arXiv subjects

Christophe Ringeval

Publications and source records attributed to Christophe Ringeval.

At least 19 recordsLinked to original sources

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↗

arXiv2026

Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]"

We point out that several terms in the third-order corrections to the slow-roll power spectra presented by Ballardini et al. [1] are incorrect. The authors of that work claim that their result differ from the ones originally presented by Auclair & Ringeval [2] due to some different approximation schemes. However, in our original work, all terms at all orders have been derived exactly and any difference between two expansions performed at the same pivot wavenumber signals a problem. As we show in this comment, Ballardini et al. [1] have misevaluated some definite three-dimensional integrals by integrating a truncated Taylor expansion instead of Taylor expanding an integral. Our claim is backed-up with a Monte-Carlo numerical integration of the incriminated three-dimensional integrals, which, unsurprisingly, matches the analytical value derived in Auclair & Ringeval [2].

astro-ph.CO↗

arXiv2025

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 $\delta N$-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↗

arXiv2025

BaBy Cosmic Tension

We show that the recently released B-mode polarisation data from the South Pole Telescope (SPT) favour a non-vanishing contribution of primordial gravitational waves of inflationary origin which is in tension with the previous BICEP-Keck (BK) measurements. Our analysis uses the third-order slow-roll primordial power spectra, with theoretically motivated priors, on the multifrequency SPT likelihoods complemented by the latest Planck satellite data products. The SPT measurements provide 1.0 bit of information gain on the first slow-roll parameter, which is higher than the 0.9 bit provided by BK even though the SPT sensitivity is five times lower. Moreover, the Bayesian dimensionality on the same parameter exceeds 1.5 for SPT versus 0.3 for BK showing that it is overconstrained by the SPT data. Even if this BB-tension could be the result of a yet to be understood foreground, our findings should motivate for a closer analysis of this unexpected B-modes excess.

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↗

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 $\Delta N=N-N_\mathrm{end}$, 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 $\Delta N$ to less than a tenth of an e-fold.

astro-ph.CO↗

arXiv2024

Vanilla Inflation Predicts Negative Running

We show that the simplest, and currently favoured, theoretical realizations of cosmic inflation yield a sharp prediction for the running of the spectral index $\alpha_\mathrm{S}$. Using latest cosmological data, we compute its marginalized posterior probability distribution over the space of nearly 300 models of single-field slow-roll inflation. The most probable value is $\alpha_\mathrm{S}=-6.3 \times 10^{-4}$, lying within the $98\%$ credible interval $-1.8 \times 10^{-3}< \alpha_\mathrm{S}< -9.1 \times 10^{-5}$. Within the landscape of all the proposed slow-roll inflationary models, positive values for the running are therefore disfavoured at more than three-sigma.

astro-ph.CO↗

arXiv2024

Cosmic Inflation at the Crossroads

The capability of Cosmic Inflation to explain the latest Cosmic Microwave Background and Baryonic Acoustic Oscillation data is assessed by performing Bayesian model comparison within the landscape of nearly three-hundred models of single-field slow-roll inflation. We present the first Bayesian data analysis based on the third-order slow-roll primordial power spectra. In particular, the fourth Hubble-flow function $\epsilon_4$ remains unbounded while the third function verifies, at two-sigma, $\epsilon_{3}\in[-0.4,0.5]$, which is perfectly compatible with the slow-roll predictions for the running of the spectral index. We also observe some residual excess of $B$-modes within the BICEP/Keck data favoring, at a non-statistically significant level, non-vanishing primordial tensor modes: $\log(\epsilon_{1}) > -3.9$, at $68\%$ confidence level. Then, for 283 models of single-field inflation, we compute the Bayesian evidence, the Bayesian dimensionality and the marginalized posteriors of all the models' parameters, including the ones associated with the reheating era. The average information gain on the reheating parameter $R_\mathrm{reh}$ reaches $1.3 \pm 0.18$ bits, which is more than a factor two improvement compared to the first Planck data release. As such, inflationary model predictions cannot meet data accuracy without specifying, or marginalizing over, the reheating kinematics. We also find that more than $40\%$ of the scenarios are now strongly disfavored, which shows that the constraining power of cosmological data is winning against the increase of the number of proposed models. In addition, about $20\%$ of all models have evidences within the most probable region and are all favored according to the Jeffreys' scale of Bayesian evidences.

