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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…
The Hopf algebra of undecorated rooted trees has tamed the combinatorics of perturbative contributions, to anomalous dimensions in Yukawa theory and scalar $\phi^3$ theory, from all nestings and chainings of a primitive self-energy…
We derive a second-order differential equation for the two-loop sunrise graph in two dimensions with arbitrary masses. The differential equation is obtained by viewing the Feynman integral as a period of a variation of a mixed Hodge…
We propose a cosmological model which could explain, in a very natural way, the apparently periodic structures of the universe, as revealed in a series of recent observations. Our point of view is to reduce the cosmological…
In this work, we investigate how cosmological correlators can be reconstructed by applying the momentum-space dispersion formula to their discontinuities, treating them as functions of momentum variables associated with the corresponding de…
We study the most general cosmological model with real scalar field which is minimally coupled to gravity. Our calculations are based on Friedmann-Lemaitre-Robertson-Walker (FLRW) background metric. Field equations consist of three…
Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat…
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…
We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a $\Lambda$CDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
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…
Cosmological correlators are fundamental observables in an expanding universe and are highly non-trivial functions even at tree-level. In this work, we uncover novel structures in the space of such tree-level correlators that enable us to…
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…
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
We investigate the embedding formalism in conjunction with the Mellin transform to determine tree-level gluon amplitudes in AdS/CFT. Detailed computations of three to five-point correlators are conducted, ultimately distilling what were…
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order…
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…
Different approaches to quantum gravity, such as loop quantum cosmology and group field theory, predict the resolution of the initial cosmological singularity via a bounce: a regular spacetime region that connects the expanding branch of…
Recently, Chamseddine and Mukhanov introduced a higher-derivative scalar-tensor theory which leads to a modified Friedmann equation allowing for bouncing solutions. As we note in the present work, this Friedmann equation turns out to…
Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly…