Related papers: Evolution systems for non-linear perturbations of …
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
We explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a…
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the…
Evolution of primordial fluctuations in a Brans-Dicke type scalar-tensor gravity theory is comprehensively investigated. The harmonic attractor model, in which the scalar field has its harmonic effective potential in the Einstein conformal…
In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in…
The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are simplified and adapted for numerical relativity. We show that the evolution equations as partial differential equations for the Ricci rotation…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
The theoretical description of materials' properties driven out of equilibrium has important consequences in various fields such as semiconductor spintronics, nonlinear optics, continuous and discrete quantum information science and…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
In this paper we propose that the accelerating expansion of the present matter-dominated universe, as suggested by the recent distance measurements of type Ia supernovae, is generated along with the evolution of space in extra dimensions.…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework…
In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as…
Parity-odd four-point correlation functions, or trispectra, of cosmic matter density fields provide a unique probe of fundamental symmetries in cosmology. Trispectra of primordial matter density fluctuations produced in the early universe…
We consider the formation of trapped surfaces in the evolution of the Einstein-scalar field system without symmetries. To this end, we follow An's strategy to analyse the formation of trapped surfaces in vacuum and for the Einstein-Maxwell…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their…
For an arbitrary strong, spherically symmetric super-horizon curvature perturbation, we present analytical solutions of the Einstein equations in terms of asymptotic expansion over the ratio of the Hubble radius to the length-scale of the…