arXiv subjects

David Stefanyszyn

Publications and source records attributed to David Stefanyszyn.

At least 19 recordsLinked to original sources

arXiv2026

A Match Made in Heaven: Linking Observables in Inflationary Cosmology

Cosmological correlation functions of inflaton and graviton perturbations are the fundamental observables of early universe cosmology and remain a primary target for observations. In this work, we ask the following question: are these observables independent of one another? We find that in the parity-odd sector of inflationary perturbation theory, the answer is a resounding no! In earlier work we derived a correlator-to-correlator factorisation formula which states that parity-odd correlators factorise into lower-point correlators under some mild assumptions on the underlying theory. In this work, we show that these assumptions are satisfied in dynamical Chern-Simons gravity where the action of minimal inflation is augmented by a coupling between the inflaton and the gravitational Chern-Simons term. Such a theory gives rise to a parity-odd trispectrum of curvature perturbations, and we show that such a trispectrum can be expressed solely in terms of the bispectrum that arises due to the minimal coupling between the inflaton and graviton, and the graviton power spectrum which receives a parity-odd correction in this theory. The trispectrum is quadratic in this mixed inflaton-graviton bispectrum and can therefore be interpreted as a ``double copy". Our final expression for the parity-odd trispectrum is a relatively simple function of the external momenta that is rational and factorised.

hep-th↗

arXiv2025

New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation

We discover a surprising relationship between exceptional effective field theories (EFTs) in de Sitter space and a notion of \textit{generalised energy conservation} (GEC) of an S-matrix defined in an extended Poincaré patch of four-dimensional de Sitter. By demanding that such an S-matrix only has support when the total energies of in and out states are equal, we constrain the coupling constants in theories of self-interacting scalars living in the exceptional series of de Sitter representations. We rediscover the theories of Dirac-Born-Infeld (DBI) and Special Galileon, and when increasing the conformal dimension we find evidence for new exceptional theories where the four-point scalar self interactions are uniquely fixed in terms of a single coupling constant. We conjecture that for each integer conformal dimension $Δ\geq 4$, there is at least one exceptional EFT that can be entirely fixed by GEC.

hep-th↗

arXiv2025

Massive Spinning Fields During Inflation: Feynman rules and correlator comparison

We consider the dynamics of massive spinning fields during inflation and the resulting signatures in the cosmological correlators of inflaton perturbations computed in the Poincaré patch of de Sitter space. There are (at least) two ways to describe the fluctuations of such new spinning degrees of freedom and these are distinguished by the symmetries of the de Sitter group that they linearly realise. The primary question we ask is: do these two set-ups yield distinct signatures in cosmological observables? After systematically deriving the Feynman rules for exchange diagrams consisting of massive spinning fields, where we discover the necessity of effective propagators that augment the naive Schwinger-Keldysh ones by delta functions corresponding to instantaneous propagation, we show that the two set-ups are indistinguishable at the level of the inflaton bispectrum but distinguishable at the level of the trispectrum and other higher-point correlation functions. The bispectrum is special since in the corresponding tree-level Feynman diagrams, only the helicity-zero modes of the spinning fields can propagate. The bispectrum correspondence holds up to the addition of contact diagrams arising from the self-interactions of the inflaton, and is consistent with the symmetries of the effective field theory of inflation. Our results suggest that the cosmological collider signals in the bispectrum are universal and do not depend on the detailed description of the massive spinning field.

hep-th↗

arXiv2025

There and Back Again: Mapping and Factorising Cosmological Observables

Cosmological correlators encode invaluable information about the wavefunction of the primordial universe. In this letter we present a duality between correlators and wavefunction coefficients that is valid to all orders in the loop expansion and manifests itself as a $\mathbb{Z}_4$ symmetry. To demonstrate the power of the duality, we derive a correlator-to-correlator factorisation (CCF) formula for the parity-odd part of cosmological correlators that relates $n$-point observables to lower-point ones via a series of diagrammatic cuts. These relations serve as the first example of physically testable cutting rules as they involve observables defined for arbitrary physical kinematics. We further show how the duality allows us to translate the cosmological optical theorem for wavefunction coefficients into statements about cosmological correlators.

hep-th↗

arXiv2024

Cosmological Correlators Through the Looking Glass: Reality, Parity, and Factorisation

We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all $n$-point functions and allow for the exchange of additional states of any mass and integer spin. Our proof makes use of a decomposition of the inflationary bulk-bulk propagator of massive spinning fields which preserves UV-convergence and ensures that the time-ordered contributions are purely real after we rotate to Euclidean time. We use this reality property to show that the maximally-connected parts of wavefunction coefficients, from which total-energy singularities originate, are purely real. In a theory where all states are in the complementary series, this reality extends to the full wavefunction coefficient. We then use our reality theorem to show that parity-odd correlators (correlators that are mirror asymmetric) are factorised and do not diverge when the total-energy is conserved. We pay special attention to the parity-odd four-point function (trispectrum) of inflationary curvature perturbations and use our reality/factorisation theorems to show that this observable is factorised into a product of cubic diagrams thereby enabling us to derive exact shapes. We present examples of couplings between the inflaton and massive spin-1 and spin-2 fields, with the parity-violation in the trispectrum driven by Chern-Simons corrections to the spinning field two-point function, or from parity-violating cubic interactions which we build within the Effective Field Theory of Inflation.

hep-th↗

arXiv2024

Soft Theorems for Boostless Amplitudes

We consider effective field theories (EFTs) of scalar fields with broken Lorentz boosts, which arise by taking the decoupling and flat-space limits of the EFT of inflation, and derive constraints that must be satisfied by the corresponding scattering amplitudes if there is an underlying non-linearly realised symmetry. We primarily concentrate on extended shift symmetries which depend on the space-time coordinates, and find that combinations of scattering amplitudes obey enhanced Adler zeros. That is, such combinations vanish as one external momentum is taken soft, with the rate at which they vanish dictated by the corresponding symmetry. In our soft theorem derivation, we pay particular care to the energy and momentum-conserving delta functions that arise due to space-time translations, and show that when acted upon by derivatives with respect to spatial momenta, they yield a tower of soft theorems which are ultimately required for closure of the underlying symmetry algebra. All of our soft theorems correspond to constraints that must be satisfied by on-shell amplitudes and, even for symmetries that depend on the time coordinate, our soft theorems only require derivatives to be taken with respect to spatial momenta. We perform a soft bootstrap procedure to find solutions to our soft theorems, and compare these solutions to what we find from an off-shell analysis using the coset construction.

hep-th↗

arXiv2023

Parity violation in the scalar trispectrum: no-go theorems and yes-go examples

We derive a set of no-go theorems and yes-go examples for the parity-odd primordial trispectrum of curvature perturbations. We work at tree-level in the decoupling limit of the Effective Field Theory of Inflation and assume scale invariance and a Bunch-Davies vacuum. We show that the parity-odd scalar trispectrum vanishes in the presence of any number of scalar fields with arbitrary mass and any parity-odd scalar correlator vanishes in the presence of any number of spinning fields with massless de Sitter mode functions, in agreement with the findings of Liu, Tong, Wang and Xianyu [1]. The same is true for correlators with an odd number of conformally-coupled external fields. We derive these results using both the (boostless) cosmological bootstrap, in particular the Cosmological Optical Theorem, and explicit perturbative calculations. We then discuss a series of yes-go examples by relaxing the above assumptions one at the time. In particular, we provide explicit results for the parity-odd trispectrum for (i) violations of scale invariance in single-clock inflation, (ii) the modified dispersion relation of the ghost condensate (non-Bunch-Davies vacuum), and (iii) interactions with massive spinning fields. Our results establish the parity-odd trispectrum as an exceptionally sensitive probe of new physics beyond vanilla inflation.

hep-th↗

arXiv2022

The graviton four-point function in de Sitter space

We compute the tree-level late-time graviton four-point correlation function, and the related quartic wavefunction coefficient, for Einstein gravity in de Sitter spacetime. We derive this result in several ways: by direct calculation, using the in-in formalism and the wavefunction of the universe; by a heuristic derivation leveraging the flat space wavefunction coefficient; and by using the boostless cosmological bootstrap, in particular the combination of the cosmological optical theorem, the amplitude limit, and the manifestly local test. We find agreement among the different methods.

