Related papers: A Tree Theorem for Inflation
During inflationary preheating, the energy stored in the inflaton field is rapidly converted into excitations of other entropy fields. This stage is characterized by exponential particle production due to parametric resonance and is…
The classical evolution and the quantum generation processes of the scalar- and tensor-type cosmological perturbations in the context of a broad class of generalized gravity theories are presented in unified forms. The exact forms of final…
In this work, we investigate the possibility of generating an inflationary mechanism within the framework of a metric-$f(R)$ modified gravity theory, formulated in the Jordan frame. We explore whether the scalar field, non-minimally coupled…
In this article we will show that the Macro-Economy and its growth can be modelled and explained exactly in principle by commonly known Field Theory from theoretical physics. We will show the main concepts and calculations needed and show…
Conditions are obtained for the existence of a warm inflationary attractor in the system of equations describing an inflaton coupled to radiation. These conditions restrict the temperature dependence of the dissipative terms and the size of…
We present a method for solving loop integrals in dimensional regularization that is particularly useful in the context of inflation. We apply this method to the calculation of the tensor power spectrum induced by scalar fluctuations in…
We consider the spectrum of primordial fluctuations produced by inflationary models where the inflaton potential is the sum of two exponential terms. A wide range of spectra result, with the only constraint being that the scalar spectrum…
We present an elementary proof of a generalization of Kirchoff's matrix tree theorem to directed, weighted graphs. The proof is based on a specific factorization of the Laplacian matrices associated to the graphs, which only involves the…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
We consider small-field models which invoke the usual framework for the effective field theory, and large-field models which go beyond that. Present and future possibilities for discriminating between the models are assessed, on the…
We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that they are solved by weighted generating…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the Color Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman…
We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model…
We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of…
Pseudo-Goldstone bosons (pGBs) can provide technically natural inflatons, as has been comparatively well-explored in the simplest axion examples. Although inflationary success requires trans-Planckian decay constants, f > Mp, several…
In the present paper, we study the non-Gaussianity of multiple-field inflation model using the method of the field equation. We start from reviewing the background and the perturbation theory of multiple-field inflation, and then derive the…
Inflation driven by a single, minimally coupled, slowly rolling field generically yields a negligible primordial non-Gaussianity. We discuss two distinct mechanisms by which a non-trivial potential can generate large non-Gaussianities.…
In this paper, we study several issues in the linear equation-of-motion (EoM) and in-in approaches of computing the two-point correlation functions in multi-field inflation. We prove the equivalence between this EoM approach and the…