About the Cauchy problem in Stelle's quadratic gravity

About One Sweep Algorithm for Solving Linear-Quadratic Optimization Problem with Unseparated Two-Point Boundary Conditions

In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new sweep algorithm which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimi...

The Cauchy Problem for Membranes

We show existence and uniqueness for timelike minimal submanifolds (world volume of p-branes) in ambient Lorentz manifolds admitting a time function in a neighborhood of the initial submanifold. The initial value formulation introduced and the conditions imposed on the initial data are given in purely geometric terms. Only an initial direction must be prescribed in order to provide uniqueness f...

Inhomogeneous Two-Parameter Abstract Cauchy Problem

20 09 Reply to ‘ A comment on ‘ The Cauchy problem of f ( R ) gravity ”

We reply to a comment by Capozziello and Vignolo about the Cauchy problem of Palatini f(R) gravity. PACS numbers: 04.50.+h, 04.20.Ex, 04.20.Cv, 02.30.Jr In [1] Capozziello and Vignolo comment on Ref. [3], which discusses the Cauchy problem of metric and Palatini f(R) gravity (see also [2]). The contentious issue is Palatini f(R) gravity in vacuo. Ref. [3] reduces the initial value problem of bo...

Quantum Cauchy problem in cosmology

We develop a general framework for effective equations of expectation values in quantum cosmology and pose for them the quantum Cauchy problem with no-boundary and tunneling wavefunctions. We apply this framework in the model with a big negative non-minimal coupling, which incorporates a recently proposed low energy (GUT scale) mechanism of the quantum origin of the inflationary Universe and st...