Quantum gravity corrections to the matter dynamics in the presence of a reference fluid

Abstract

We analyze the effect induced on standard quantum field theory (in a functional approach) by quantum gravity corrections to a pure classical background. In the framework of the Kuchař and Torre proposal for a gravity-matter theory constrained to a Gaussian reference frame, materialized as a fluid in the system evolution, we consider a Born-Oppenheimer separation of the system, regarding the gravity degrees of freedom as the slow varying component and the matter plus the Gaussian fluid as fast quantum coordinates. The slow gravity component obeys the Wheeler-DeWitt equation, and we consider a Wentzel-Kramer-Brillouin expansion of its quantum dynamics via a Planckian parameter. The main issue of the proposed scenario is that, on one hand, we recover a modified quantum field theory in the presence of a Hermitian Hamiltonian (not affected by nonunitarity as in other approaches) and, on the other hand, we get the Gaussian fluid as a physical clock for such an amended quantum theory (verifying the correct energy conditions). We also show its equivalence with the kinematical action method, used in a previous work, in the homogeneous setting. Then, we implement the proposed paradigm to describe the dynamics of a homogeneous free massless scalar field, living on an isotropic universe, in the presence of a cosmological constant. We completely solve the dynamics up to the first order correction in the Planckian parameter to the standard quantum field theory. We determine the explicit form of the modified scalar field wave function, due to quantum features of the cosmic scale factor evolution. Phenomenological considerations and discussions are provided.

Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group

“…Furthermore, it was shown that the cases (g + = 1, g − = 0) and (g + = 0, g − = 1) correspond to an extension of general relativity that includes solutions corresponding to an additional effective pressureless perfect fluid matter source. Interestingly, such a matter source has been of prior interest as a possible solution to the problem of time in quantum gravity [25,27,[30][31][32]. We find it encouraging that in the present models, the perfect fluid arises 'naturally' from the theory and does not have to be independently posited.…”

“…When the fields are complexified, they become genuinely independent objects. Equation (31) defines the property of selfdualness (here F +IJ ) or anti-self-dualness (here F −IJ ). It is possible to parameterize a self-dual or anti-self-dual Lorentz tensor in terms of a field E I as follows:…”

On the Appearance of Time in the Classical Limit of Quantum Gravity

“…Thus, the wave function is presented as a product of gravitational and matter wave functions. According to another assumption accepted in [9], the energy of matter fields is much smaller with respect to the energy of gravity, and the gravitational wave function must satisfy constraint equations for pure gravity. In this approach, one obtains equations for pure gravity in each order of expansion, but not only in the order O(M), where we have obtained Hamilton-Jacobi equation (22).…”

“…In other approaches, the time derivative appears in equations of quantum geometrodynamics as a consequence of introducing a reference frame. In [9], the origin of time is introducing the Kuchař-Torre reference fluid [40]. This results in additional terms that can be combined to define a time derivative, which appears in the left-hand side of (18).…”

“…In other approaches, time appears as a result of fixing a reference frame. In [9], time appears due to introducing the Kuchař-Torre reference fluid. Introducing a reference frame is an essential part of the extended phase space approach [12][13][14][15], where the physical content of the universe, that is, its geometry and matter fields spreading in space, is described from the viewpoint of an observer in a certain reference frame (see also [16]).…”