Related papers: The method of generating functions in exact scalar…
The solution generating methods discovered earlier for integrable reductions of Einstein's and Einstein - Maxwell field equations (such as soliton generating techniques, B$\ddot{a}$cklund or symmetry transformations and other…
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…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
We derive a new parametric class of exact cosmological solutions to Brans-Dicke theory of gravity with a self-interacting scalar field and a barotropic perfect fluid of ordinary matter, by assuming a linear relationship between the Hubble…
We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations.…
In this paper, we study how to construct f(R) gravity models. Cosmological observations and local gravity tests imply that a viable f(R) model should be very close to the LCDM model. We create procedures to construct viable LCDM-like f(R)…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
We solve isotropic, homogeneous cosmological models containing a self-interacting scalar field. Calculations are performed in four and two-dimensional spacetimes. We find several exact solutions that have an inflationary regime or has a…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
The future astronomical imaging surveys are set to provide precise constraints on cosmological parameters, such as dark energy. However, production of synthetic data for these surveys, to test and validate analysis methods, suffers from a…
We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar…
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We discuss a method of calculating the key cosmological parameters on the basis of a selected scale factor by using exact solutions of the background equations. We specify the formulas for calculating the power spectrum, the spectral…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.
A dark energy model with a phantom scalar field, an usual scalar field and the string field theory inspired polynomial potential has been constructed. A two-parameter set of exact solutions to the Friedmann equations has been found. We have…
New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar…
A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a…
By using the gravitational decoupling through the minimal geometric deformation approach (MGD-decoupling), we show a simple and powerful method to generate physically acceptable exact analytical solutions for anisotropic stellar…