Measure problem in cosmology

@article{Gibbons2008MeasurePI,
  title={Measure problem in cosmology},
  author={G. W. Gibbons and Neil Turok},
  journal={Physical Review D},
  year={2008},
  volume={77},
  pages={063516}
}
The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a 'magnetic flux' of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat Friedmann-Lemaitre-Robertson-Walker universes. We show that the divergence is removed if we… 

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References

SHOWING 1-10 OF 63 REFERENCES
Canonical measure and the flatness of a FRW universe
We consider the claim of Hawking and Page that the canonical measure applied to Friedmann--Robertson--Walker models with a massive scalar field can solve the flatness problem, i.e. , regardless of
Wave Function of the Inflationary Universe
If one is interested in cosmological models with inflation occurring at or near the Planck energy then the effects of quantum gravity have to be taken into account. We may still hope to use an
Essay: An Alternative to Inflation
Inflationary models are generally credited with explaining the large scale homogeneity, isotropy, and flatness of our universe as well as accounting for the origin of structure (i.e., the deviations
Wave Function of the Universe
TLDR
A proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three- geometries as a boundary.
The adiabatic invariance of the action variable in classical dynamics
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well known that such systems possess an adiabatic invariant which coincides with the action
Difficulties with Inflationary Cosmology a
The problems posed for inflationary cosmological models by (1) the large-scale homogeneity of the universe and (2) the second law of thermodynamics are considered theoretically. The analyses of
Nonlinear evolution of long-wavelength metric fluctuations in inflationary models.
  • SalopekBond
  • Physics
    Physical review. D, Particles and fields
  • 1990
TLDR
This work describes a formalism for following the nonlinear propagation of long-wavelength metric and scalar-field fluctuations and performs an expansion in spatial gradients of the Arnowitt-Deser-Misner equations and retains only terms up to first order.
Inflationary Theory and Alternative Cosmology
Recently Hollands and Wald argued that inflation does not solve any of the major cosmological problems. We explain why we disagree with their arguments. They also proposed a new speculative mechanism
Populating the landscape: A Top down approach
We put forward a framework for cosmology that combines the string landscape with no boundary initial conditions. In this framework, amplitudes for alternative histories for the universe are
...
...