arXiv subjects

Baptiste Blachier

Publications and source records attributed to Baptiste Blachier.

11 recordsLinked to original sources

arXiv2026

Excursion-set for Primordial Black Holes I: white noise and moving barrier

In the excursion-set formalism, the mass distribution of primordial black holes (PBHs) is derived from the first-passage time of a random walk describing the density contrast as the coarse-graining scale varies. We address two recent concerns that have been raised about this approach. First, it was argued that the random walks are subject to colored (i.e. correlated over time) noise, making the first-passage-time problem cumbersome. We show that this arises from an incorrect separation of drift and noise when sampling on the Hubble-crossing surface: if Fourier modes are uncorrelated, the noise is strictly white. Moreover, sampling along the Hubble-crossing surface precludes using the density dispersion as a time variable, explaining some pathologies. Sampling instead on a synchronous surface removes both issues. This requires solving a first-passage-time problem with a moving barrier, for which we provide an efficient numerical framework. Second, it was suggested that cloud-in-cloud (i.e. that large black holes may engulf smaller ones) is irrelevant for PBHs and that the excursion set is therefore not needed. While valid for widely separated scales, this statement fails for broad power spectra with enhanced continua of modes. We further show that Press-Schechter estimates neglecting boundary evolution can break down even without cloud-in-cloud effects.

astro-ph.CO↗

arXiv2026

Compaction function in stochastic inflation: a \texttt{FOREST} of type I and II primordial black holes

We show how to compute the compaction function within stochastic inflation, by solving the random field dynamics on stochastic binary trees. In this framework, the compaction function is directly related to the ratio of the volumes emerging from the sibling and child branches of a given node. This construction also determines whether or not the areal radius of a perturbation increases monotonically with the radial coordinate, thereby distinguishing between type-I and type-II fluctuations. As an application, we investigate primordial black hole (PBH) formation in a single-field toy model with a constant potential slope, using stochastic-tree realizations generated with the public code \texttt{FOREST}. In the classical regime, where quantum diffusion is subdominant, the PBH mass function is narrowly distributed and type-II fluctuations are strongly suppressed relative to type I. By contrast, in the quantum and near-critical (i.e. close to eternal inflation) regimes, the PBH mass distribution spans several orders of magnitude, the overall PBH abundance is enhanced, and type-II fluctuations outnumber type I. In that case cloud-in-cloud effects are also important, highlighting the need for a better understanding of the evolution and collapse of type-II fluctuations in order to obtain robust PBH predictions when stochastic effects are significant.

astro-ph.CO↗

arXiv2026

Friction in Stochastic Inflation

We solve time-reversed stochastic inflation in the semi-infinite flat potential with a constant drift term and derive an exact expression for the probability distribution of the curvature fluctuations. It exhibits exponential decaying tails which contrast to the Levy-like power law behaviour encountered without friction. Such a non-vanishing drift acts as a regulator for the conventional ``forward'' stochastic $δN$-formalism, which is otherwise ill-defined in the unbounded and flat potentials typical of plateau models of inflation. This setup therefore allows us to compare the curvature distribution derived from both approaches, reverse and forward in time. Up to similar exponential tails, we find quantitative differences. In particular, in the classical-like limit of very large drift, the tails become Gaussian but only in the time-reversed picture. As a toy model of eternal inflation, we finally discuss the case of negative drift in which inflation never ends for many field trajectories. The forward approach becomes pathological whereas the reverse formalism gives back a finite curvature distribution with always exponential tails. All these differences end up being related to the very definition of the background which is ambiguous when a classical trajectory does not exist.

astro-ph.CO↗

arXiv2026

Time-reversed stochastic inflation in the quantum well

Time-reversed stochastic inflation solves the stochastic evolution of the inflationary universe backward in time, by counting the number of e-folds from the end of quantum diffusion towards some initial state. The point of view of observers attached to the end-of-inflation hypersurface is thus enforced. In this work, we exactly solve time-reversed stochastic inflation in a flat and bounded potential, the so-called quantum well. At given lifetime, the field behaviour is found to be either indistinguishable from the one obtained in a semi-infinite flat potential, or, subject to enhanced stochasticity where any memory of the initial state is erased. The derived distribution of curvature perturbations reduces to the semi-infinite result for small fluctuations while it develops exponential tails for the large ones. Such tails arise for both positive and negative values, and decay twice as fast as the one obtained in the standard forward stochastic inflation. These differences may have important consequences for tail-sensitive phenomena, such as primordial black hole formation.

astro-ph.CO↗

arXiv2025

Time-reversed Stochastic Inflation

Cosmic inflation may exhibit stochastic periods during which quantum fluctuations dominate over the semi-classical evolution. Extracting observables in these regimes is a notoriously difficult program as quantum randomness makes them fully probabilistic. However, among all the possible quantum histories, the ones which are relevant for Cosmology are conditioned by the requirement that stochastic inflation ended. From an observational point of view, it would be more convenient to model stochastic periods as starting from the time at which they ended and evolving backwards in times. We present a time-reversed approach to stochastic inflation, based on a reverse Fokker-Planck equation, which allows us to derive non-perturbatively the probability distribution of the field values at a given time before the end of the quantum regime. As a motivated example, we solve the flat semi-infinite potential and derive a new and exact formula for the probability distribution of the quantum-generated curvature fluctuations. It is normalisable while exhibiting tails slowly decaying as a Levy distribution. Our reverse-time stochastic formalism could be applied to any inflationary potentials and quantum diffusion eras, including the ones that can lead to the formation of primordial black holes.

astro-ph.CO↗

arXiv2025

Harvesting primordial black holes from stochastic trees with $\texttt{FOREST}$

We introduce a novel framework to implement stochastic inflation on stochastic trees, modelling the inflationary expansion as a branching process. Combined with the $δN$ formalism, this allows us to generate real-space maps of the curvature perturbation that fully capture quantum diffusion and its non-perturbative backreaction during inflation. Unlike lattice methods, trees do not proceed on a fixed background since new spacetime units emerge dynamically as trees unfold, naturally incorporating metric fluctuations. The recursive structure of stochastic trees also offers remarkable numerical efficiency, and we develop the FOrtran Recursive Exploration of Stochastic Trees ($\texttt{FOREST}$) tool and demonstrate its performance. We show how primordial black holes blossom at unbalanced nodes of the trees, and how their mass distribution can be obtained while automatically accounting for the "cloud-in-cloud" effect. In the "quantum-well" toy model, we find broad mass distributions, with mild power laws terminated by exponential tails. We finally compare our results with existing approximations in the literature and discuss several prospects.

astro-ph.CO↗

arXiv2024

Clocking the End of Cosmic Inflation

Making observable predictions for cosmic inflation requires determining when the wavenumbers of astrophysical interest today exited the Hubble radius during the inflationary epoch. These instants are commonly evaluated using the slow-roll approximation and measured in e-folds $ΔN=N-N_\mathrm{end}$, in reference to the e-fold $N_\mathrm{end}$ at which inflation ended. Slow roll being necessarily violated towards the end of inflation, both the approximated trajectory and $N_\mathrm{end}$ are determined at, typically, one or two e-folds precision. Up to now, such an uncertainty has been innocuous, but this will no longer be the case with the forthcoming cosmological measurements. In this work, we introduce a new and simple analytical method, on top of the usual slow-roll approximation, that reduces uncertainties on $ΔN$ to less than a tenth of an e-fold.

astro-ph.CO↗

arXiv2024

Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects

Using an excursion-set approach, we revisit the initial spatial clustering of Primordial Black Holes (PBHs) originating from the Hubble re-entry of large Gaussian density fluctuations in the early universe. We derive the two-point correlation functions of PBHs, properly accounting for the "cloud-in-cloud" mechanism. Our expressions naturally and intrinsically correlate the formation of pairs of PBHs, which is a key difference with the Poisson model of clustering. Our approach effectively includes short-range exclusion effects and clarifies the clustering behaviors at small scale: PBHs are anti-correlated at short distances. Using a scale-independent collapse threshold, we derive explicit expressions for the excess probability to find pairs of PBHs separated by a distance $r$, as well as the excess probability to find pairs with asymmetric mass ratio. Our framework is model-independent by construction and we discuss possible other applications.

astro-ph.CO↗

arXiv2023

Einstein vs Hawking: Black hole binaries and cosmological expansion

This note aims at investigating two different situations where the classical general relativistic dynamics competes with the evolution driven by Hawking evaporation. We focus, in particular, on binary systems of black holes emitting gravitational waves and gravitons, and on the cosmological evolution when black holes are immersed in their own radiation bath. Several non-trivial features are underlined in both cases.

gr-qc↗

arXiv2023

Spatial Curvature from Super-Hubble Cosmological Fluctuations

We revisit how super-Hubble cosmological fluctuations induce, at any time in the cosmic history, a non-vanishing spatial curvature of the local background metric. The random nature of these fluctuations promotes the curvature density parameter to a stochastic quantity for which we derive novel non-perturbative expressions for its mean, variance, higher moments and full probability distribution. For scale-invariant Gaussian perturbations, such as those favored by cosmological observations, we find that the most probable value for the curvature density parameter $Ω_\mathrm{K}$ today is $-10^{-9}$, that its mean is $+10^{-9}$, both being overwhelmed by a standard deviation of order $10^{-5}$. We then discuss how these numbers would be affected by the presence of large super-Hubble non-Gaussianities, or, if inflation lasted for a very long time. In particular, we find that substantial values of $Ω_\mathrm{K}$ are obtained if inflation lasts for more than a billion e-folds.

astro-ph.CO↗

arXiv2023

Competitive effects between gravitational radiation and mass variation for two-body systems in circular orbits

This work provides, at lower order, general analytical solutions for the orbital separation, merging time, and orbital frequency of binary systems emitting gravitational waves while being submitted to mass variations. Specific features, depending on the exponent of the mass derivative, are investigated in details. Two phenomenologically interesting cases are explicitly considered : i) binaries formed by two light primordial black holes submitted to Hawking evaporation and ii) bodies driven by a Bondi accretion of phantom dark energy. It is shown that three different regimes arise, including an intricate non-monotonic behaviour of the system. We study subtle imprints that could be associated with those phenomena. A careful analysis of the conditions of validity of the different hypotheses performed is finally carried out.

gr-qc↗