astro-ph.CO↗

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 $\Omega_\mathrm{K}$ 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 $\Omega_\mathrm{K}$ are obtained if inflation lasts for more than a billion e-folds.

astro-ph.CO↗

arXiv2022

Slow-Roll Inflation at N3LO

The next generation of cosmological observations will be sensitive to small deviations from a pure power law in the primordial power spectrum of the curvature perturbations. In the context of slow-roll inflation, these deviations are expected and correspond to the so-called running of the spectral index. Their measurement would bring as much information as the discovery of deviations from scale invariance. However, robust parameter inference requires to marginalize over any possible higher order uncertainties, which have been, up to now, not fully determined. We tackle this issue by deriving the inflationary scalar and tensor slow-roll power spectra at next-to-next-to-next to leading order (N3LO), fully expanded around an observable pivot wavenumber, for all single field inflationary models having minimal and non-minimal kinetic terms. Our result therefore encompasses string-inspired inflationary models having a varying speed of sound.

astro-ph.CO↗

arXiv2022

Stochastic gravitational waves from long cosmic strings

We compute the expected strain power spectrum and energy density parameter of the stochastic gravitational wave background (SGWB) created by a network of long cosmic strings evolving during the whole cosmic history. As opposed to other studies, the contribution of cosmic string loops is discarded and our result provides a robust lower bound of the expected signal that is applicable to most string models. Our approach uses Nambu-Goto numerical simulations, running during the radiation, transition and matter eras, in which we compute the two-point unequal-time anisotropic stress correlators. These ones act as source terms in the linearised equations of motion for the tensor modes, that we solve using an exact Green's function integrator. Today, we find that the rescaled strain power spectrum $(k/\mathcal{H}_0)^2 \mathcal{P}_h$ peaks on Hubble scales and exhibits, at large wavenumbers, high frequency oscillations around a plateau of amplitude $100 (GU)^2$. Most of the high frequency power is generated by the long strings present in the matter era, the radiation era contribution being smaller.

astro-ph.CO↗

arXiv2021

Interferences in the Stochastic Gravitational Wave Background

Although the expansion of the Universe explicitly breaks the time-translation symmetry, cosmological predictions for the stochastic gravitational wave background (SGWB) are usually derived under the so-called stationary hypothesis. By dropping this assumption and keeping track of the time dependence of gravitational waves at all length scales, we derive the expected unequal-time (and equal-time) waveform of the SGWB generated by scaling sources, such as cosmic defects. For extinct and smooth enough sources, we show that all observable quantities are uniquely and analytically determined by the holomorphic Fourier transform of the anisotropic stress correlator. Both the strain power spectrum and the energy density parameter are shown to have an oscillatory fine structure, they significantly differ on large scales while running in phase opposition at large wavenumbers $k$. We then discuss scaling sources that are never extinct nor smooth and which generate a singular Fourier transform of the anisotropic stress correlator. For these, we find the appearance of interferences on top of the above-mentioned fine-structure as well as atypical behaviour at small scales. For instance, we expect the rescaled strain power spectrum $k^2 \mathcal{P}_h$ generated by long cosmic strings in the matter era to oscillate around a scale invariant plateau. These singular sources are also shown to produce orders of magnitude difference between the rescaled strain spectra and the energy density parameter suggesting that only the former should be used for making reliable observable predictions. Finally, we discuss how measuring such a fine structure in the SGWB could disambiguate the possible cosmological sources.

astro-ph.CO↗

arXiv2020

Irreducible cosmic production of relic vortons

The existence of a scaling network of current-carrying cosmic strings in our Universe is expected to continuously create loops endowed with a conserved current during the cosmological expansion. These loops radiate gravitational waves and may stabilise into centrifugally supported configurations. We show that this process generates an irreducible population of vortons which has not been considered so far. In particular, we expect vortons to be massively present today even if no loops are created at the time of string formation. We determine their cosmological distribution, and estimate their relic abundance today as a function of both the string tension and the current energy scale. This allows us to rule out new domains of this parameter space. At the same time, given some conditions on the string current, vortons are shown to provide a viable and original dark matter candidate, possibly for all values of the string tension. Their mass, spin and charge spectrum being broad, vortons would have an unusual phenomenology in dark matter searches.

