Related papers: A Tree Theorem for Inflation
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
Using a generating function approach, the correlation coefficients of four different graph-theoretical indices, namely the number of independent vertex subsets, the number of matchings, the number of subtrees and the Wiener index, are…
The most general tree-level boundary correlation functions of quantum fields in inflationary spacetime involve multiple exchanges of massive states in the bulk, which are technically difficult to compute due to the multi-layer nested time…
Recently we introduced an inflationary setup in which the inflaton fields are matrix valued scalar fields with a generic quartic potential, M-flation. In this work we study the landscape of various inflationary models arising from…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the…
We show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of…
The methods of effective field theory are used to study generic theories of inflation with a single inflaton field. For scalar modes, the leading corrections to the ${\cal R}$ correlation function are found to be purely of the $k$-inflation…
We provide a new representation of an $\mathbb R$-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between the $\mathbb R$-trees with radial and river…
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…
Using the theoretical basis developed by Yao and Zeilberger, we consider certain graph families whose structure results in a rational generating function for sequences related to spanning tree enumeration. Said families are Powers of Cycles…
Given a graph, we can form a spanning forest by first sorting the edges in some order, and then only keep edges incident to a vertex which is not incident to any previous edge. The resulting forest is dependent on the ordering of the edges,…
We apply symbolic method to deduce functional equation which generating function of counting sequence of dependency trees must satisfy. Then we use Lagrange inversion theorem to obtain concrete expression of the counting sequence. We apply…
A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields -…
We discuss a recursive formula for number of spanning trees in a graph. The paper is written primary for school students.
We propose a new approach for calculating the curvature perturbations produced during inflation in the stochastic formalism. In our formalism, the fluctuations of the e-foldings are directly calculated without perturbatively expanding the…
We explore a new possibility that some inflaton fields in multi-field inflation models satisfy the observed value of the spectral index so that the curvature perturbation generated by them through post-inflationary dynamics may be relevant…
The delta-N formalism is considered to calculate the evolution of the curvature perturbation in generalized multi-field inflation models. The result is consistent with the usual calculation of the standard kinetic term. For the calculation…
The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses…
Inflation offers a simple model for very early evolution of our Universe and the origin of primordial perturbations on large scales. Over the last 25 years we have become familiar with the predictions of single-field models, but inflation…