Nonlocal gravity and the diffusion equation

We propose a nonlocal scalar-tensor model of gravity with pseudodifferential operators inspired by the effective action of p-adic string and string field theory on flat spacetime. An infinite number of derivatives act both on the metric and scalar field sector. The system is localized via the diffusion equation approach and its cosmology is studied. We find several exact dynamical solutions, also in the presence of a barotropic fluid, which are stationary in the diffusion flow. In particular, and contrary to standard general relativity, there exist solutions with exponential and power-law scale factor also in an open universe, as well as solutions with sudden future singularities or a bounce. Also, from the point of view of quantum field theory, spontaneous symmetry breaking can be naturally realized in the class of actions we consider.Comment: 18 pages, 5 figures. v2: typos corrected, references added. Major changes are an expansion of the discussion of homogeneous perturbations and the inclusion of cosmological fluids in the dynamic

Qualitative Approach to Semi-Classical Loop Quantum Cosmology

Recently the mechanism was found which allows avoidance of the cosmological singularity within the semi-classical formulation of Loop Quantum Gravity. Numerical studies show that the presence of self-interaction potential of the scalar field allows generation of initial conditions for successful slow-roll inflation. In this paper qualitative analysis of dynamical system, corresponding to cosmological equations of Loop Quantum Gravity is performed. The conclusion on singularity avoidance in positively curved cosmological models is confirmed. Two cases are considered, the massless (with flat potential) and massive scalar field. Explanation of initial conditions generation for inflation in models with massive scalar field is given. The bounce is discussed in models with zero spatial curvature and negative potentials.Comment: Online at http://www.iop.org/EJ/abstract/1475-7516/2004/07/01

Stable Spin Precession at one Half of Equilibrium Magnetization in Superfluid 3He-B

New stable modes of spin precession have been observed in superfluid 3He-B. These dynamical order parameter states include precession with a magnetization S=pS_{eq} which is different from the equilibrium value S_{eq}. We have identified modes with p=1, 1/2 and \approx 0. The p=1/2 mode is the second member of phase correlated states of a spin superfluid. The new states can be excited in the temperature range 1-T/T_c \lesssim 0.02 where the energy barriers between the different local minima of the spin-orbit energy are small. They are stable in CW NMR due to low dissipation close to T_c.Comment: submitted to Physical Review Letters, 4 pages, revtex, 4 Figures in ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-96005.p