Related papers: A new nonlinear instability for scalar fields
In this paper, we study the effective field theory (EFT) of dark energy for the $k$-essence model beyond linear order. Using particle-mesh $N$-body simulations that consistently solve the dark energy evolution on a grid, we find that the…
Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the…
We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial…
In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension $d\geq1$, with a non-Lipschitz coefficient noisy term. The equation…
We consider SU(2) gauge theory with a scalar field in the fundamental representation. The model is known to contain electric field solutions sourced by the scalar field that are distinct from embedded Maxwell electric fields. We examine the…
It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial derivative of the state. This higher spatial derivative (termed…
In this note cosmological models coming out of the String Field Theory (SFT) in application to the Dark Energy are reviewed. A way of constructing solutions in the case of linear models is outlined, cosmological perturbations and…
We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar…
We consider theories with a nontrivial coupling between the matter and dark energy sectors. We describe a small scale instability that can occur in such models when the coupling is strong compared to gravity, generalizing and correcting…
The space-time of the Universe has been perturbed under a scalar field $\phi$ considering the minimum coupling between {\phi} and the background metric. The solutions of Einstein field equations have been obtained under perturbed geometry…
A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to…
Starting from the equation of motion of the quantum operator of a real scalar field phi in de Sitter space-time, a simple differential equation is derived which describes the evolution of quantum fluctuations <phi^2> of this field. Full de…
Recently, a new interesting instability of a charged scalar field in the Reissner-Nordstr\"om-de Sitter background has been found (arXiv:1405.4931v2) through the time-domain integration of the perturbation equation. We investigate further…
We discuss spacetime instability for effective field theories of quantum gravity. The effective action of gravity introduces infinite higher derivative curvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu }, R_{\mu\nu\kappa\lambda}…
We consider a non-linear parabolic partial differential equation (PDE) on $\mathbb R^d$ with a distributional coefficient in the non-linear term. The distribution is an element of a Besov space with negative regularity and the non-linearity…
We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory(EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
We develop the effective field theory (EFT) of perturbations in the context of scalar-tensor theories with a spacelike scalar profile on arbitrary black hole backgrounds. Our construction of the EFT is based on the fact that in the unitary…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…