arXiv subjects

Gonzalo A. Palma

Publications and source records attributed to Gonzalo A. Palma.

At least 19 recordsLinked to original sources

arXiv2026

Strongly mixed cosmological collider at unequal sound speeds

We derive the canonically normalized modes of a two-field inflationary system with arbitrary constant quadratic mixing and unequal sound speeds $c_φ$ and $c_σ$ for the curvature and isocurvature perturbations, respectively. A Laplace representation reduces the coupled dynamics to a second-order Heun equation and gives the exact late-time curvature power spectrum for arbitrary values of the mixing parameter and entropy mass. The sound-speed ratio $r_c=c_σ/c_φ$ controls the separation between the two sound horizons. At fixed nonzero mixing and $r_c\ll1$, the power exhibits power-law enhancement, growth as $\ln^2(1/r_c)$, or bounded oscillations in $\ln r_c$, depending on the mass and mixing. For $r_c\gg1$, the correction to the unmixed spectrum vanishes as $\ln r_c/r_c^2$ at fixed mass and mixing. Using the same normalized modes, we compute the tree-level bispectrum for three representative cubic interactions, with the mixing parameter treated exactly. For heavy entropy fields, unequal speeds modify the collider amplitude and phase while preserving the strict squeezed frequency set by the final entropy mass. The power-normalized amplitude can vary nonmonotonically with $r_c$, and a sound-speed hierarchy can delay the approach to this asymptotic regime.

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arXiv2026

From the Wavefunction of the Universe to In-In-Correlators: A Perturbative Map to All Orders

Both the Wavefunction of the Universe and the Schwinger-Keldysh in-in formalism are central tools for analyzing primordial cosmological observables, such as equal-time correlation functions. While their conceptual equivalence is well established, a systematic and explicit map between their diagrammatic expansions has remained elusive. In this article, I construct such a map by analyzing the relation between the two frameworks at the diagrammatic level. I show that diagrams contributing to correlation functions in the Wavefunction of the Universe approach can be uniquely reorganized into Schwinger-Keldysh diagrams. This correspondence holds to all orders in perturbation theory, including arbitrary numbers of interaction vertices and loops.

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arXiv2026

Schwinger-Keldysh Cosmological Cutting Rules

In this work, we study the realisation of unitarity-based cutting rules for primordial cosmological correlators computed within the Schwinger-Keldysh path integral formalism. While cutting rules have been previously derived for wavefunction coefficients, here we examine them directly at the level of cosmological observables expressed diagrammatically. The resulting rules closely resemble those familiar from flat-space scattering amplitudes, but with an additional subtlety: in order to express the discontinuity of a correlator as the product of lower-order correlators, one must introduce a specific combinations of diagrams which do not appear in the computation of observables themselves. We explicitly verify these rules for several classes of correlators, both at tree level and with loop corrections, arising from theories involving different types of interactions.

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arXiv2026

Revisiting stochastic inflation with perturbation theory

A long-standing problem in primordial cosmology is to understand the precise relation between the stochastic formalism and standard perturbation theory for light scalar fields in inflationary spacetimes. A complete correspondence between the two frameworks has remained elusive, even for a single self-interacting spectator field on a fixed de Sitter background. In this Letter, we revisit the assumptions underlying the derivation of the Langevin and Fokker-Planck equations that form the basis of the stochastic approach. We show that the standard stochastic treatment is effectively equivalent to neglecting super-long-wavelength modes beyond the observable range described by these equations. Using perturbation theory, we quantify how these modes enter through virtual loop effects and demonstrate that, once treated consistently, they induce definite corrections to both the Langevin and Fokker-Planck equations.

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arXiv2026

Pushing the Primordial Frontier: Exact Linear Solutions in Multifield Inflation

We present exact analytic solutions for the linear dynamics of a two-field inflationary system in which the primordial curvature perturbation $ζ$ is coupled to an isocurvature perturbation $σ$ of entropy mass $μ$. The solutions are valid for arbitrary values of $μ$ and the dimensionless interaction strength $λ$, within a quasi-de Sitter background. They therefore provide analytic control over the strong mixing regime in which $ζ$ interacts with light isocurvature fields, commonly associated with rapid-turn inflation. As a first application, we derive the amplitude of the primordial power spectrum in closed form, obtaining an expression that interpolates between the weakly mixed, strongly mixed, light-field, and heavy-field regimes. These results open the way to analytic studies of multifield observables beyond the power spectrum, including non-Gaussianity, particle production, and loop corrections.

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arXiv2026

Pushing the Primordial Frontier: Cosmological Collider Signatures at Strong Mixing

We develop an analytic treatment of primordial non-Gaussianity in multifield inflation that is nonperturbative in the constant curvature--isocurvature mixing strength $λ$. Using exact linear solutions for the coupled curvature perturbation $ζ$ and isocurvature perturbation $σ$, we construct dressed propagators and derive exact integral representations for the tree-level bispectra generated by the interactions $\dotζ^2σ$, $\dotζ\,σ^2$, and $σ^3$. This formalism resums curvature--isocurvature transfer to all orders in $λ$ and applies for arbitrary values of the entropy mass $μ$. We obtain closed-form expressions for the leading squeezed limit of the bispectrum contributions and recover the well-known cosmological-collider and quasi-single-field results in the weak-mixing limit. In the strong-mixing regime, where conventional transfer perturbation theory breaks down, we find that both the power spectrum and the bispectrum can be dramatically enhanced, giving rise to distinctive nonperturbative scaling laws for the reduced non-Gaussian amplitude. Together, these results open a new analytic window onto multifield inflation beyond the weak-coupling approximation and establish a framework for studying cosmological-collider signals, primordial-black-hole production, and loop corrections in strongly mixed inflationary dynamics.

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arXiv2025

Non-Gaussian statistics of de Sitter spectators: A perturbative derivation of stochastic dynamics

Scalar fields interacting with the primordial curvature perturbation during inflation may communicate their statistics to the latter. This situation motivates the study of how the probability density function (PDF) of a light spectator field $φ$ in a pure de Sitter space-time, becomes non-Gaussian under the influence of a scalar potential ${\mathcal V(φ)}$. One approach to this problem is offered by the stochastic formalism introduced by Starobinsky and Yokoyama. It results in a Fokker-Planck equation for the time-dependent PDF $ρ(φ, t)$ describing the statistics of $φ$ which, in the limit of equilibrium gives one back the solution $ρ(φ) \propto \exp \big[ - \frac{8 π^2}{3 H^4} {\mathcal V(φ)} \big]$. We study the derivation of $ρ(φ, t)$ using quantum field theory tools. Our approach yields an almost Gaussian distribution function, distorted by minor corrections comprised of terms proportional to powers of $\mathcal O_φ{\mathcal V(φ)}$, where $\mathcal O_φ$ stands for a derivative operator acting on ${\mathcal V(φ)}$ proportional to $ΔN$, the number of $e$-folds succeeding the Hubble-horizon crossing of $φ$'s wavelengths. This general form is obtained perturbatively and remains valid even with loop corrections. Our solution satisfies a Fokker-Planck equation that receives corrections with respect to the one found within the stochastic approach, allowing us to comment on the validity of the standard equilibrium solution for generic potentials. We posit that higher order corrections to the Fokker-Planck equation may become important towards the equilibrium.

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arXiv2025

Confronting infrared divergences in de Sitter: loops, logarithms and the stochastic formalism

A well-established result in quantum field theory in four-dimensional de Sitter space is that the vacuum state of a massless scalar field breaks the de Sitter isometry group, leading to time-dependent (secular) growth in correlation functions computed in inflationary coordinates. This behavior is widely believed to extend to more general theories involving light scalar fields with weak non-derivative interactions. In such cases, secular growth is thought to be further amplified by loop corrections, and the stochastic formalism is often regarded as the appropriate framework to resum these infrared effects. In this article we challenge this prevailing view. A crucial distinction must be made between two cases: a massless scalar field protected by a shift symmetry, and a light scalar without such a symmetry. In the former, the shift symmetry enforces derivative interactions, yielding observables in which secular growth plays no physical role. In the latter, although correlation functions develop infrared divergences in the massless limit, they remain fully invariant under the de Sitter isometry group. We analyze the structure of these divergences arising from loop integrals and show that, in the soft-momentum limit, they do not alter the time dependence of tree-level correlators. In fact, using a de Sitter-invariant renormalization scheme based on Wilson's axioms for integration, these divergences can be systematically removed order by order. We therefore conclude that neither massless nor light scalar fields in de Sitter space exhibit genuine secular growth. We further discuss the implications of these findings for the validity and scope of the stochastic approach to inflation.

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arXiv2025

A note on loop resummation in de Sitter spacetime with the wavefunction of the universe approach

We analyze the computation of $n$-point correlation functions in de Sitter spacetime, including loop corrections, using the wavefunction of the universe approach. This method consists of two stages employing distinct Feynman rules. First, one must compute the wavefunction coefficients using interactions as vertices. Then, in the second stage, one computes correlation functions using wavefunction coefficients as vertices. For massless fields, loop corrections in the first stage are free of infrared (IR) divergences, which leads to the question of how this matches the well-known IR behavior of correlators obtained via other methods. By considering a scalar field with an arbitrary potential, we compute $n$-point correlation functions to first order in the potential but to all orders in loops. We find that, although loop integrals in the first stage are indeed IR convergent, the second procedure reintroduces the IR divergence. We discuss how this induces renormalization of the interaction potential such that the final result combining both steps exactly matches the form of $n$-point functions previously calculated with other methods.

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arXiv2025

Particle creation from non-geodesic trajectories in multifield inflation

Particle production in de Sitter spacetime arises from the exponential expansion of space, rendering the Bunch-Davies vacuum perceived as a particle-containing state by late-time observers. For states defined as eigenstates of both momentum and the Hamiltonian, the Bunch-Davies vacuum exhibits a constant particle density per physical momentum. We explore particle production beyond this baseline, focusing on deviations from exact de Sitter conditions and non-gravitational interactions, such as slow-roll inflation or interactions arising from the coupling of inflation to other fields. Using Bogoliubov transformations, we calculate the number density of energy/momentum eigenstates. In single-field inflation, this density captures the observed spectral index of the primordial power spectrum, while in two-field models, it reflects the non-gravitational coupling driving background trajectory turning. We present analytical results applicable to various scenarios involving particle production from non-adiabatic processes during inflation.

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arXiv2025

Regularizing infrared divergences in de Sitter spacetime: Loops, dimensional regularization, and cutoffs

Correlation functions of light scalar fields in de Sitter spacetime, computed via standard perturbation theory, often exhibit secular growth characterized by time-dependent divergent terms in the form of powers of $\ln a(t)$, where $a(t)$ is the scale factor describing cosmic expansion. It is widely believed that loop corrections further enhance this secular growth. We argue that this is not necessarily the case: Loop corrections can be systematically handled using standard perturbative techniques, such as dimensional regularization, without introducing new $\ln a(t)$ terms. We focus on a canonical massless scalar field $φ$ with self-interactions described by a potential $\mathcal{V}(φ)$, and analyze correlation functions represented by diagrams with a single vertex and an arbitrary number of loops. In this framework, infrared divergences can be systematically eliminated with counterterms at each order in perturbation theory, leading to loop-corrected correlation functions that are indistinguishable from their tree-level forms, with no secular growth from loops. Furthermore, adopting a Wilsonian perspective, we explore the role of cutoffs in computing loop corrections within effective field theory and identify the effective potential $\mathcal{V}_{\rm eff}(φ)$, which guarantees cutoff-independent observables. We conclude that when infrared comoving cutoffs are used to regularize loop integrals, time-dependent Wilsonian coefficients are necessary to maintain cutoff-free correlation functions. Neglecting this time dependence results in secular growth from loops.

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arXiv2023

Unifying attractor and non-attractor models of inflation under a single soft theorem

We study the generation of local non-Gaussianity in models of canonical single field inflation when their backgrounds are either attractor or non-attractor. We show that the invariance of inflation under space-time diffeomorphisms can be exploited to make powerful statements about the squeezed limit of the primordial bispectrum of curvature perturbations, valid to all orders in slow roll parameters. In particular, by neglecting departures from the adiabatic evolution of long-wavelength modes (for instance, produced in sharp transitions between slow-roll and ultra slow-roll phases), we derive a general expression for the bispectrum's squeezed limit in co-moving coordinates. This result consists in the standard Maldacena's consistency relation (proportional to the spectral index of the power spectrum) plus additional terms containing time derivatives of the power spectrum. In addition, we show that it is always possible to write the perturbed metric in conformal Fermi coordinates, independently of whether the inflationary background is attractor or non-attractor, allowing the computation of the physical primordial bispectrum's squeezed limit as observed by local inertial observers. We find that in the absence of sudden transitions between attractor and non-attractor regimes, observable local non-Gaussianity is generically suppressed. Our results imply that large local non-Gaussianity is not a generic consequence of non-attractor backgrounds.

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arXiv2022

Inflation: Theory and Observations

Cosmic inflation provides a window to the highest energy densities accessible in nature, far beyond those achievable in any realistic terrestrial experiment. Theoretical insights into the inflationary era and its observational probes may therefore shed unique light on the physical laws underlying our universe. This white paper describes our current theoretical understanding of the inflationary era, with a focus on the statistical properties of primordial fluctuations. In particular, we survey observational targets for three important signatures of inflation: primordial gravitational waves, primordial non-Gaussianity and primordial features. With the requisite advancements in analysis techniques, the tremendous increase in the raw sensitivities of upcoming and planned surveys will translate to leaps in our understanding of the inflationary paradigm and could open new frontiers for cosmology and particle physics. The combination of future theoretical and observational developments therefore offer the potential for a dramatic discovery about the nature of cosmic acceleration in the very early universe and physics on the smallest scales.

astro-ph.CO↗

arXiv2022

Snowmass Theory Frontier: Astrophysics and Cosmology

We summarize progress made in theoretical astrophysics and cosmology over the past decade and areas of interest for the coming decade. This Report is prepared as the TF09 "Astrophysics and Cosmology" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.

