Related papers: A Tree Theorem for Inflation

A new model for inflation using modified gravity in the Palatini formalism is constructed. Here non-minimal coupling of scalar field h with the curvature R as a general function f(R,h) is considered. Explicit inflation models for some…

We study the possibility that inflation is driven by a scalar field together with a vector field minimally coupled to gravity. By assuming an effective potential that incorporates both fields into the action, we explore two distinct…

Inflation is now a basic ingredient of the modern cosmology. After reviewing the basic characteristics of inflation, we briefly discuss inflation in string and brane theories, focusing on the problem of the exit from inflation in these…

Seemingly unrelated models of inflation that originate from different physical setups yield, in some cases, identical predictions for the currently constrained inflationary observables. In order to classify the available models, we propose…

An energetic justification of a thermal component during inflation is given. The thermal component can act as a heat reservoir which induces thermal fluctuations on the inflaton field system. We showed previously that such thermal…

Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained.…

The article provides an explicit algebraic expression for the generating function of walks on graphs. Its proof is based on the scattering theory for the differential Laplace operator on non-compact graphs.

We propose a model of inflation in the framework of brane cosmology driven by background supergravity. Starting from bulk supergravity we construct the inflaton potential on the brane and employ it to investigate for the consequences to…

The paper describes an explicit combinatorial formula for a harmonic vector for the Laplacian of a directed graph with arbitrary edge weights. This result was motivated by questions from mathematical economics, and the formula plays a…

The solution of the classical field equation generates the sum of all tree graphs. We show that the classical equation reduces to an easily solved ordinary differential equation for certain multiparticle threshold amplitudes and compute…

We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help…

Whichever could be the real theory of gravitation, the corresponding low-energy effective lagrangian will probably contain higher derivative terms. In this work we study the general conditions on those terms in order to produce enough…

We calculate the tree-level bispectrum of the inflaton field perturbation directly from the field equations, and construct the corresponding f_NL parameter. Our results agree with previous ones derived from the Lagrangian. We argue that…

We examine a scalar-tensor model of gravity that is globally scale-invariant. When adapted to a spatially flat Robertson-Walker metric, the equations of motion describe a dynamical system that flows from an unstable de Sitter space to a…

We study the possibility that inflation is driven by a massive vector field with SO(3) global symmetry nonminimally coupled to gravity. From an E^3-invariant Robertson-Walker metric we propose an Ansatz for the vector field, allowing us to…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…

A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous group $G$ and a discrete…

Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…

An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…