astro-ph.CO↗

arXiv2019

Lensing anomalies from the epoch of reionisation

Reionisation blurring is a non-linear correction to the cosmic microwave background that acts similar to weak gravitational lensing and that can be computed from linear perturbations through a blurring potential. Its impact on the cosmic microwave background is roughly two order of magnitude smaller than that of lensing, in isolation. But the blurring potential is strongly correlated with the lensing potential thereby generating a potentially observable cross-correlation. We compute for the first time the inclusive impact of reionisation blurring on the temperature angular power spectrum and discuss how much it could induce lensing anomalies

astro-ph.CO↗

arXiv2019

Cosmic string loop production functions

Numerical simulations of Nambu-Goto cosmic strings in an expanding universe show that the loop distribution relaxes to an universal configuration, the so-called scaling regime, which is of power law shape on large scales. Precise estimations of the power law exponent are, however, still matter of debate while numerical simulations do not incorporate all the radiation and backreaction effects expected to affect the network dynamics at small scales. By using a Boltzmann approach, we show that the steepness of the loop production function with respect to loops size is associated with drastic changes in the cosmological loop distribution. For a scale factor varying as a(t)~t^nu, we find that sub-critical loop production functions, having a Polchinski-Rocha exponent chi < (3nu-1)/2, yield scaling loop distributions which are mostly insensitive to infra-red (IR) and ultra-violet (UV) assumptions about the cosmic string network. For those, cosmological predictions are expected to be relatively robust, in accordance with previous results. On the contrary, critical and super-critical loop production functions, having chi >= (3nu-1)/2, are shown to be IR-physics dependent and this generically prevents the loop distribution to relax towards scaling. In the latter situation, we discuss the additional regularisations needed for convergence and show that, although a scaling regime can still be reached, the shape of the cosmological loop distribution is modified compared to the naive expectation. Finally, we discuss the implications of our findings.

astro-ph.CO↗

arXiv2019

A Large Mass Hierarchy from a Small Non-minimal Coupling

We propose a simple but novel cosmological scenario where both the Planck mass and the dark energy scale emerge from the same super-Hubble quantum fluctuations of a non-minimally coupled ultra-light scalar field during primordial inflation. The current cosmic and solar-system observations constrain the non-minimal coupling to be small.

astro-ph.CO↗

arXiv2019

Inflation after Planck: Judgment Day

Inflation is considered as the best theory of the early universe by a very large fraction of cosmologists. However, the validity of a scientific model is not decided by counting the number of its supporters and, therefore, this dominance cannot be taken as a proof of its correctness. Throughout its history, many criticisms have been put forward against inflation. The final publication of the Planck Cosmic Microwave Background data represents a benchmark time to study their relevance and to decide whether inflation really deserves its supremacy. In this paper, we categorize the criticisms against inflation, go through all of them in the light of what is now observationally known about the early universe, and try to infer and assess the scientific status of inflation. Although we find that important questions still remain open, we conclude that the inflationary paradigm is not in trouble but, on the contrary, has rather been strengthened by the Planck data.

astro-ph.CO↗

arXiv2018

Optical Follow-up of Planck Cluster Candidates with Small Instruments

We report on the search for optical counterparts of Planck Sunyaev-Zel'dovich (SZ) cluster candidates using a 0.6 meter non-professional telescope. Among the observed sources, an unconfirmed candidate, PSZ2 G156.24+22.32, is found to be associated with a region of more than 100 galaxies within a 3 arcminutes radius around the Sunyaev-Zel'dovich maximum signal coordinates. Using 14 hours of cumulated exposure over the Sloan color filters g', r', i', and, z', we estimate the photometric redshift of these galaxies at zphot=0.29 +- 0.08. Using the red-sequence galaxy method gives a photometric redshift of 0.30 +0.03 -0.05. Combined with the Planck SZ proxy mass function, this would favor a cluster of 4.4 x 10^{14} solar masses. This result suggests that a dedicated pool of observatories equipped with such instruments could collectively contribute to optical follow-up programs of massive cluster candidates at moderate redshifts.

astro-ph.CO↗