Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Corrections to the Friedmann Equations from LQG for a Universe with a
  Free Scalar Field   In loop quantum cosmology the quantum dynamics is well understood. We
approximate the full quantum dynamics in the infinite dimensional Hilbert space
by projecting it on a finite dimensional submanifold thereof, spanned by
suitably chosen semiclassical states. This submanifold is isomorphic with the
classical phase space and the projected dynamical flow provides effective
equations incorporating the leading quantum corrections to the classical
equations of motion. Numerical work has been done using quantum states which
are semiclassical at late times. These states follow the classical trajectory
until the density is on the order of 1% of the Planck density then deviate
strongly from the classical trajectory. The effective equations we obtain
reproduce this behavior to surprising accuracy.

25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex