Welcome

Fabio Finelli

Lennart Balkenhol: Implications for Inflation of the CMB-BAO tension The scalar spectral index, ns, plays a central role in testing inflationary models, with its precise value shaping theoretical and observational priorities. Recent analyses combining the latest cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data suggest a shift toward higher ns values compared to the Planck results. This comes with implications for inflation; previously preferred models appear to be now disfavoured by the data (>2 sigma). In this talk, I explore how this shift in ns arises due to differences between CMB and BAO data and caution against interpreting joint constraints in the context of inflation, until this emerging CMB-BAO tension is resolved.

Antonio Raffaelli: Knot reconstruction of the scalar primordial power spectrum with Planck, ACT, and SPT CMB data We investigate a non-parametric Bayesian method for reconstructing the primordial power spectrum of scalar perturbations using temperature and polarisation data from the Planck, ACT, and SPT CMB experiments. We use the reconstructed scalar primordial power spectrum to derive several quantities related to inflationary dynamics, such as the effective scalar spectral index, slow-roll parameters for a slow and sudden variation of the background, and the speed of sound.

Emanuele Fondi: N-body simulations of primordial features with GENGARS Primordial non-Gaussianity (PNG) represents a window into the nature of inflation, and large-scale structure (LSS) surveys can promisingly sharpen its constraints. To fully exploit this potential, cosmological simulations play a crucial role, allowing us to study the signatures and test the detectability of primordial features from LSS. I will present GENGARS, a framework to generate non-Gaussian initial conditions for N-body simulations from an arbitrary separable PNG shape. Building on the reduced-bispectrum-kernel formulation, we employ a Schwinger parameterization that improves efficiency by order of magnitudes, while preserving accuracy. I will outline the method and validation against 2LPT-PNG on the standard local, equilateral and orthogonal cases, emphasizing control of the induced large-scale primordial power spectrum correction, a critical requirement for accurate PNG simulations. I will then discuss how the same pipeline naturally accommodates non-standard templates, such as oscillatory PNG, and show their imprint on late-time statistics.

Zucheng Gao: Parity in Composite-Field Galaxy Correlators Detecting parity violation on cosmological scales would provide a striking clue to new physics. Large-scale structure offers the raw statistical power -- many three-dimensional modes -- to make such tests. However, for scalar observables, like galaxy clustering, the leading parity-sensitive observable is the trispectrum, whose high dimensionality makes the measurement and noise estimation challenging. We present two late-time parity-odd kurto spectra that compress the parity-odd scalar trispectrum into one-dimensional, power-spectrum-like observables. They are built by correlating (i) two appropriately weighted quadratic composite fields, or (ii) a linear and cubic composite field, constructed from dark matter (DM) or galaxy overdensity fields. We develop an FFTLog pipeline for efficient theoretical predictions of the two observables. We then validate the estimators for a specific parity-odd primordial template on perturbative DM field, and on DM and halo fields in full N-body \texttt{Quijote} simulations, with and without parity-odd initial conditions, in real and redshift space. For DM, the variance is dominated by the parity-even contribution -- i.e., the gravitationally induced parity-even trispectrum -- and is efficiently suppressed by phase-matched fiducial subtraction. For halos, discreteness-driven stochasticity dominates and is not appreciably reduced by subtraction; however, optimal weighting and halo-matter cross kurto spectra considerably mitigate this noise and enhance the signal. Using controlled down-sampling of the matter field, we empirically calibrate how the parity-even variance scales with number density and volume, and provide an illustrative forecast for the detectability of parity-odd kurto spectra in a Euclid-like spectroscopic galaxy survey.

Zhong-Zhi Xianyu

Invited talk

Arthur Poisson

Nathan Belrhali

Xi Tong: Unitary renormalisation and the quantum breaking of cosmological reality Cosmological correlators and the associated wavefunction coefficients serve as a smoking gun towards the physics of inflation at high energy scales. In minimal setups of single-field inflation, wavefunction coefficients are purely real at tree-level due to unitarity, locality and scale invariance, leading to the so-called no-go theorems on parity violation. Such parity-violating correlators are therefore null tests of fundamental principles. Yet interestingly, there exists a twist of plot when quantum loops are involved. We show that such cosmological reality must be spontaneously broken by the renormalisation of UV divergences in de Sitter loops. More specifically, unitarity and analyticity dictate a universal imaginary part from the logarithmic running of the real part of the wavefunction coefficients. We then discuss the implications related to this universality.

Xiangwei Wang, Interact or Twist: Cosmological Correlators from Field Redefinitions Revisited In cosmology, correlation functions on a late-time boundary can arise from both field redefinitions and bulk interactions, which are usually believed to generate distinct results. In this letter, we propose a counterexample showcasing that correlators from local field redefinitions can be identical to the ones from bulk interactions. In particular, we consider a two-field model in de Sitter space, where the field space gets twisted by field redefinitions to yield a nontrivial reheating surface. We then exploit conformal symmetry to compute the three-point function, and show that the result takes the form of contact correlators with a total-energy singularity. Our finding suggests that in the effective field theory, a class of lower-dimensional operators, which were overlooked previously, may lead to nontrivial signals in cosmological correlators. As an illustration, we apply our result to cosmic inflation and derive a possibly leading signature of the Higgs in the primordial bispectrum.

Thomas Colas: An Open System Approach to Gravity Effective field theories in particle physics are usually designed for experiments where the initial state — the vacuum before a scattering event — is as clean and isolated as possible. Yet many physical systems, from condensed matter to cosmology, evolve in noisy and dissipative environments. Over the past decade, this recognition has driven progress at the interface between high-energy physics and condensed-matter. Motivated by these insights, I will present a framework for gravitational dynamics that combines General Relativity with the Schwinger–Keldysh formalism. I will show how symmetries, locality, and unitarity constrain dissipation and noise, and illustrate the approach by deriving the most general conservative and dissipative dynamics of scalar and tensor perturbations during single-clock inflation. I will conclude by discussing future prospects for dissipative dark sectors in the late universe.

Cliff Burgess

Fumiya Sano: Decoherence of primordial perturbations in the view of a local observer We study quantum decoherence of curvature perturbations at superhorizon scales caused by the gravitational nonlinearities. We show that cubic gravitational couplings, constrained by the spatial diffeomorphism invariance, lead to infrared (IR) and ultraviolet (UV) divergences in the decoherence rate at one loop. These divergences arise from fluctuations of deep IR modes which look like a background mode for a local observer and violent zero-point fluctuations in the deep UV, respectively. We argue that these divergences are unobservable, as they vanish when considering proper observables. We consider correlators defined using the geodesic distance for IR divergences and time-averaged correlators for UV divergences. To account for these observer's perspectives, we propose to consider an effective quantum state, defined in terms of actual observables, as a more appropriate probe of the quantum coherence of the system measured by an observer. We then evaluate the finite decoherence rate induced by superhorizon environment during inflation and at late universe. This talk is based on the paper arXiv:2504.10472.

Francescopaolo Lopez: Quantum signatures and decoherence during inflation from deep subhorizon perturbations In order to shed light on the quantum to classical transition of the primordial perturbations in single field inflation, we investigate the decoherence and associated quantum corrections to the correlation functions of large-scale (superhorizon) scalar curvature perturbations. The latter are considered as an open quantum system which undergoes decoherence induced by a time-dependent environment of deep subhorizon tensorial modes (i.e. primordial gravitational waves) through the trilinear interactions predicted by General Relativity. We first prove that a time dependent subhorizon environment of gravitational waves can be relevant for decoherence during inflation, by considering derivativeless interactions, which, in our case, give the most important results. Our results show that important non-Markovian effects pop up, instead, when dealing with derivative interactions. When considering the interplay between derivativeless and derivative interactions, decoherence is slowed down. This underlines the importance of accounting for all the interactions in open quantum-system calculations in an inflationary setting. We finally compute the quantum corrections to cosmological correlation functions. We observe a resummation of the quantum corrections, which is a general property of quantum master equations.

Lennard Dufner: An Open System Approach to Gravitational Waves Several major open problems in cosmology involve spacetime-filling media with unknown microphysics, and can only be probed through their gravitational effects. This observation motivates a systematic open-system approach, in which gravity evolves in the presence of a generic, unobservable environment. In this talk, I will present a general framework for open gravitational dynamics, based on the Schwinger-Keldysh path integral formalism. Applied to inflation, the framework recovers the Open Effective Field Theory of Inflation in the decoupling limit and naturally extends it to include gravitational interactions. These yield both conservative and dissipative corrections to graviton propagation. Remarkably, the leading gravitational birefringence is dissipative, while conservative birefringence only appears at higher derivative order — contrary to the electromagnetic case.

Sebastian Cespedes: On the UV realisations of \lambda phi^4 in de Sitter I will present an effective field theory (EFT) that captures the dominant late-time behavior of massless spectator fields in de Sitter space in the presence of heavy internal fields. As expected, when the mass of these internal fields is large, the leading term reproduces the infrared-divergent contributions to correlation functions obtained in the single-field description. Remarkably, even when the mass of the spectator field is below the Hubble scale, there still exists an EFT description organized in terms of leading local operators with subdominant nonlocal corrections. Crucially, this EFT describes a mixed rather than a pure state, and its four-point functions display logarithmically growing divergences at late times. In this regime, standard perturbation theory breaks down and must be reorganized. The resulting EFT is not obtained by integrating out heavy modes in the Wilsonian sense, but instead emerges from an explicit expansion of the time-evolution operator. The outcome is a local, Markovian, and generically non-unitary effective theory that resums the leading infrared behavior of the full theory to all orders. I will discuss its structure, diagrammatic interpretation, and implications for resumming loop corrections to inflationary correlators even when the heavy fields never go on shell.

Angelo Caravano

Dick Bond

Tom Morrison: All things in the theory of pinG ponGs: generic primordial intermittent nonGaussianity and outlier trajectories in scalar and correlated gravitational wave signals I will summarize key results from a series of 4 papers in collaboration with Dick Bond and Jonathan Braden: (1) Relating stochastic inflation to the results of state-of-the-art lattice simulations, complete with component separation of nonGaussianity; (2) Spatial localization of primordial intermittent nonGaussianity (pinGs) and the statistics of rare events; (3) The role of outlier trajectories (ponGs) in the generation of pinGs; and (4) The graviational wave response and their nonlinear correlation to an associated scalar nonGaussian signal, unlike the classical zero-point fluctuation r case.

Yoann Launay: Stochastic Inflation in Numerical Relativity A set of 3+1 equations for stochastic inflation can be obtained in a gauge invariant manner, incorporating all scalar and tensorial perturbation degrees of freedom and without gradient expansion. We demonstrate a numerical implementation of the stochastic equations cast in the BSSN formulation of Numerical Relativity.

Alessio Notari: On strong backreaction in axion inflation

Andrea Costantini: Primordial correlators from Multi-point propagators Accurate predictions of correlators of the primordial curvature perturbation are critical for connecting inflationary models to cosmological observations. Numer- ical methods employing differential equations, such as the transport approach, have been extensively used to compute the evolution of these correlators. In this talk, I will present a novel numerical implementation of the transport formalism. We use Multi-point propagators (MPPs), that link non-linearly evolved fields to their values at some earlier time. This method recasts the direct evolution of correlators into a system of differential equations for MPPs. We benchmark the MPP approach against the established PyTransport code across a range of models, and I will discuss the essential applications of the new method to models than can lead to enhanced fluctuations on small scales.

Outreach public talk, Sébastien Renaux-Petel (in French)

Yuko Urakawa

Matteo Braglia

Thomas Hertog: On the Origin of Inflation The no-boundary wave function can explain the origin of inflation but it favors a low amount of inflation, in conflict with observations. It has been thought that this puzzling property is universal, i.e. independent of the model of inflaton, posing a real conundrum for inflationary theory. We revisit this problem for k-inflation and give evidence that the no-boundary probabilities can be reversed in k-inflation, leading to the prediction of a large amount of inflation.

Arttu Rajantie: A Tale of Two Potentials The effective potential of a scalar field is a powerful tool in quantum field theory. Loosely speaking, it can be interpreted as the quantum corrected classical potential of the field, and in cosmology it is widely used to describe the evolution of the inflaton and other scalars during inflation and vacuum transition probabilities, among other things. However, for light scalar fields its standard definition has an infrared problem, which means that it is dominated by very long-wavelength fluctuations. In this talk, I discuss an alternative definition, known as the constraint effective potential, dating back to 1980s. In Minkowski spacetime, the two definitions are equivalent, but in de Sitter spacetime they are not, and crucially the constraint effective potential does not suffer from the same infrared problem. I demonstrate this with an explicit one-loop calculation of the two effective potentials for a real scalar field in de Sitter in dimensional regularisation. I compare the resulting potentials and their physical interpretations, and in particular, I argue that the constraint effective potential is the correct one to use in certain common cosmological applications, for example stochastic inflation. This work was carried out in collaboration with Lucas Vicente Garcia-Consuegra.

Sriramkumar Lakshmanan: Departures from slow roll inflation and magnetogenesis The primordial magnetic fields are generated during inflation by breaking the conformal invariance of the electromagnetic action through a coupling to the inflaton. Often, a parity violating term is also added to the action to generate helical magnetic fields. In this talk, I will first show that departures from slow roll inflation (as it occurs in scenarios involving a phase of ultra slow roll), which generate strong features in the scalar power spectrum, inevitably lead to sharp features in the power spectra of the electromagnetic fields and also suppress their strengths on large scales. Thereafter, I will illustrate that such challenges can be circumvented in two-field models of inflation to arrive at spectra of magnetic fields of the required strength and shape. Lastly, I will describe the evaluation of the three-point cross-correlation between the curvature perturbations and magnetic fields in slow roll and ultra slow roll inflation, and discuss the validity of the consistency relation in the squeezed limit.

Oksana Iarygina: Axion inflation with non-Abelian gauge fields Currently, the search for primordial gravitational waves is largely focused on detecting the parity-odd polarization pattern in the Cosmic Microwave Background - the B-modes. Accurately interpreting B-mode measurements depends heavily on understanding their production mechanisms. A particularly compelling scenario involves gravitational wave generation through the interaction of axion with gauge fields during inflation. I will present recent advances in axion inflation with non-Abelian gauge fields, focusing on the signatures in the primordial gravitational wave background and their correlation with primordial magnetic fields. I will conclude with a discussion of how the Schwinger effect at the end of inflation can nearly exclude axion magnetogenesis as a viable scenario.

Mario Ballardini

Adam Andrews

Poster presentations

Juan Garcia-Bellido

Chiara Animali

Ilia Musco

Eemeli Tomberg: Curvature profiles from stochastic inflation Stochastic inflation is a method for computing super-Hubble perturbations beyond the small-perturbation limit. I show how to obtain the radial profile of the curvature perturbations in a random patch of space using this method. The profiles turn out to be spiky, far from the smooth mean profiles often considered in the literature. Based on extensive numerical simulations, I discuss the profiles' structure and its implications for the formation of primordial black holes.

Ricardo Zambujal Ferreira: Stupendously Large Primordial Black Holes and Domain Walls The inflationary diffusion of scalar fields with discrete symmetries can generate a gas of closed domain walls after inflation, which later collapse into primordial black holes (PBHs) upon horizon re-entry. This mechanism predicts a distinctive, nearly flat PBH mass distribution, avoiding some issues of critical collapse. We show that QCD axion models with decay constants near the inflationary Hubble scale (f_a \sim 10^8 GeV) can produce PBHs making up ∼1% of dark matter, consistent with CMB isocurvature bounds.

Encieh Erfani: Clustering and formation of primordial black holes in excursion set theory In this talk, I investigate the formation and clustering of Primordial Black Holes within the framework of Excursion Set Theory (EST). Our results show that an enhanced power spectrum not only increases the formation of PBHs in specific mass ranges but also enhances their clustering probability. We find a one-to-one correspondence between the blue-tilted spectral index and the mass ranges in which PBHs form and cluster.

Oliver Philcox

Josu Aurrekoetxea

Kai Hei Trevor Cheung: Massive spinning fields during inflation We compare two setups incorporating new massive spinning degrees of freedom during inflation within the framework of the effective field theory of inflation (EFToI). Even though they differ on which symmetries are linearly realised, since they couple to the inflaton, it is possible they yield same signatures on cosmological correlators. We will see that their signatures are the same at bispectrum, but not higher-point correlators. There will also be a portion dedicated to the Feynman rules when calculating the correlators in these setups involving non-dynamical modes.

Denis Werth: Positive Geometry in Cosmological Correlators

Chen Yang: Strongly Coupled Sectors in Inflation Understanding the microscopic origin of primordial fluctuations remains a central challenge in inflationary cosmology. In this talk, I will explore a scenario where curvature perturbations interact with a strongly coupled, gapless sector known as unparticles. This setup allows for analytic control of cosmological correlators and reveals novel bispectrum shapes with distinctive phenomenological signatures. If time permits, I will also comment on possible model realizations and gapped scenarios.

Yuhang Zhu: The Integro-differential Bootstrap for Cosmological Correlators

David Wands

Gonzalo Palma

Spyros Sypsas: Revisiting stochastic inflation with perturbation theory. Using perturbation theory, we compute the one-point probability density function for primordial fluctuations valid to first order in the potential. We examine under which conditions our solution respects the Fokker-Planck equation encountered within the stochastic approach. We identify discrepancies and elucidate their origins, allowing us to shed light on the status of the stochastic formalism.

Nadine Nussbaumer: Light scalars in de Sitter: the stochastic story Light, polynomially self-interacting scalars in de Sitter notoriously generate infrared (IR) divergences: on superhorizon scales, their fluctuations grow so large that perturbation theory breaks down. We address this problem using non-perturbative techniques from stochastic inflation, by encoding the superhorizon dynamics in a probability distribution involving composite operators of the light scalar. We find that these composites behave as late-time conformal primaries, with their position-space four-point function collapsing to a strikingly simple power law. We conjecture a new physical picture: light interacting scalars in de Sitter effectively hadronize on superhorizon scales, producing a tower of composite states. We then explore whether this emergent spectrum can be captured within a weakly coupled effective field theory, which would amount to recasting the stochastic scalar IR-dynamics in terms of new, effective degrees of freedom.

Jaime Calderon Figueroa: Stochastic instantons and the tail of the inflationary density perturbation In the stochastic $\delta N$ formalism, the statistics of the primordial density perturbations can be mapped to the first-passage distribution of a stochastic process. In this talk, I will present a general framework to evaluate the rare-event tail of this distribution, based on an instanton approximation to a path integral representation of the transition probability. I will show how this stochastic description can be derived from a more fundamental formulation via the Schwinger-Keldysh path integral, where integrating out short-wavelength modes yields an influence functional that encodes the noise statistics underlying the stochastic approach. Finally, I will apply this method to a number of cases, highlighting its connections with, and advantages over, the existing methodologies.