hep-th↗

arXiv2022

On Graviton non-Gaussianities in the Effective Field Theory of Inflation

We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders in derivatives. Working in perturbation theory, we construct all cubic interactions that can contribute to tree-level graviton bispectra, showing that they all come from EFToI operators containing two or three powers of the extrinsic curvature and its covariant derivatives: all other operators can be removed by field redefinitions or start at higher-order in perturbations. For operators cubic in the extrinsic curvature, where the single-clock consistency relations are satisfied without a correction to the graviton two-point function, we use the Manifestly Local Test (MLT) to efficiently extract the effects of evolving graviton fluctuations to the end of inflation. Despite the somewhat complicated nature of the bulk interactions, the final boundary correlators take a very compact form. For operators quadratic in the extrinsic curvature, the leading order bispectra are a sum of contact and single exchange diagrams, which are tied together by spatial diffeomorphisms, and to all orders in derivatives we derive these bispectra by computing the necessary bulk time integrals. For single exchange diagrams we exploit factorisation properties of the bulk-bulk propagator for massless gravitons and write the result as a finite sum over residues. Perhaps surprisingly, we show these single exchange contributions have only total-energy poles and also satisfy the MLT.

hep-th↗

arXiv2022

The Boostless Bootstrap and BCFW Momentum Shifts

In a recent paper [1], three-particle interactions without invariance under Lorentz boosts were constrained by demanding that they yield tree-level four-particle scattering amplitudes with singularities as dictated by unitarity and locality. In this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using BCFW momentum shifts. We point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite BCFW parameter z, is not strictly necessary to obtain non-trivial constraints for the three-particle interactions.

hep-th↗

arXiv2022

Bootstrapping Large Graviton non-Gaussianities

Gravitational interferometers and cosmological observations of the cosmic microwave background offer us the prospect to probe the laws of gravity in the primordial universe. To study and interpret these datasets we need to know the possible graviton non-Gaussianities. To this end, we derive the most general tree-level three-point functions (bispectra) for a massless graviton to all orders in derivatives, assuming scale invariance. Instead of working with explicit Lagrangians, we take a bootstrap approach and obtain our results using the recently derived constraints from unitarity, locality and the choice of vacuum. Since we make no assumptions about de Sitter boosts, our results capture the phenomenology of large classes of models such as the effective field theory of inflation and solid inflation. We present formulae for the infinite number of parity-even bispectra. Remarkably, for parity-odd bispectra, we show that unitarity allows for only a handful of possible shapes: three for graviton-graviton-graviton, three for scalar-graviton-graviton and one for scalar-scalar-graviton, which we bootstrap explicitly. These parity-odd non-Gaussianities can be large, for example in solid inflation, and therefore constitute a concrete and well-motivated target for future observations.

hep-th↗

arXiv2022

The Boostless Bootstrap: Amplitudes without Lorentz boosts

Poincaré invariance is a well-tested symmetry of nature and sits at the core of our description of relativistic particles and gravity. At the same time, in most systems Poincaré invariance is not a symmetry of the ground state and is hence broken spontaneously. This phenomenon is ubiquitous in cosmology where Lorentz boosts are spontaneously broken by the existence of a preferred reference frame in which the universe is homogeneous and isotropic. This motivates us to study scattering amplitudes without requiring invariance of the interactions under Lorentz boosts. In particular, using on-shell methods and assuming massless, relativistic and luminal particles of any spin, we show that the allowed interactions around Minkowski spacetime are severely constrained by unitarity and locality in the form of consistent factorization. The existence of an interacting massless spin-2 particle enforces (analytically continued) three-particle amplitudes to be Lorentz invariant, even those that do not involve a graviton, such as cubic scalar couplings. We conjecture this to be true for all n-particle amplitudes. Also, particles of spin S > 2 cannot self-interact nor can be minimally coupled to gravity, while particles of spin S > 1 cannot have electric charge. Given the growing evidence that free gravitons are well described by massless, luminal relativistic particles, our results imply that cubic graviton interactions in Minkowski must be those of general relativity up to a unique Lorentz-invariant higher-derivative correction of mass dimension 9. Finally, we point out that consistent factorization for massless particles is highly IR sensitive and therefore our powerful at-space results do not straightforwardly apply to curved spacetime.

hep-th↗

arXiv2021

From Locality and Unitarity to Cosmological Correlators

In the standard approach to deriving inflationary predictions, we evolve a vacuum state in time according to the rules of a given model. Since the only observables are the future values of correlators and not their time evolution, this brings about a large degeneracy: a vast number of different models are mapped to the same minute number of observables. Furthermore, due to the lack of time-translation invariance, even tree-level calculations require an increasing number of nested integrals that quickly become intractable. Here we ask how much of the final observables can be "bootstrapped" directly from locality, unitarity and symmetries. To this end, we introduce two new bootstrap tools to efficiently compute cosmological correlators/wavefunctions. The first is a Manifestly Local Test (MLT) that any $n$-point (wave)function of massless scalars or gravitons must satisfy if it is to arise from a manifestly local theory. When combined with a sub-set of the recently proposed Bootstrap Rules, this allows us to compute explicitly all bispectra to all orders in derivatives for a single scalar. Since we don't invoke soft theorems, this can also be extended to multi-field inflation. The second is a partial energy recursion relation that allows us to compute exchange correlators. Combining a bespoke complex shift of the partial energies with Cauchy's integral theorem and the Cosmological Optical Theorem, we fix exchange correlators up to a boundary term. The latter can be determined up to contact interactions using unitarity and manifest locality. As an illustration, we use these tools to bootstrap scalar inflationary trispectra due to graviton exchange and inflaton self-interactions.

hep-th↗

arXiv2020

The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales

In contrast to massless spinning particles, scalars are not heavily constrained by unitarity and locality. Off-shell, no gauge symmetries are required to write down manifestly local theories, while on-shell consistent factorisation is trivial. Instead a useful classification scheme for scalars is based on the symmetries they can non-linearly realise. Motivated by the breaking of Lorentz boosts in cosmology, in this paper we classify the possible symmetries of a shift-symmetric scalar that is assumed to non-linearly realise Lorentz boosts as, for example, in the EFT of inflation. Our classification method is algebraic; guided by the coset construction and inverse Higgs constraints. We rediscover some known phonon theories within the superfluid and galileid classes, and discover a new galileid theory which we call the $\textit{extended galileid}$. Generic galileids correspond to the broken phase of galileon scalar EFTs and our extended galileids correspond to special subsets where each galileon coupling is fixed by an additional symmetry. We discuss the broken phase of theories that also admit a perturbation theory around Poincaré invariant vacua and we show that the so-called exceptional EFTs, the DBI scalar and special galileon, do not admit such a broken phase. Concentrating on DBI we provide a detailed account of this showing that the scattering amplitudes are secretly Poincaré invariant when the theory is expanded around the superfluid background used in the EFT of inflation. We point out that DBI is an exception to the common lore that the residue of the total energy pole of cosmological correlators is proportional to the amplitude. We also discuss the inevitability of poles in $2 \rightarrow 2$ scattering amplitudes when boost are spontaneously broken meaning that such theories do not admit Adler zeros and generalisations even in the presence of a shift symmetry.

hep-th↗

arXiv2019

UV Constraints on Massive Spinning Particles: Lessons from the Gravitino

Self-interacting massive particles with spin $\geq 1$ unavoidably violate unitarity; the question is at what scale. For spin-$1$ the strong coupling scale (at which perturbative unitarity is lost) cannot be raised by any finite tuning of the interactions, while for spin-$2$ there exists a special tuning of the Wilson coefficients which can raise this scale (and enjoys numerous special properties such as ghost-freedom). Here, we fill in the missing piece by describing how the self-interactions of a massive spin-$3/2$ field, or "massive gravitino", become strongly coupled at high energies. We show that while several different structures appear in the leading order potential, the strong coupling scale cannot be raised (in the absence of additional fields). At the level of the off-shell Lagrangian, it is always the non-linear symmetries of the longitudinal Stuckelberg mode that dictate the strong coupling, and we show that in general it is only possible to parametrically raise the strong coupling scale if Wess-Zumino structures exist. We complement this off-shell approach with a first analysis of positivity bounds for a massive spin-$3/2$ particle, showing that any potential self-interaction which contributes to an on-shell 2-to-2 elastic process at tree level must vanish if this low-energy theory is to have a standard UV completion. We identify the mixing between the longitudinal mode and the transverse modes as the main obstacle to positivity, and clarify how the non-Abelian nature of non-linear (dRGT) massive gravity allows it to satisfy positivity where all known spin $\geq 3/2$ Abelian theories fail. Our results imply that a massive gravitino cannot appear alone in a controlled EFT---it must be accompanied by other particles, e.g.~as part of a supermultiplet. Together with the spin-$1$ and spin-$2$ cases, we suggest features which will persist in even higher spin massive theories.

hep-th↗

arXiv2019

Symmetric Superfluids

We present a complete classification of symmetric superfluids, namely shift-symmetric and Poincaré invariant scalar field theories that have an enlarged set of classically conserved currents at leading order in derivatives. These theories arise in the decoupling limit of the effective field theory of shift-symmetric, single-clock cosmologies and our results pick out all models with couplings fixed by additional symmetry. Remarkably, in $ D\geq 2 $ spacetime dimensions there are only two possibilities: the Dirac-Born-Infeld theory and Scaling Superfluids with Lagrangian $ (-\partial_μϕ\partial^μϕ)^α$, for some real $ α$. The scaling symmetry present for any $ α$ is further enhanced to the full conformal group only for $ α=D/2 $, and to infinitely many additional generators for $ α=1/2 $. We discuss the stability of Scaling Superfluids and point out that all coupling constants are determined by the speed of sound.

hep-th↗

arXiv2019

An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry

We present a novel approach to classify supersymmetric effective field theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These enhancements arise due to non-linearly realised symmetries on the Goldstone modes of such EFTs and we classify the algebras that these symmetries can form. Our main focus is on so-called exceptional algebras which lead to field-dependent transformation rules and EFTs with the maximum possible soft enhancement at a given derivative power counting. We adapt existing techniques for Poincaré invariant theories to the supersymmetric case, and introduce superspace inverse Higgs constraints as a method of reducing the number of Goldstone modes while maintaining all symmetries. Restricting to the case of a single Goldstone supermultiplet in four dimensions, we classify the exceptional algebras and EFTs for a chiral, Maxwell or real linear supermultiplet. Moreover, we show how our algebraic approach allows one to read off the soft weights of the different component fields from superspace inverse Higgs trees, which are the algebraic cousin of the on-shell soft data one provides to soft bootstrap EFTs using on-shell recursion. Our Lie-superalgebraic approach extends the results of on-shell methods and provides a complementary perspective on non-linear realisations.

hep-th↗

arXiv2019

An Algebraic Classification of Exceptional EFTs

We classify four-dimensional effective field theories (EFTs) with enhanced soft limits, which arise due to non-linearly realised symmetries on the Goldstone modes of such theories. We present an algorithm for deriving all possible algebras that can be non-linearly realised on a set of Goldstone modes with canonical propagators, linearly realised Poincaré symmetries and interactions at weak coupling. We then perform a full classification of the cases with multiple scalars or multiple spin-$1/2$ fermions as the Goldstone modes. In each case there are only a small number of algebras consistent with field-dependent transformation rules, leading to the class of exceptional EFTs including the scalar sector of Dirac-Born-Infeld, Special Galileon and Volkov-Akulov theories. We also discuss the coupling of a $U(1)$ gauge vector to the exceptional scalar theories, showing that there is a Special Galileon version of the full Dirac-Born-Infeld theory. This paper is part I in a series of two papers, with the second providing an algebraic classification of supersymmetric theories.

hep-th↗