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Testing loop quantum cosmology
Loop quantum cosmology predicts that quantum gravity effects resolve the
big-bang singularity and replace it by a cosmic bounce. Furthermore, loop
quantum cosmology can also modify the form of primordial cosmological
perturbations, for example by reducing power at large scales in inflationary
models or by suppressing the tensor-to-scalar ratio in the matter bounce
scenario; these two effects are potential observational tests for loop quantum
cosmology. In this article, I review these predictions and others, and also
briefly discuss three open problems in loop quantum cosmology: its relation to
loop quantum gravity, the trans-Planckian problem, and a possible transition
from a Lorentzian to a Euclidean space-time around the bounce point.Comment: 20 pages. Invited review for special edition "Testing quantum gravity
with cosmology" of Comptes Rendus Physiqu
The Matter Bounce Scenario in Loop Quantum Cosmology
In the matter bounce scenario, a dust-dominated contracting space-time
generates scale-invariant perturbations that, assuming a nonsingular bouncing
cosmology, propagate to the expanding branch and set appropriate initial
conditions for the radiation-dominated era. Since this scenario depends on the
presence of a bounce, it seems appropriate to consider it in the context of
loop quantum cosmology where a bouncing universe naturally arises. For a
pressureless collapsing universe in loop quantum cosmology, the predicted power
spectrum of the scalar perturbations after the bounce is scale-invariant and
the tensor to scalar ratio is negligibly small. A slight red tilt can be given
to the scale-invariance of the scalar perturbations by a scalar field whose
equation of state is , where is a small
positive number. Then, the power spectrum for tensor perturbations is also
almost scale-invariant with the same red tilt as the scalar perturbations, and
the tensor to scalar ratio is expected to be .
Finally, for the predicted amplitude of the scalar perturbations to agree with
observations, the critical density in loop quantum cosmology must be of the
order .Comment: 9 page
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
We study quantization ambiguities in loop quantum cosmology that arise for
space-times with non-zero spatial curvature and anisotropies. Motivated by
lessons from different possible loop quantizations of the closed
Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open
holonomies of the extrinsic curvature, which due to gauge-fixing can be treated
as a connection, leads to the same quantum geometry effects that are found in
spatially flat cosmologies. More specifically, in contrast to the quantization
based on open holonomies of the Ashtekar-Barbero connection, the expansion and
shear scalars in the effective theories of the Bianchi type II and Bianchi type
IX models have upper bounds, and these are in exact agreement with the bounds
found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and
Bianchi type I models in loop quantum cosmology. We also comment on some
ambiguities present in the definition of inverse triad operators and their
role.Comment: 34 pages, v2: minor change
Why are the effective equations of loop quantum cosmology so accurate?
We point out that the relative Heisenberg uncertainty relations vanish for
non-compact spaces in homogeneous loop quantum cosmology. As a consequence, for
sharply peaked states quantum fluctuations in the scale factor never become
important, even near the bounce point. This shows why quantum back-reaction
effects remain negligible and explains the surprising accuracy of the effective
equations in describing the dynamics of sharply peaked wave packets. This also
underlines the fact that minisuperspace models ---where it is global variables
that are quantized--- do not capture the local quantum fluctuations of the
geometry.Comment: 6 pages, v2: Clarifications and references adde
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