Riccardo Impavido: Inflationary Fossils Beyond Perturbation Theory In this work we provide the missing link between two approaches aimed at characterizing the effect of long perturbation modes in Inflation. We consider the Inflationary Fossils' approach (arXiv:1203.0302 and related works) that characterizes the power-spectrum of the inflaton field in presence of other long and non dynamical fossil fields, and a technique, appeared in arXiv:2103.09244, that computes, beyond perturbation theory, the power-spectrum of a scalar field in presence of a large fluctuation of a second field. We clarify a few points on the applicability of the non-perturbative technique. We prove in five distinct cases that the non-perturbative approach, once expanded to first order in the coupling, matches the perturbative result following the Fossils' approach. We believe that this non-perturbative technique extends to all orders the Fossils' approach, resumming infinitely many diagrams of standard in-in perturbation theory.

Jacopo Fumagalli

Shi Pi

Mariam Tarek Mohamed Abdelaziz: The Effects of Primordial Gravitational Waves on the Large-Scale Structure Primordial Gravitational Waves (PGWs) are a key prediction of inflation, with ongoing efforts to detect them through CMB polarization patterns and direct interferometric searches. In this talk, I will present a novel approach to probing PGWs through their impact on Large-Scale Structure (LSS). While PGWs are often assumed to have a negligible effect on structure formation, our study shows that they can source second-order scalar perturbations. These "tensor-induced scalar modes" emerge upon horizon entry, modifying the matter density contrast and leaving distinct imprints on the matter power spectrum. This mechanism also introduces an intrinsic source of non-Gaussianity in the density field, providing a unique observational signature. I will discuss how different PGW power spectra shape this imprint and evaluate its detectability in future galaxy surveys like Euclid and SKA.

Mohammad Ali Gorji: Oscillations and parity violation in gravitational wave background from extra tensor modes Spectator fields which provide additional tensor degrees of freedom, on top of the standard metric tensor perturbations, can produce significant amounts of gravitational waves (GWs). Employing the effective field theory approach for spin-2 fields, we find a universal prediction that linear mixing between the metric and extra tensor modes inevitably induces oscillatory features in the GW spectrum. Moreover, parity-violating operators in the spin-2 sector can imprint chiral signatures on the resulting GW background. These results provide a model-independent characterization of the key signatures and observational implications of such scenarios which can be detected with future GW detectors.

Hugo Holland: The separate universe approach and gauge fixing procedures for multifield inflation models. The separate universe approach (SUA) is a powerful tool offering us a simple way to compute cosmic inhomogeneities at large scales including their non-linear evolution. It consists in describing the universe as a collection of independent patches which are taken to be homogeneous and isotropic. The assumptions one has to do to apply the SUA and its simplifications need to be checked, notably in multifield models of inflation. In this talk I will present the validity conditions of the SUA in non-linear sigma models by matching it to a complete cosmological perturbation theory computation taken to large scales. In particular I will dive into the subtleties of gauge fixing procedures and how they compare in both schemes.

Jan Tränkle: Constraining the inflaton potential with gravitational waves from oscillons Observations of the cosmic microwave background (CMB) lend strong evidence for the paradigm of cosmic inflation, but the specific form of the inflaton potential remains unknown. Under certain conditions, the oscillating inflaton condensate filling the Universe after inflation can fragment and form interesting non-linear structures known as oscillons. These long-lived soliton-like field configurations can dominate the Universe for several e-folds of expansion, leading to an early matter-dominated phase preceding the standard radiation era. In this talk, I will show how the rapid decay of the oscillons leads to an enhanced production of induced gravitational waves (GWs), whose energy density can saturate the observational bound on the effective number of relativistic species. We leverage this bound to constrain the inflaton mass, cubic, and quartic self-coupling in generic models that admit oscillon formation, providing novel and complementary constraints in regions of parameter space that are inaccessible with CMB observations alone.