Related papers: Operator Method and Recursion Relations for Inflat…
We expand the Einstein-Hilbert action with a positive cosmological constant up to the fourth order in terms of gravity fluctuations, and then use the in-in formalism to calculate the four-point correlation function for gravitational waves,…
The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce…
Attractor inflation is a particularly robust framework for developing inflationary models that are insensitive to the details of the potential. Such models are most often considered in the metric formulation of gravity. However, non-minimal…
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification…
In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach…
We discuss a new class of identities between correlation functions which arise from a local Z_2 invariance of the partition function of the q-state Potts model on general graphs or lattices. Their common feature is to relate the thermal…
We compute all string tree level correlation functions of vertex operators in $c<1$ string theory. This is done by using the ring structure of the theory. In order to study the multicritical behaviour, we calculate the correlation functions…
We calculate and investigate the relativistic correlation function for bipartite systems of spin-1/2 in vector and spin-1 particles in tensor states. We show that the relativistic correlation function, which depends on particles momenta,…
The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to…
Given a simple recursive function, we show how to extract from it a reversible and an classical iterative part. Those parts can synchronously cooperate under a Producer/Consumer pattern in order to implement the original recursive function.…
We present a new general construction of recursion operator from zero curvature representation. Using it, we find a recursion operator for the stationary Nizhnik--Veselov--Novikov equation and present a few low order symmetries generated…
We derive an extension of the quantum regression theorem to calculate out-of-time-order correlation functions in Markovian open quantum systems. While so far mostly being applied in the analysis of many-body physics, we demonstrate that…
CppTransport is a numerical platform that can automatically generate and solve the evolution equations for the 2- and 3-point correlation functions (in field space and for the curvature perturbation) for any inflationary model with…
The concept of time correlation functions is a very convenient theoretical tool in describing relaxation processes in multiparticle systems because, on one hand, correlation functions are directly related to experimentally measured…
A brief review of inflation is presented. After having demonstrated the generality of the inflationary mechanism, the emphasize is put on its simplest realization, namely the single field slow-roll inflationary scenario. Then, it is shown…
We introduce a simple model for addressing the controversy in the study of financial systems, sometimes taken as brownian-like processes and other as critical systems with fluctuations of arbitrary magnitude. The model considers a…
We have studied inflationary paradigm through an inflationary equation of state. With a single parameter equation of state as a function of the scalar field responsible for accelerated expansion, we find an observationally viable model…
The inflationary mechanism of mode amplification predicts that the state of each mode with a given wave vector is correlated to that of its partner mode with the opposite vector. This implies nonlocal correlations which leave their imprint…
We present a method to analytically compute the quantum corrected two-point correlation function of a scalar field in leading order at each loop in a homogeneous, isotropic and spatially flat spacetime where the expansion rate is time…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…