38 research outputs found
Effective equations for isotropic quantum cosmology including matter
Effective equations often provide powerful tools to develop a systematic
understanding of detailed properties of a quantum system. This is especially
helpful in quantum cosmology where several conceptual and technical
difficulties associated with the full quantum equations can be avoided in this
way. Here, effective equations for Wheeler-DeWitt and loop quantizations of
spatially flat, isotropic cosmological models sourced by a massive or
interacting scalar are derived and studied. The resulting systems are
remarkably different from that given for a free, massless scalar. This has
implications for the coherence of evolving states and the realization of a
bounce in loop quantum cosmology.Comment: 42 page
Effective Equations of Motion for Quantum Systems
In many situations, one can approximate the behavior of a quantum system,
i.e. a wave function subject to a partial differential equation, by effective
classical equations which are ordinary differential equations. A general method
and geometrical picture is developed and shown to agree with effective action
results, commonly derived through path integration, for perturbations around a
harmonic oscillator ground state. The same methods are used to describe
dynamical coherent states, which in turn provide means to compute quantum
corrections to the symplectic structure of an effective system.Comment: 31 pages; v2: a new example, new reference
Quantum Gravity and Higher Curvature Actions
Effective equations are often useful to extract physical information from
quantum theories without having to face all technical and conceptual
difficulties. One can then describe aspects of the quantum system by equations
of classical type, which correct the classical equations by modified
coefficients and higher derivative terms. In gravity, for instance, one expects
terms with higher powers of curvature. Such higher derivative formulations are
discussed here with an emphasis on the role of degrees of freedom and on
differences between Lagrangian and Hamiltonian treatments. A general scheme is
then provided which allows one to compute effective equations perturbatively in
a Hamiltonian formalism. Here, one can expand effective equations around any
quantum state and not just a perturbative vacuum. This is particularly useful
in situations of quantum gravity or cosmology where perturbations only around
vacuum states would be too restrictive. The discussion also demonstrates the
number of free parameters expected in effective equations, used to determine
the physical situation being approximated, as well as the role of classical
symmetries such as Lorentz transformation properties in effective equations. An
appendix collects information on effective correction terms expected from loop
quantum gravity and string theory.Comment: 28 pages, based on a lecture course at the 42nd Karpacz Winter School
of Theoretical Physics ``Current Mathematical Topics in Gravitation and
Cosmology,'' Ladek, Poland, February 6-11, 200
Coordinate time dependence in Quantum Gravity
The intuitive classical space-time picture breaks down in quantum gravity,
which makes a comparison and the development of semiclassical techniques quite
complicated. Using ingredients of the group averaging method to solve
constraints one can nevertheless introduce a classical coordinate time into the
quantum theory, and use it to investigate the way a semiclassical continuous
description emerges from discrete quantum evolution. Applying this technique to
test effective classical equations of loop cosmology and their implications for
inflation and bounces, we show that the effective semiclassical theory is in
good agreement with the quantum description even at short scales.Comment: 35 pages, 17 figure. Revised version. To appear in Phys. Rev.
Effective constraints of loop quantum gravity
Within a perturbative cosmological regime of loop quantum gravity corrections
to effective constraints are computed. This takes into account all
inhomogeneous degrees of freedom relevant for scalar metric modes around flat
space and results in explicit expressions for modified coefficients and of
higher order terms. It also illustrates the role of different scales
determining the relative magnitude of corrections. Our results demonstrate that
loop quantum gravity has the correct classical limit, at least in its sector of
cosmological perturbations around flat space, in the sense of perturbative
effective theory.Comment: 44 pages, 6 figure
Effective Constraints for Quantum Systems
An effective formalism for quantum constrained systems is presented which
allows manageable derivations of solutions and observables, including a
treatment of physical reality conditions without requiring full knowledge of
the physical inner product. Instead of a state equation from a constraint
operator, an infinite system of constraint functions on the quantum phase space
of expectation values and moments of states is used. The examples of linear
constraints as well as the free non-relativistic particle in parameterized form
illustrate how standard problems of constrained systems can be dealt with in
this framework.Comment: 40 page
Singularities in Isotropic Non-Minimal Scalar Field Models
Non-minimally coupling a scalar field to gravity introduces an additional
curvature term into the action which can change the general behavior in strong
curvature regimes, in particular close to classical singularities. While one
can conformally transform any non-minimal model to a minimally coupled one,
that transformation can itself become singular. It is thus not guaranteed that
all qualitative properties are shared by minimal and non-minimal models. This
paper addresses the classical singularity issue in isotropic models and extends
singularity removal in quantum gravity to non-minimal models.Comment: 12 page
Optimization of the Touchscreen-Based Visuomotor Conditional Learning Task in Mice
The translational gap between animal models and clinical trials is a longstanding, yet largely unresolved, limitation in the study of cognition. This discrepancy is largely due to the differences in how cognition is assessed in animal models compared to those in clinical populations. In the stimulus-response (S-R) learning literature, for example, the techniques used to assess the acquisition of habitual behaviour differ greatly across species, leading to poor cross-species translation and often conflicting results. As a result, we set out to optimize a S-R learning task in mice using the touchscreen-based operant technologies. Similar to human studies, this touchscreen technique encourages animals to respond to visual stimuli displayed on a touchscreen according to a specific rule. Allowing for very similar, if not identical, cognitive assays in mice and men, this technique promotes high translational potential and a high degree of standardisation. Originally developed for rats, the Visuomotor Conditional Learning (VMCL) task encourages animals to learn arbitrary associations between visual stimuli and motor responses. In naĂŻve C57BL/6 mice, we sought to optimize VMCL task parameters to promote better and more efficient responding, identifying the length of inter-trial intervals and the limited hold period as two potential candidates. The validation of this task will provide a novel means through which to study the neural correlates of S-R learning, and its use in conjunction with fiber photometry recordings may be provided
Formation and Evolution of Structure in Loop Cosmology
Inhomogeneous cosmological perturbation equations are derived in loop quantum
gravity, taking into account corrections in particular in gravitational parts.
This provides a framework for calculating the evolution of modes in structure
formation scenarios related to inflationary or bouncing models. Applications
here are corrections to the Newton potential and to the evolution of large
scale modes which imply non-conservation of curvature perturbations possibly
noticeable in a running spectral index. These effects are sensitive to
quantization procedures and test the characteristic behavior of correction
terms derived from quantum gravity.Comment: 4 page
Cosmological vector modes and quantum gravity effects
In contrast to scalar and tensor modes, vector modes of linear perturbations
around an expanding Friedmann--Robertson--Walker universe decay. This makes
them largely irrelevant for late time cosmology, assuming that all modes
started out at a similar magnitude at some early stage. By now, however,
bouncing models are frequently considered which exhibit a collapsing phase.
Before this phase reaches a minimum size and re-expands, vector modes grow.
Such modes are thus relevant for the bounce and may even signal the breakdown
of perturbation theory if the growth is too strong. Here, a gauge invariant
formulation of vector mode perturbations in Hamiltonian cosmology is presented.
This lays out a framework for studying possible canonical quantum gravity
effects, such as those of loop quantum gravity, at an effective level. As an
explicit example, typical quantum corrections, namely those coming from inverse
densitized triad components and holonomies, are shown to increase the growth
rate of vector perturbations in the contracting phase, but only slightly.
Effects at the bounce of the background geometry can, however, be much
stronger.Comment: 20 page