Cosmic voids and filaments from quantum gravity

Using computer simulations, we study the geometry of a typical quantum universe, i.e., the geometry one might expect before a possible period of inflation. We display it using coordinates defined by means of four classical scalar fields satisfying the Laplace equation with nontrivial boundary conditions. They are a close analogue of the harmonic coordinate condition used in the context of GR (Kuchar and Torre in Phys Rev D 43:419–441, 1991). It is highly nontrivial that these ideas can be applied to understand the structures which appear in very irregular and fluctuating geometries. The field configurations reveal cosmic web structures surprisingly similar to the ones observed in the present-day universe.

GENERAL SPHERICAL SYMMETRY SOLUTION TO EINSTEIN EQUATIONS AND NEWTONIAN GRAVITY MODIFICATION AT SMALL LENGTH SCALE

In this paper, we first we present a general spherical symmetry solution, independent of any coordinate condition, to the Einstein equations. By using this solution, we obtain different cases in different coordinate conditions, such as Schwarzschild solution, Fock solution, which have different forms of f(r). Then, we obtain a modified formula with respect to f(r) of the Newtonian gravity. This formula may describe the gravity at small length scale.

FOURTH-ORDER TOPOLOGICAL TENSOR CURRENT AND FOCK'S COORDINATE CONDITION

From ϕ-mapping method we construct a fouth-order topological tensor current in general. It is shown that the inner structure of this topological tensor current is labelled by the δ-function δ(ϕ), which represents some four-dimensional singular manifolds. By investigating the total expansion of δ(ϕ), these singular manifolds carry the topological numbers βiηi naturally, which does not involve any concrete models. As the generalization of Nielsen's Lagrangian and Nambu's action for strings, we present a new coordinate condition in general relativity, which includes the Fock's coordinate condition as a special case.