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arXiv2022

Primordial gravitational waves from excited states

We show that a scalar excited state with large occupation numbers during inflation leads to an enhancement of tensor modes and a characteristic pattern of order-one oscillations in the associated stochastic gravitational wave background (SGWB) sourced during inflation. An effective excited state, i.e. a departure from the Bunch-Davies vacuum, can emerge dynamically as the result of a transient non-adiabatic evolution, e.g. a sharp feature along the inflationary history. We provide an explicit example in a multifield context where the sharp feature triggering the excited state is identified with a strong turn in the inflationary trajectory. En passant, we derive a universal expression for the tensor power spectrum sourced at second order by an arbitrary number of scalar degrees of freedom during inflation, crucially taking into account the nontrivial structure of the Hilbert space in multifield setups. The SGWB sourced during inflation can overcome the standard scalar-induced SGWB sourced at horizon re-entry of the fluctuations after inflation, while being less constrained by perturbativity and backreaction bounds. In addition, one may entertain the possibility of detecting both since they peak at different frequencies exhibiting oscillations with distinct periods.

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arXiv2022

Four-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: On-sky Receiver Performance at 40, 90, 150, and 220 GHz Frequency Bands

The Cosmology Large Angular Scale Surveyor (CLASS) observes the polarized cosmic microwave background (CMB) over the angular scales of 1$^\circ \lesssim θ\leq$ 90$^\circ$ with the aim of characterizing primordial gravitational waves and cosmic reionization. We report on the on-sky performance of the CLASS Q-band (40 GHz), W-band (90 GHz), and dichroic G-band (150/220 GHz) receivers that have been operational at the CLASS site in the Atacama desert since June 2016, May 2018, and September 2019, respectively. We show that the noise-equivalent power measured by the detectors matches the expected noise model based on on-sky optical loading and lab-measured detector parameters. Using Moon, Venus, and Jupiter observations, we obtain power-to-antenna-temperature calibrations and optical efficiencies for the telescopes. From the CMB survey data, we compute instantaneous array noise-equivalent-temperature sensitivities of 22, 19, 23, and 71 $\mathrm{μK}_\mathrm{cmb}\sqrt{\mathrm{s}}$ for the 40, 90, 150, and 220 GHz frequency bands, respectively. These noise temperatures refer to white noise amplitudes, which contribute to sky maps at all angular scales. Future papers will assess additional noise sources impacting larger angular scales.

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arXiv2021

The hand-made tail: Non-perturbative tails from multifield inflation

It is becoming increasingly clear that large but rare fluctuations of the primordial curvature field, controlled by the tail of its probability distribution, could have dramatic effects on the current structure of the universe -- {\it e.g.} via primordial black-holes. However, the use of standard perturbation theory to study the evolution of fluctuations during inflation fails in providing a reliable description of how non-linear interactions induce non-Gaussian tails. Here, we use the stochastic inflation formalism to study the non-perturbative effects from multi-field fluctuations on the statistical properties of the primordial curvature field. Starting from the effective action describing multi-field fluctuations, we compute the joint probability density function and show that enhanced non-Gaussian tails are a generic feature of slow-roll inflation with additional degrees of freedom.

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arXiv2020

Seeding primordial black holes in multifield inflation

The inflationary origin of primordial black holes (PBHs) relies on a large enhancement of the power spectrum $Δ_ζ$ of the curvature fluctuation $ζ$ at wavelengths much shorter than those of the cosmic microwave background anisotropies. This is typically achieved in models where $ζ$ evolves without interacting significantly with additional (isocurvature) scalar degrees of freedom. However, quantum gravity inspired models are characterized by moduli spaces with highly curved geometries and a large number of scalar fields that could vigorously interact with $ζ$ (as in the cosmological collider picture). Here we show that isocurvature fluctuations can mix with $ζ$ inducing large enhancements of its amplitude. This occurs whenever the inflationary trajectory experiences rapid turns in the field space of the model leading to amplifications that are exponentially sensitive to the total angle swept by the turn, which induce characteristic observable signatures on $Δ_ζ$. We derive accurate analytical predictions and show that the large enhancements required for PBHs demand non-canonical kinetic terms in the action of the multifield system.

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