相关论文: The method of generating functions in exact scalar…
We propose a novel, potentially useful generating technique for constructing exact solutions of inflationary scalar field cosmologies with non-trivial potentials. The generating scheme uses the so-called superpotential and is inspired by…
The new classes of homogeneous cosmological models for the scalar fields are build in the context of Lyra's geometry. The different types of exact solution for the model are obtained by applying two procedures, viz the generating function…
We construct the $F(R)$ gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The functions $F(R)$ are obtained explicitly. We…
Exact cosmological models for a scalar field in Lyra geometry are studied in the presence of a time-varying effective cosmological term originated from the specific interaction of an auxiliary $\Lambda$ - term with the displacement vector.…
We investigate a mechanism that generates the exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover allmost all known solutions, and allows one to derive new solutions as well. In…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
A homogeneous and isotropic model of the Universe is considered in the framework of the five-dimensional Projective Unified Field Theory in which the gravitation is described by both space-time curvature and some hypothetical scalar field…
We study the cosmological model based on Einstein-Gauss-Bonnet gravity with non-minimal coupling of a scalar field to a Gauss-Bonnet term in 4D Friedmann universe. We show how constructing the exact solutions by the method based on a…
A simple algebraic method to obtain exact solutions to the scalar field equations in spatially flat FRW cosmology is derived. The field potential fuction is reduced to two terms which can be used to determine some characteristic…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
The superpotential method is a reconstruction technique which has proven useful to build exact cosmological solutions. We here employ the superpotential method in order to reconstruct the features necessary for the inflaton potential to…
We propose a new reconstruction method for scalar--tensor gravity based on the use of conformal transformations. The new method allows the derivation of a set of interesting exact cosmological solutions in brans Dicke gravity as well as…
We present a method for generating exact diagonal $G_2$-cosmological solutions in dilaton gravity coupled to a radiation perfect fluid and with a cosmological potential of a special type. The method is based on the symmetry group of the…
An exact scalar field cosmological model is constructed from the exact solution of the field equations. The solutions are exact and no approximation like slow roll is used. The model gives inflation, solves horizon and flatness problems.…
This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function…
We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs…
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…
We employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the…
In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…
In this paper, we first describe how to find the generating function for the sum of the areas under generalized Dyck paths (with an arbitrary set of steps) using Motzkin paths as a motivating example. We then focus on Motzkin and Dyck…