Related papers: A new nonlinear instability for scalar fields
A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing…
Using the non-canonical model of scalar field, the cosmological consequences of a pervasive, self-interacting, homogeneous and rolling scalar field are studied. In this model, the scalar field potential is nonlinear and decreases in…
We investigate SU(2) gauge theory in a constant chromomagnetic field in three dimensions both in the continuum and on the lattice. Using a variational method to stabilize the unstable modes, we evaluate the vacuum energy density in the…
We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential…
We analyse the implications of the presence of spatial curvature in modified gravity models. As it is well known, the current standard cosmological model, the $\Lambda$CDM, is assumed to be spatially flat based on the results of many…
We propose a dark energy model where a scalar field $\phi$ has nonlinear self-interactions in the presence of a dilatonic coupling with the Ricci scalar. This belongs to a sub-class of theories beyond Horndeski, which accommodates covariant…
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in $\mathbb{R}^n$ is given in terms of an infinite-dimensional dynamical system. The dynamical system is on the space of boundary data for…
New measurements of the expansion rate of the Universe have plunged the standard model of cosmology into a severe crisis. In this letter, we propose a simple resolution to the problem that relies on a first order phase transition in a dark…
The Ricci dark energy (RDE) proposed to explain the accelerating expansion of the universe requires its parameter $\alpha < 1$, whose value will determine the behavior of RDE. In this Letter, we study the scalar perturbation of RDE with and…
We apply the effective potential method to study the vacuum stability of the bounded from above $(-\phi^{6})$ (unstable) quantum field potential. The stability ($\partial E/\partial b=0)$ and the mass renormalization ($\partial^{2}…
We propose a new Dark Energy parametrization based on the dynamics of a scalar field. We use an equation of state $w=(x-1)/(x+1)$, with $x=E_k/V$, the ratio of kinetic energy $E_k=\dot\phi^2/2$ and potential $V$. The eq. of motion gives…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
We consider multidimensional gravitational models with a nonlinear scalar curvature term and form fields in the action functional. In our scenario it is assumed that the higher dimensional spacetime undergoes a spontaneous compactification…
We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
The nonlinear oscillations of a scalar field are shown to have cosmological equations of state with $w = p / \rho$ ranging from $-1 < w < 1$. We investigate the possibility that the dark energy is due to such oscillations.
We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully…
This work focuses on the regularization by nonlinear noise for a class of partial differential equations that may only have local solutions. In particular, we obtain the global existence, uniqueness and the Feller property for stochastic 3D…
We analyze in detail the quantum instability which characterizes charged scalar field on three special de Sitter charged black hole backgrounds. In particular, we compute exactly the imaginary part of the effective action for scalar charged…
We study the properties of cosmological density perturbations in a multi-component system consisting of a scalar field and a perfect fluid. We discuss the number of degrees of freedom completely describing the system, introduce a full set…