Related papers: A Tree Theorem for Inflation

We perform the analysis of the trispectrum of curvature perturbations generated by the interactions characterizing a general theory of single-field inflation obtained by effective field theory methods. We find that curvature-generated…

A specific scale factor in Robertson-Walker metric with the prospect of giving the overall cosmic history in a unified picture roughly is considered. The corresponding energy-momentum tensor is identified as that of two scalar fields where…

The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact…

We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general…

Thermal field theory is applied to particle production rates in inflationary models, leading to new results for catalysed, or two-stage decay, where massive fields act as decay channels for the production of light fields. A numerical…

We present a version of the matrix-tree theorem, which relates the determinant of a matrix to sums of weights of arborescences of its directed graph representation. Our treatment allows for non-zero column sums in the parent matrix by…

This is a version of the author's Ph.D. thesis. The methods of effective field theory are used to study generic theories of inflation with a single inflaton field and to perform a general analysis of the associated non-Gaussianities. We…

Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified as the expectation value of a quantum field, evolving in a quantum effective potential.…

We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop…

We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the…

We study the height of a spanning tree $T$ of a graph $G$ obtained by starting with a single vertex of $G$ and repeatedly selecting, uniformly at random, an edge of $G$ with exactly one endpoint in $T$ and adding this edge to $T$.

Let $T$ be a tree on $n$ vertices. We can regard the edges of $T$ as transpositions of the vertex set; their product (in any order) is a cyclic permutation. All possible cyclic permutations arise (each exactly once) if and only if the tree…

It is well-known that the number of spanning trees, denoted by $\tau(G)$, in a connected multi-graph $G$ can be calculated by the Matrix-Tree theorem and Tutte's deletion-contraction theorem. In this short note, we find an alternate method…

We present Feynman type diagrams for calculating the n-point function of the primordial curvature perturbation in terms of scalar field perturbations during inflation. The diagrams can be used to evaluate the corresponding terms in the…

In construction of an inflationary model, one usually assumes that the matter sector of the gravitational action is minimally coupled to the background. It means that the matter (inflaton) part of the action is coupled with the same metric…

Using the matrix-forest theorem and the Parisi-Sourlas trick we formulate and solve a one-matrix model with non-polynomial potential which provides perturbation theory for massive spinless fermions on dynamical planar graphs. This is a…

We consider the correlation function of an arbitrary number of local observables in quantum field theory. We show that, at tree level in the strong field regime, these correlations arise solely from fluctuations in the initial state. We…

We give a generic argument that string theory provides a natural setting for warm inflationary cosmology. We then explore a specific model with an inflaton modulus field coupled to fields that provide the continuous dissipation needed for…

The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…

We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…