# 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…

## 197 Citations

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## References

SHOWING 1-10 OF 63 REFERENCES

Canonical measure and the flatness of a FRW universe

- Physics
- 1995

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

- Physics
- 1984

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

- Physics
- 2002

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

- Mathematics
- 1983

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

- Physics
- 2006

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

- Physics
- 1989

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.

- PhysicsPhysical review. D, Particles and fields
- 1990

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

- Physics
- 2002

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

- Physics
- 2006

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…