Related papers: Canonical Differential Equations for Cosmology fro…
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…
The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
We provide a first principle definition of cosmological correlation functions for a large class of scalar toy models in arbitrary FRW cosmologies, in terms of novel geometries we name {\it weighted cosmological polytopes}. Each of these…
We show that the wavefunction of the universe in theories of conformally coupled scalars in power-law Friedmann-Robertson-Walker (FRW) cosmologies satisfies a graphical coaction, by means of which we can understand its complete analytic…
We present a connection between the physics of cosmological time evolution and the mathematics of positive geometries, roughly analogous to similar connections seen in the context of scattering amplitudes. We consider the wavefunction of…
The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast into an iterative differential system of basis functions. These functions can be encoded within…
In this paper we explore the mathematical properties of wavefunction coefficients in power-law FRW cosmologies, and establish their relation to cluster algebras. We focus on the particular contributions to the wavefunction coefficient…
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…
Feynman integrals whose associated geometries extend beyond the Riemann sphere, such as elliptic curves and Calabi-Yau varieties, are increasingly relevant in modern precision calculations. They arise not only in collider cross-section…
Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent…
The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic…
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…
Recently considerable efforts have been devoted to computing cosmological correlators and the corresponding wavefunction coefficients, as well as understanding their analytical structures. In this note, we revisit the computation of these…
We study the coaction of cosmological wavefunction coefficients of conformally coupled scalars in FRW background of a two-site example, which turns out to have an elegant diagrammatic interpretation. We show how the coaction acts on the…
A number of diagrammatic "cutting rules" have recently been developed for the wavefunction of the Universe which determines cosmological correlation functions. These leverage perturbative unitarity to relate particular "discontinuities" in…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the…
As a point of departure it is suggested that Quantum Cosmology is a topological concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological…