Related papers: Differential Equations for Massive Correlators
The basic observables in cosmology are known as in-in correlators. Recent calculations have revealed that in-in correlators in four dimensional de Sitter space exhibit hidden simplicity stemming from a close relation to scattering…
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…
We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential…
The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…
In this paper, we elaborate on the connection between leading singularities and canonical bases of Feynman integrals beyond polylogarithms. We start by discussing a notion of leading singularities in dimensional regularization, which can be…
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…
We present a systematic method for computing cosmological amplitudes, including in-in correlators and wavefunction coefficients, in FRW spacetime. Specializing to cases with conformally-coupled external scalars and massive scalar exchanges,…
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…
Observables in expanding universes are crucial to understand the physics of the early universe. In these lectures, we review some recent progress in understanding their mathematical structure and extract the physics encoded in them. After…
This paper is dedicated to scrutinizing the cosmology in massive gravity. A matter field of the dark sector is coupled to an effective composite metric while a standard matter field couples to the dynamical metric in the usual way. For this…
The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
We study a surprising phenomenon in which Feynman integrals in $D=4-2\varepsilon$ space-time dimensions as $\varepsilon \to 0$ can be fully characterized by their behavior in the opposite limit, $\varepsilon \to \infty$. More concretely, we…
An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…
An intrinsic time of homogeneous models is global. The Friedmann equation by its sense ties time intervals. Exact solutions of the Friedmann equation in Standard cosmology and Conformal cosmology are presented. Theoretical curves…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
Correlators of large-scale fluctuations produced during cosmic inflation are major observables of inflationary cosmology. In cosmological collider physics, many interesting correlators are generated through loop processes. However,…
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 problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central…
The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial / topological argument. These functions are then extended into a larger family of…