arXiv subjects

Sadra Jazayeri

Publications and source records attributed to Sadra Jazayeri.

At least 19 recordsLinked to original sources

arXiv2026

The Massive Flat Space Limit of Cosmological Correlators

Identifying useful flat-space limits for cosmological correlators, where they can be expressed in terms of observables in Minkowski space is nontrivial due to their scale-invariant nature. In recent years, it has been shown that momentum-space correlators encode flat-space amplitudes at specific singularities that emerge in the complex plane of their kinematics after analytical continuation. This flat-space limit is massless in the sense that the amplitude corresponds to the ultraviolet regime of the associated flat-space process, where the masses of the internal propagators are effectively zero. In this paper, we introduce a novel massive flat-space (MFS) limit, in which the internal masses in the corresponding flat-space Feynman graph remain finite. Our proposal applies to arbitrary graphs with light external legs and heavy internal lines, using a double-scaling limit. In this limit, the external energies, treated as independent variables, approach zero in inverse proportion to the propagator masses, which are sent to infinity. We present a general reduction formula that expresses diagrams in this limit in terms of amputated Feynman graphs in flat space. Our findings underscore the deep connections between the rich structure of massive Feynman integrals and the properties of cosmological correlators involving the exchange of heavy fields. Using this reduction formula, we compute sample one-loop contributions from heavy particles to inflationary correlators in the small sound-speed regime, revealing novel bispectrum shapes. The non-Gaussian signals we uncover, which are especially pronounced around the equilateral configuration, cannot be reproduced by adding local terms to the effective field theory of single-field inflation. Instead, they are captured by incorporating prescribed spatially non-local operators into the EFT.

hep-th↗

arXiv2026

Every Wrinkle Carries A Memory: An Integro-differential Bootstrap for Features in Cosmological Correlators

Motivated by cosmological observations, we push the cosmological bootstrap program beyond the de Sitter invariance lamppost by considering correlators that explicitly break scale invariance, thereby exhibiting primordial features. For exchange processes involving heavy fields with time-dependent masses and sound speeds, we demonstrate that locality in the bulk implies a set of integro-differential equations for correlators on the boundary. These scale-breaking boundary equations come with a built-in memory kernel in momentum-kinematic space encapsulating the universe's evolution during inflation. Specialising to heavy fields with sinusoidal masses such as those found in axion monodromy scenarios, we show that a powerful synthesis of microcausality and analyticity allows an analytical solution of these equations at leading order in the amplitude of mass oscillations. Meanwhile, we also unveil non-perturbative information in the integro-differential equations by resumming apparent infrared divergences as parametric resonances. In addition, we provide a first-of-its-kind example of numerical bootstrap that directly maps out the solution space of such boundary equations. Finally, we compute the bispectrum and uncover, in the squeezed limit, a scale-breaking cosmological collider signal, whose amplitude can be exponentially enhanced (with respect to the Boltzmann suppression) due to particle production triggered by high-frequency mass oscillations.

hep-th↗

arXiv2026

Cosmological Correlator Discontinuities from Scattering Amplitudes

Recent theoretical work has revealed that basic observables of quantum field theory in de Sitter space, known as in-in or cosmological correlators, exhibit surprisingly simple mathematical structure reminiscent of scattering amplitudes in flat space. For many theories, this simplicity can be made manifest using a set of ``cosmological dressing rules'' which uplift flat-space Feynman diagrams to in-in correlators in de Sitter space by attaching auxiliary propagators to the interaction vertices. In this paper, we show that discontinuities of cosmological correlators with respect to internal energy variables can be obtained by applying auxiliary propagators to unitarity cuts of flat space Feynman diagrams. Moreover, discontinuities with respect to external energy variables can be obtained by cutting auxiliary propagators attached to Feynman diagrams. This observation in turn implies highly non-trivial constraints on cosmological correlators in the form of simple sum rules. We illustrate these ideas in a number of examples at tree-level and 1-loop for conformally coupled scalar theories, although they hold more generally. Finally, we show how to reconstruct cosmological correlators from their discontinuities using dispersion relations, providing a powerful new approach to computing cosmological observables by systematically reconstructing them from data uplifted from flat space.

hep-th↗

arXiv2025

Bispectrum Islands

Inspired by the amplitude bootstrap program, the spirit of this work is to constrain the space of consistent inflationary correlation functions - specifically, the bispectrum of curvature perturbations - using fundamental principles such as unitarity, locality, analyticity, and symmetries. To this end, we assume a setup for inflation in which de Sitter isometries are only mildly broken by the slow roll of the inflaton field, and study the bispectrum imprinted by a generic hidden sector during inflation. Assuming that the hidden sector's contributions to primordial non-Gaussianity are dominated by the exchange of a scalar operator (which does not preclude high-spin UV completions), we derive nontrivial positivity constraints on the resulting bispectrum $B(k_1,k_2,k_3)$. In particular, we show that $B$ must be negative in a certain region around the equilateral configuration. For instance, for isosceles triangles (with $k_2=k_3$) this region is given by $0.027\lesssim k_3/k_1\leq 2$. Furthermore, we demonstrate that unitarity imposes upper and lower bounds on the bispectrum shape, thereby carving out a Bispectrum Island where consistent shapes in our setup can reside. We complement our analysis by contemplating alternative setups where the coupling to the hidden sector is allowed to strongly break de Sitter boosts. We also identify situations that would push the bispectrum off the island and the profound physical features they would reveal.

hep-th↗

arXiv2025

Cosmological Bootstrap in Slow Motion

Speed matters. How the masses and spins of new particles active during inflation can be read off from the statistical properties of primordial density fluctuations is well understood. However, not when the propagation speeds of the new degrees of freedom and of the curvature perturbation differ, which is the generic situation in the effective field theory of inflationary fluctuations. Here we use bootstrap techniques to find exact analytical solutions for primordial 2-,3- and 4-point correlators in this context. We focus on the imprints of a heavy relativistic scalar coupled to the curvature perturbation that propagates with a reduced speed of sound $c_s$, hence strongly breaking de Sitter boosts. We show that akin to the de Sitter invariant setup, primordial correlation functions can be deduced by acting with suitable weight-shifting operators on the four-point function of a conformally coupled field induced by the exchange of the massive scalar. However, this procedure requires the analytical continuation of this seed correlator beyond the physical domain implied by momentum conservation. We bootstrap this seed correlator in the extended domain from first principles, starting from the boundary equation that it satisfies due to locality. We further impose unitarity, reflected in cosmological cutting rules, and analyticity, by demanding regularity in the collinear limit of the four-point configuration, in order to find the unique solution. Equipped with this, we unveil that heavy particles that are lighter than $H/c_s$ leave smoking gun imprints in the bispectrum in the form of resonances in the squeezed limit, a phenomenon that we call the low speed collider. We characterise the overall shape of the signal as well as its unusual logarithmic mass dependence, both vividly distinct from previously identified signatures of heavy fields. (abridged)

hep-th↗

arXiv2023

Parity Violation from Emergent Non-Locality During Inflation

Parity violation in the early universe holds great promise for uncovering new physics. In particular, the primordial scalar four-point correlation function is allowed to develop a parity-violating component when massive spinning particles coupled to a helical chemical potential are present during inflation. In this paper, we explore the rich physics of such a parity-violating trispectrum in the presence of a reduced speed of sound for the Goldstone boson of broken time translations. We show that this signal can be significantly large while remaining under perturbative control, offering promising observational prospects for future cosmological surveys. In the limit of a reduced sound speed, the dynamics admits an effective non-local description organized as a time-derivative expansion. This reveals that parity violation arises due to emergent non-locality in the single-field effective theory. At leading order, this effective theory yields a compact trispectrum template, written in terms of elementary functions. We then conduct a comprehensive analysis of the kinematic dependence of this parity-violating trispectrum and reveal new features. In addition to the low-speed collider resonance, we find a new class of signals lying in the internal soft-limit of the correlator. This signal is characterized by an oscillatory pattern periodic in the momentum ratio, with a frequency determined by the speed of sound and the chemical potential, making it drastically distinct from the conventional cosmological collider signal.

hep-th↗

arXiv2023

Shapes of the Cosmological Low-Speed Collider

Massive particles produced during inflation leave specific signatures in soft limits of correlation functions of primordial fluctuations. When the Goldstone boson of broken time translations acquires a reduced speed of sound, implying that de Sitter boosts are strongly broken, we introduce a novel discovery channel to detect new physics during inflation, called the cosmological low-speed collider signal. This signal is characterised by a distinctive resonance lying in mildly-soft kinematic configurations of cosmological correlators, indicating the presence of a heavy particle, whose position enables to reconstruct its mass. We show that this resonance can be understood in terms of a non-local single field effective field theory, in which the heavy field becomes effectively non-dynamical. This theory accurately describes the full dynamics of the Goldstone boson and captures all multi-field physical effects distinct from the non-perturbative particle production leading to the conventional cosmological collider signal. As such, this theory provides a systematic and tractable way to study the imprint of massive fields on cosmological correlators. We conduct a thorough study of the low-speed collider phenomenology in the scalar bispectrum, showing that large non-Gaussianities with new shapes can be generated, in particular beyond weak mixing. We also provide a low-speed collider template for future cosmological surveys.

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↗

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↗

arXiv2021

Cutting Cosmological Correlators

The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum mechanical wavefunction of the universe. Here we ask what the imprint of quantum mechanics is on the late time observables. We show that the requirement of unitary time evolution, colloquially the conservation of probabilities, fixes the analytic structure of the wavefunction and of all the cosmological correlators it encodes. In particular, we derive in perturbation theory an infinite set of single-cut rules that generalize the Cosmological Optical Theorem and relate a certain discontinuity of any tree-level $n$-point function to that of lower-point functions. Our rules are closely related to, but distinct from the recently derived Cosmological Cutting Rules. They follow from the choice of the Bunch-Davies vacuum and a simple property of the (bulk-to-bulk) propagator and are astoundingly general: we prove that they are valid for fields with a linear dispersion relation and any mass, any integer spin and arbitrary local interactions with any number of derivatives. They also apply to general FLRW spacetimes admitting a Bunch-Davies vacuum, including de Sitter, slow-roll inflation, power-law cosmologies and even resonant oscillations in axion monodromy. We verify the single-cut rules in a number of non-trivial examples, including four massless scalars exchanging a massive scalar, as relevant for cosmological collider physics, four gravitons exchanging a graviton, and a scalar five-point function.

hep-th↗

arXiv2021

The Cosmological Optical Theorem

The unitarity of time evolution, or colloquially the conservation of probability, sits at the heart of our descriptions of fundamental interactions via quantum field theory. The implications of unitarity for scattering amplitudes are well understood, for example through the optical theorem and cutting rules. In contrast, the implications for in-in correlators in curved spacetime and the associated wavefunction of the universe, which are measured by cosmological surveys, are much less transparent. For fields of any mass in de Sitter spacetime with general local interactions, which need not be invariant under de Sitter isometries, we show that unitarity implies an infinite set of relations among the coefficients $ ψ_{n} $ of the wavefunction of the universe with $ n $ fields, which we name Cosmological Optical Theorem. For contact diagrams, our result dictates the analytic structure of $ ψ_{n} $ and strongly constrains its form. For example, any correlator with an odd number of conformally-coupled scalar fields and any number of massless scalar fields must vanish. For four-point exchange diagrams, the Cosmological Optical Theorem yields a simple and powerful relation between $ ψ_{3} $ and $ ψ_{4} $, or equivalently between the bispectrum and trispectrum. As explicit checks of this relation, we discuss the trispectrum in single-field inflation from graviton exchange and self-interactions. Moreover, we provide a detailed derivation of the relation between the total-energy pole of cosmological correlators and flat-space amplitudes. We provide analogous formulae for sub-diagram singularities. Our results constitute a new, powerful tool to bootstrap cosmological correlators.

