Sp}(4,\mathbb{R})$ and its Lie algebra, from which we construct the four-mode squeezed states and discuss their structure. We also study the reduced single-field system obtained by tracing out one of the two fields. This procedure being easier in the phase space, it motivates the use of the Wigner function which we introduce as an alternative description of the state. It allows us to discuss environmental effects in the case of linear interactions. In particular, we find that there is always a range of interaction coupling for which decoherence occurs without substantially affecting the power spectra (hence the observables) of the system.

quant-ph↗

arXiv2021

Unavoidable shear from quantum fluctuations in contracting cosmologies

Contracting cosmologies are known to be flawed with a shear instability, where the contribution from the anisotropic stress to the overall energy density grows as $a^{-6}$, with $a$ the scale factor. Classically, whether or not this contribution becomes important before the bounce depends on its initial value, which can always be sufficiently fine tuned to make it irrelevant. However, vacuum quantum fluctuations inevitably provide a non-vanishing source of anisotropic stress. In this work, we compute the minimum amount of shear that is obtained if one assumes that it vanishes initially, but lets quantum fluctuations build it up. In practice, we consider a massless test scalar field, and describe its quantum fluctuations by means of the stochastic "inflation" (though here applied to a contracting phase) formalism. We find that, if the equation-of-state parameter of the contraction satisfies $w>-1/9$, regardless of when the contracting phase is initiated, the time at which the shear becomes sizeable is always when the Hubble scale approaches the Planck mass (which is also where the bounce is expected to take place). However, if $w<-1/9$, the shear backreaction becomes important much earlier, at a point that depends on the overall amount of contraction.

astro-ph.CO↗

arXiv2020

Canonical transformations and squeezing formalism in cosmology

Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part of this work we study the symplectic structure associated with linear canonical transformations. After reviewing salient mathematical properties of the symplectic group in a pedagogical way, we introduce the squeezing formalism, and show how any linear dynamics can be cast in terms of an invariant representation. In the second part, we apply these results to the case of cosmological perturbations, and focus on scalar field fluctuations during inflation. We show that different canonical variables select out different vacuum states, and that this leaves an ambiguity in observational predictions if initial conditions are set at a finite time in the past. We also discuss how the effectiveness of the quantum-to-classical transition of cosmological perturbations depends on the set of canonical variables used to describe them.

astro-ph.CO↗

arXiv2019

Quantum fields in the background spacetime of a loop quantum gravity black hole

The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the propagation of quantum fields in this background. The cross sections for scalar particles and fermions are explicitly calculated. The Teukolsky-Chandrasekhar procedure used to derived the fermionic radial equation of motion for usual spacetimes is entirely generalized to a much larger class. The resulting radial equation can be used in quite a lot of other contexts.

gr-qc↗

arXiv2019

Fast and easy super-sample covariance of large scale structure observables

We present a numerically cheap approximation to super-sample covariance (SSC) of large scale structure cosmological probes, first in the case of angular power spectra. It necessitates no new elements besides those used for the prediction of the considered probes, thus relieving analysis pipelines from having to develop a full SSC modeling, and reducing the computational load. The approximation is asymptotically exact for fine redshift bins $Δz \rightarrow 0$. We furthermore show how it can be implemented at the level of a Gaussian likelihood or a Fisher matrix forecast, as a fast correction to the Gaussian case without needing to build large covariance matrices. Numerical application to a Euclid-like survey show that, compared to a full SSC computation, the approximation recovers nicely the signal-to-noise ratio as well as Fisher forecasts on cosmological parameters of the $w$CDM cosmological model. Moreover it allows for a fast prediction of which parameters are going to be the most affected by SSC and at which level. In the case of photometric galaxy clustering with Euclid-like specifications, we find that $σ_8$, $n_s$ and the dark energy equation of state $w$ are particularly heavily affected. We finally show how to generalize the approximation for probes other than angular spectra (correlation functions, number counts and bispectra), and at the likelihood level, allowing for the latter to be non-Gaussian if needs be. We release publicly a Python module allowing to implement the SSC approximation, as well as a notebook reproducing the plots of the article, at https://github.com/fabienlacasa/PySSC

astro-ph.CO↗

arXiv2018

Secondary CMB anisotropies from magnetized halos --I: Power spectra of the Faraday rotation angle and conversion rate

Magnetized plasmas within halos of galaxies leave their footprint on the polarized anisotropies of the cosmic microwave background. The two dominant effects for astrophysical halos are Faraday rotation generating rotation of the plane of linear polarization, and Faraday conversion inducing a leakage from linear polarization to circular polarization. We revisit these sources of secondary anisotropies by computing the angular power spectra of the Faraday rotation angle and of the Faraday conversion rate by the large scale structures. To this end, we use the halo model and we pay special attention to the impact of magnetic field projections. Assuming magnetic fields of halos to be uncorrelated, we found a vanishing 2-halo term, and angular power spectra peaking at multipoles $\ell\sim10^4$. The Faraday rotation angle is dominated by the contribution of thermal electrons. For the Faraday conversion rate, we found that both thermal electrons and relativistic, non-thermal electrons contribute equally in the most optimistic case for the density and Lorentz factor of relativistic electrons, while in more pessimistic cases the thermal electrons give the dominant contribution. Assuming the magnetic field to be independent of the halo mass, the angular power spectra for both effects roughly scale with the amplitude of matter perturbations as $\simσ_8^3$, and with a very mild dependence with the density of cold dark matter. Introducing a dependence of the magnetic field strength with the halo mass leads to an increase of the scaling with the amplitude of matter fluctuations, up to $\simσ_8^{9.5}$ for Faraday rotation and $\simσ_8^{15}$ for Faraday conversion for a magnetic field strength scaling linearly with the halo mass.

astro-ph.CO↗

arXiv2018

A first step towards the inflationary trans-planckian problem treatment in Loop Quantum Cosmology

For most initial conditions, cosmologically relevant physical modes were trans-planckian at the bounce time, often by many magnitude orders. We improve the usual loop quantum cosmology calculation of the primordial power spectra -- in the inflationary framework -- by accounting for those trans-planckian effects through modified dispersion relations. This can induce drastic changes in the spectrum, making it either compatible or incompatible with observational data, depending on the details of the choices operated.

gr-qc↗

arXiv2017

Stochastic inflation in phase space: Is slow roll a stochastic attractor?

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, "slow roll", which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure - where wavelengths smaller than the Hubble radius are integrated out - preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

gr-qc↗