548 research outputs found
Conserved quantities in isotropic loop quantum cosmology
We develop an action principle for those models arising from isotropic loop
quantum cosmology, and show that there is a natural conserved quantity for
the discrete difference equation arising from the Hamiltonian constraint. This
quantity relates the semi-classical limit of the wavefunction at large
values of the spatial volume, but opposite triad orientations. Moreover, there
is a similar quantity for generic difference equations of one parameter arising
from a self-adjoint operator.Comment: 6 pages, to be published in Europhysics Letter
Generating function techniques for loop quantum cosmology
Loop quantum cosmology leads to a difference equation for the wave function
of a universe, which in general has solutions changing rapidly even when the
volume changes only slightly. For a semiclassical regime such small-scale
oscillations must be suppressed, by choosing the parameters of the solution
appropriately. For anisotropic models this is not possible to do numerically by
trial and error; instead, it is shown here for the Bianchi I LRS model how this
can be done analytically, using generating function techniques. Those
techniques can also be applied to more complicated models, and the results
gained allow conclusions about initial value problems for other systems.Comment: 22 pages, 5 figures; version to appear in CQ
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