Hayden Lee

We express the scalar four-point correlator of the Q -model associated with the proposed minimal higher-spin de Sitter/Sp( N ) correspondence as an integral over the orthogonal Grassmannian OGr ( 4 , 8 ) . The full, crossing-symmetric higher-spin Grassmannian correlator is given by ( S 2 + T 2 + U 2 ) / ( S T U ) , where S , T , U are the Grassmannian Mandelstam variables. Remarkably, this has the same form as the field-theory limit of the Veneziano amplitude, despite encoding an infinite massless higher-spin tower associated with the opposite, tensionless regime. For the scalar sector considered here, the Grassmannian contour gives the full correlator, with no dispersive reconstruction required. We verify the formula by evaluating the contour integral and matching it to the complete momentum-space result, and analyze its singularities and higher-spin residues directly in Grassmannian space.

A bstract: We study momentum-space correlators in minimal higher-spin gravity in dS ₄ using its holographic vector-model description. Connected n -point functions in this model are represented by three-dimensional one-loop integrals and are rational functions of the boundary kinematics. We show that the four-point function displays a nontrivial geometric feature: its physical singularity is governed by a Ptolemy relation for the dual momentum quadrilateral. At five points, the pentagon integral introduces an apparent leading Landau singularity, which we show is spurious and disappears once the Gram constraint is imposed. We derive a representation of the five-point function free of spurious singularities and organized in terms of graph-theoretic building blocks. We then verify the conformal invariance of these correlators and discuss their behavior in the soft, collapsed, and Ptolemy limits. This structure suggests a combinatorial bootstrap for higher-spin correlators at general multiplicity, in which conformal invariance and the physical singularities emerge from the underlying graph combinatorics.

A bstract: We uncover a geometric organization of the differential equations for the wave-function coefficients of conformally coupled scalars in power-law cosmologies. To do this, we introduce a basis of functions inspired by a decomposition of the wavefunction into time-ordered components. Representing these basis functions and their singularities by graph tubings, we show that a remarkably simple rule for the merger of tubes produces the differential equations for arbitrary tree graphs (and loop integrands). We find that the basis functions can be assigned to the vertices, edges, and facets of convex geometries (in the simplest cases, collections of hypercubes) which capture the compatibility of mergers and define how the basis functions are coupled in the differential equations. This organization of functions also simplifies solving the differential equations. The merger of tubes is shown to reflect the local properties of bulk physics, in particular the collapse of time-ordered propagators. Taken together, these observations demystify the origin of the kinematic flow observed in these equations [1].

Primordial non-Gaussianities (PNGs) are imprints in the initial density field sourced by the dynamics of inflation. These dynamics can induce scale dependence, oscillations, and other features in the primordial bispectrum. We analyze a suite of over thirty PNG templates, including those used in the Planck analyses of the Cosmic Microwave Background (CMB), and resolve their signatures in the deeply nonlinear regime of the late-time density field. Using simulations, we forecast results from a lensing analysis of the Year-10 data from the Rubin Observatory Legacy Survey of Space and Time (LSST). We find that lensing achieves sensitivity comparable to the CMB for many models, and even surpasses it for templates whose features peak on smaller scales, k ≳ 0.2 h /Mpc. Many templates generate non-monotonic behaviors in mass and length scales, providing a distinct phenomenology in the resulting late-time structure. We simulate, for the first time, resonant signatures consistently in both the primordial power spectrum and bispectrum. The constraints on their amplitudes ( A _pk , f _NL ) are essentially independent, as each affects structure formation in distinct ways. Overall, we find that lensing data can provide competitive and complementary constraints on these models, and can deliver leading constraints when the primordial features are predominantly on smaller scales. The data products are publicly released as part of the Ulagam simulation suite. Our initial conditions generator is publicly available at https://github.com/DhayaaAnbajagane/Aarambam .

Primordial non-Gaussianities (PNGs) are features in the initial density field that provide a window into the nonlinear dynamics of particles during the inflationary epoch. Among them, a distinctive set of signatures from “cosmological collider physics” originates through interactions of the inflaton with heavy particles active at high energies. The amplitude and form of these signatures depend on the strength and nature of the interactions. The corresponding features in large-scale structure have been studied predominantly through the use of perturbation theory, restricted to the linear regime of the density field. In this work, we implement a method for running cosmological simulations with arbitrary bispectra signals in their initial density field, and produce a simulation suite of over thirty PNG-generating templates, resolving the corresponding collider signatures in the strongly nonlinear regime of the density field. We detail the signals in a variety of late-time measurements — the matter power spectra, matter bispectra, the halo abundance, and halo bias. We then forecast the potential constraints on the signal amplitudes using weak lensing measurements from the Year-10 dataset of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). The second and third moments of the lensing convergence field produce constraints that are competitive and complementary to those from the Cosmic Microwave Background. The data products are publicly released as part of the Ulagam simulation suite. Our initial conditions generator is also publicly available at https://github.com/DhayaaAnbajagane/Aarambam .

A bstract: The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ ³ theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic space. In this Letter, we introduce a new perspective on these differential equations. We show that, in the simplified setting of conformally coupled scalars in power-law Friedmann-Robertson-Walker spacetimes, the equations for arbitrary tree-level processes can be obtained from a small number of simple combinatorial rules. While this “kinematic flow” is defined purely in terms of boundary data, it reflects the physics of bulk time evolution. The unexpected regularity of the equations suggests the existence of an autonomously defined mathematical structure from which cosmological correlations and the time evolution of the associated spacetime emerge.

A bstract: Recently, an interesting pattern was found in the differential equations satisfied by the Feynman integrals describing tree-level correlators of conformally coupled scalars in a power-law FRW cosmology [1, 2]. It was proven that simple and universal graphical rules predict the equations for arbitrary graphs as a flow in kinematic space. In this note, we show that the same rules — with one small addition — also determine the differential equations for loop integrands. We explain that both the basis of master integrals and the singularities of the differential equations can be represented by tubings of marked graphs. An important novelty in the case of loops is that some basis functions can vanish, and we present a graphical rule to identify these vanishing functions. Taking this into account, we then demonstrate that the kinematic flow correctly predicts the differential equations for all loop integrands.

We present a classification of conformally-invariant three-point tensor structures in d dimensions that parallels the classification of three-particle scattering amplitudes in d + 1 dimensions. Using a set of canonically-normalized weight-shifting operators, we construct a basis of three-point structures involving conserved currents or stress tensors and non-conserved spinning operators, directly from their amplitude counterparts. As an application, we also examine the conformal block expansion of the four-point functions of external currents and stress tensors in this amplitude basis. Our results can be useful for conformal bootstrap applications involving spinning correlators as well as Witten diagram computations in anti-de Sitter space.