Related papers: Differential equations and recursive solutions for…
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 correlators of large-scale fluctuations belong to the most important observables in modern cosmology. Recently, there have been considerable efforts in analytically understanding the cosmological correlators and the related wavefunction…
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…
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…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
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,…
It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…
We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by parts identities, (relative) twisted cohomology and the method…
The time-ordered multilayer integrals have long been cited as major challenges in the analytical study of cosmological correlators and wavefunction coefficients. The recently proposed family tree decomposition technique solved these time…
Primordial perturbations in our universe are believed to have a quantum origin, and can be described by the wavefunction of the universe (or equivalently, cosmological correlators). It follows that these observables must carry the imprint…
Cosmological correlation functions are central observables in modern cosmology, as they encode properties of the early universe. In this paper, we derive novel canonical differential equations for wavefunction coefficients in power-law FRW…
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…
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…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
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…
Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties,…
In this work we perform a systematic study of the singularity structure of inflationary correlations at 1-loop. We explicitly compute a few diagrams and find a pattern emerging in the singularities produced. Motivated by this, we derive…
We introduce the theory of non-linear cosmological perturbations using the correspondence limit of the Schr\"odinger equation. The resulting formalism is equivalent to using the collisionless Boltzman (or Vlasov) equations which remain…
We derive discontinuity relations, also known as cutting rules, and explore the analytic properties of cosmological correlators, fundamental observables of the primordial universe. Our emphasis is on how these relations arise from unitarity…
Cosmological correlators are very important objects in cosmology as they offer us a huge amount of information of the early universe. They reside on the future boundary of a de Sitter space and can be calculated by two methods. First method…