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

Spatial Curvature at the Sound Horizon

The effect of spatial curvature on primordial perturbations is controlled by $ Ω_{K,0}/c_{s}^{2} $, where $ Ω_{K,0} $ is today's fractional density of spatial curvature and $ c_{s} $ is the speed of sound during inflation. Here we study these effects in the limit $ c_{s}\ll 1 $. First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation. This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes. Second, there are curvature corrections to primordial correlators, which are not scale invariant. We provide explicit formulae for these corrections to the power spectrum and the bispectrum to linear order in curvature in single-clock inflation. We show that the large-scale CMB anisotropies could provide interesting new constraints on these curvature effects, and therefore on $ Ω_{K,0}/c_{s}^{2} $, but it is necessary to go beyond our linear-order treatment.

astro-ph.CO↗

arXiv2019

Symmetric Scalars

We provide a complete classification of Poincaré-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called $P(X,ϕ)$ theories, in two or more spacetime dimensions. We find only three possibilities: Dirac-Born-Infeld, Cuscuton and Scaling theories. The latter two classes of actions involve an arbitrary function of the scalar field. As an application, we use the scaling symmetry to derive an infinite set of constraints on the Wilsonian coefficients of the low-energy Effective Field Theory. Furthermore, we study the extension of these results to cosmological (FLRW) and (Anti-)de Sitter spacetimes. We find in particular that the Cuscuton action has a generic set of symmetries around any background spacetime that possesses Killing vector fields, while the DBI actions have well-known analogues that we summarize explicitly.

hep-th↗

arXiv2019

Cherenkov in the Sky: Measuring the Sound Speed of Primordial Scalar Fluctuations

We consider production of additional relativistic particles coupled to the inflaton. We show that the imprints of these particles on the spectrum of primordial perturbations can be used for the direct measurement of the speed of sound of scalar perturbations, regardless of the mechanism of the production of this species. We study a model where these relativistic localized sources are decay products of heavier particles generated via a resonance mechanism. These particles emit in-phase inflaton particles which interfere constructively on the the so-called sound boom, leading to an "inflationary Cherenkov effect". The resulting shock waves lead to distinctive patterns on the temperature anisotropies of the cosmic microwave background. Moreover, we show that the model predicts unique features on the power spectrum of curvature perturbation and sizeable flattened non-gaussianity for a suitable range of parameters.

astro-ph.CO↗

arXiv2019

Solid Soft Theorems

We derive cosmological soft theorems for solids coupled to gravity. To this end, we first derive all cosmological adiabatic modes for solids, which display the interesting novelty of non-vanishing anisotropic stresses on large scales. Then, from the corresponding symmetries of the action of perturbations we compute the leading order related soft theorems using the operator product expansion. For the scalar bispectrum, we re-derive the result that Maldacena's consistency relation is recovered only upon angular averaging over the long mode direction. In addition, we find theorems for soft tensor and vector perturbations. In passing, we also clarify the derivation of these soft theorems in gauges where no residual diffeomorphisms exist.

hep-th↗

arXiv2019

Systematics of Adiabatic Modes: Flat Universes

Adiabatic modes are cosmological perturbations that are locally indistinguishable from a (large) change of coordinates. At the classical level, they provide model independent solutions. At the quantum level, they lead to soft theorems for cosmological correlators. We present a systematic derivation of adiabatic modes in spatially-flat cosmological backgrounds with asymptotically-perfect fluids. We find several new adiabatic modes including vector, time-dependent tensor and time-dependent scalar modes. The new vector and tensor modes decay with time in standard cosmologies but are the leading modes in contracting universes. We present a preliminary derivation of the related soft theorems. In passing, we discuss a distinction between classical and quantum adiabatic modes, we clarify the subtle nature of Weinberg second adiabatic mode and point out that the adiabatic nature of a perturbation is a gauge dependent statement.

astro-ph.CO↗

arXiv2017

Bubble nucleation and inflationary perturbations

In this work we study the imprints of bubble nucleation on primordial inflationary perturbations. We assume that the bubble is formed via the tunneling of a spectator field from the false vacuum of its potential to its true vacuum. We consider the configuration in which the observable CMB sphere is initially outside of the bubble. As the bubble expands, more and more regions of the exterior false vacuum, including our CMB sphere, fall into the interior of the bubble. The modes which leave the horizon during inflation at the time when the bubble wall collides with the observable CMB sphere are affected the most. The bubble wall induces non-trivial anisotropic and scale dependent corrections in the two point function of the curvature perturbation. The corrections in the curvature perturbation and the diagonal and off-diagonal elements of CMB power spectrum are estimated.

gr-qc↗