相关论文: Norm-inflation results for the BBM equation

We study numerically the inhomogeneous pre-big-bang inflation in a spherically symmetric space-time. We find that a large initial inhomogeneity suppresses the onset of the pre-big-bang inflation. We also find that even if the pre-big-bang…

We analyze the onset of inflation for a simple single-field model when the system begins with significant inhomogeneities on length-scales shorter than the initial Hubble radius. We incorporate certain nonlinear interactions among the…

We study inflation driven by a scalar potential arising from composite-sector dynamics, inspired by generalized composite Higgs models. The introduction of a non-minimal coupling, possessing the same functional form as the potential,…

We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo…

The initial value problem $u(x,y,0)=u_0(x,y)$ for the Novikov-Veselov equation $$\partial_tu+(\partial ^3 + \overline{\partial}^3)u +3(\partial (u\overline{\partial}^{-1}\partial…

The pre-big bang scenario describes the evolution of the Universe from an initial state approaching the flat, cold, empty, string perturbative vacuum. The choice of such an initial state is suggested by the present state of our Universe if…

In the early Universe matter can be described as a conformal invariant ultra-relativistic perfect fluid, which does not contribute, on classical level, to the evolution of the isotropic and homogeneous metric. If we suppose that there is…

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient…

We consider the Cauchy problem of the nonlinear heat equation $u_t -\Delta u= u^{b},\ u(0,x)=u_0$, with $b\geq 2$ and $b\in \mathbb{N}$. We prove that initial data $u_0\in \mathcal{S}(\mathbb{R}^{n})$ (the Schwartz class)arbitrarily small…

We present a rigorous and comprehensive investigation of a generalized inflationary perturbation theory designed to address persistent large-scale anomalies in the Cosmic Microwave Background (CMB). Motivated by the Trans-Planckian problem…

We consider the nonlinear Schr\"odinger equation $iu_t + \Delta u= \lambda |u|^{\frac {2} {N}} u $ in all dimensions $N\ge 1$, where $\lambda \in {\mathbb C}$ and $\Im \lambda \le 0$. We construct a class of initial values for which the…

In this paper, we investigate the minimization problem : $$ \inf_{ \displaystyle{\begin{array}{lll} u \in H_0^1(\Omega), v \in H_0^1(\Omega),\\ \quad \| u \|_{L^{q}} =1, \quad \| v \|_{L^{q}} = 1 \end{array}}} \left[ \frac{1}{2}…

Inflation provides a suitable environment for the formation of Primordial Black Holes(PBHs). In this article, we examine the formation of primordial black holes in the Mutated Hilltop inflation model coupled with the Einstein-Gauss-Bonnet…

We study the three-dimensional cubic nonlinear wave equation (NLW) with random initial data below $L^2(\mathbb{T}^3)$. By considering the second order expansion in terms of the random linear solution, we prove almost sure local…

We revisit the local well-posedness theory of nonlinear Schr\"odinger and wave equations in Sobolev spaces $H^s$ and $\dot{H}^s$, $0< s\leq 1$. The theory has been well established over the past few decades under Sobolev initial data…

Understanding how a field theory propagates the information contained in a given initial state is essential for quantifying the sensitivity of the cosmic microwave background to physics above the Hubble scale during inflation. Here we…

The parameter space for A-term inflation is explored with $W=\lambda_p \phi^p/(p M_P^{p-3})$. With p=6 and \lambda_p~1, the observed spectrum and spectral tilt can be obtained with soft mass of order 10^2 GeV but not with a much higher…

We prove the existence of global solutions to the energy-supercritical wave equation in R^{3+1} u_{tt}-\Delta u + |u|^N u = 0, u(0) = u_0, u_t(0) = u_1, 4<N<\infty, for a large class of radially symmetric finite-energy initial data.…

In the very early Universe the matter may be described by the free radiation, that is by the set of massless fields with negligible interactions between them. Then the dominating quantum effect is the trace anomaly which comes from the…

Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured…