Related papers: Comments on the Canonical Measure in Cosmology
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…
General relativity has a Hamiltonian formulation, which formally provides a canonical (Liouville) measure on the space of solutions. In ordinary statistical physics, the Liouville measure is used to compute probabilities of macrostates, and…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
We use cosmography to present constraints on the kinematics of the Universe, without postulating any underlying theoretical model. To this end, we use a Monte Carlo Markov Chain analysis to perform comparisons to the supernova Ia Union 2…
The implementation of a Planck-scale high frequency and short wavelength cutoff in quantum theories on expanding backgrounds may have potentially nontrivial implications, such as the breaking of local Lorentz invariance and the existence of…
We argue that in the context of eternal inflation in the landscape, making predictions for cosmological -- and possibly particle physics -- observables requires a measure on the possible cosmological histories as opposed to one on the vacua…
Our universe may be contained in one among a diverging number of bubbles that nucleate within an eternally inflating multiverse. A promising measure to regulate the diverging spacetime volume of such a multiverse is the scale-factor cutoff,…
Simple cosmological models are used to show that gravitation can be quantized as an ordinary gauge system if the Hamilton-Jacobi equation for the model under consideration is separable. In this situation, a canonical transformation can be…
Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system…
We consider approaches to cosmological parameter estimation in the inflationary cosmology, focussing on the required accuracy of the initial power spectra. Parametrizing the spectra, for example by power-laws, is well suited to testing the…
Making observable predictions for cosmic inflation requires determining when the wavenumbers of astrophysical interest today exited the Hubble radius during the inflationary epoch. These instants are commonly evaluated using the slow-roll…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
Inflation predicts that quantum fluctuations determine the large scale structure of the Universe. This raises the striking possibility that quantum mechanics, developed to describe nature at short distances, can be tested by studying nature…
We calculate power spectra of cosmological perturbations at high accuracy for two classes of inflation models. We classify the models according to the behaviour of the Hubble distance during inflation. Our approximation works if the Hubble…
Cosmography, as an integral branch of cosmology, strives to characterize the Universe without relying on pre-determined cosmological models. This model-independent approach utilizes Taylor series expansions around the current epoch,…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
Bayesian model averaging is a procedure to obtain parameter constraints that account for the uncertainty about the correct cosmological model. We use recent cosmological observations and Bayesian model averaging to derive tight limits on…
In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…
The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification…
It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant Lambda gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that…