[工程科技]SolvingtheProblemofTimeinGeneralRelativityandCosmologywithPhantomsandk--Esse.pdf

Solving the Problem of Time in General Relativity and Cosmology with Phantoms and k – Essence T. Thiemann∗ 6 0 0 2 MPI f. Gravitationsphysik, Albert-Einstein-Institut, l Am M¨uhlenberg 1, 14476 Potsdam, Germany u J 7 1 and 1 v Perimeter Institute for Theoretical Physics, 0 8 31 Caroline Street N, Waterloo, ON N2L 2Y5, Canada 3 7 0 Preprint AEI-2006-056 6 0 / h p - Abstract o r t We show that if the Lagrangean for a scalar field coupled to General Relativity only contains s a derivatives, then it is possible to completely deparametrise the theory. This means that : 1. Physical observables, i.e. functions which Poisson commute with the spatial diffeomorphism and v i Hamiltonian constraints of General Relativity, can be easily constructed. X 2. The physical time evolution of those observables is generated by a natural physical Hamiltonian r a which is (constrained to be) positive. The mechanism by which this works is due to Brown and Kuchaˇr. In order that the physical Hamiltonian is close to the Hamiltonian of the standard model and the one used in cosmology, the required Lagrangean must be that of a Dirac – Born – Infeld type. Such matter has been indepen- dently introduced previously by cosmologists in the context of k – essence due to Armendariz-Picon, Mukhanov and Steinhardt in order to solve the cosmological coincidence (dark energy) problem. We arrive at it by totally unrelated physical considerations originating fro