Semiclassical solutions of generalized Wheeler-DeWitt cosmology

Abstract

We consider an extension of WDW minisuperpace cosmology with additional interaction terms that preserve the linear structure of the theory. General perturbative methods are developed and applied to known semiclassical solutions for a closed Universe filled with a massless scalar. The exact Feynman propagator of the free theory is derived by means of a conformal transformation in minisuperspace. As an example, a stochastic interaction term is considered and first order perturbative corrections are computed. It is argued that such an interaction can be used to describe the interaction of the cosmological background with the microscopic d.o.f. of the gravitational field. A Helmoltz-like equation is considered for the case of interactions that do not depend on the internal time and the corresponding Green's kernel is obtained exactly.The possibility of linking this approach to fundamental theories of Quantum Gravity is investigated.

Quantum Cosmology from Group Field Theory Condensates: a Review

“…Nevertheless, it is interesting to study the behaviour of nonlinear quantum cosmology models such as (4.18) in their own right, if only as toy models for the effective dynamics of GFT condensates. For instance, a linear but nonlocal extension of the Wheeler-DeWitt equation was recently studied in [49].…”

Quantum relativistic cosmology: dynamical interpretation and tunneling universe

“…The WdW equation, since that time when it was proposed until now, has inspired several researches in accordance with the original proposals of Wheeler and DeWitt. Among these researches, we can mention investigations on quantum cosmology in the 1980's [5][6][7] and recently [8][9][10][11][12][13][14][15][16][17][18][19]. Along this line of research which uses the WdW equation, we can also mention very recent works with studies concerning the tunneling wave function of the universe [20], the interaction of multiverse and effects on the cosmic microwave background [21] and about the consistence of the WdW equation in a modified theory of gravity [22].…”

Spinorial Wheeler–DeWitt wave functions inside black hole horizons

“…Of cource, the general solution is written by X → X + X 0 , where X 0 is a constant, due to the translational invariance of the system 6. Graphical representation of wave packets of similar wave functions in quantum cosmology are dealt with[29][30][31] et al…”