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The future of the universe is discussed in terms of several models. These include the closed, open, and critical models of the universe. Black holes and speculation on what may happen to life in the cosmological models are also discussed. (JN)

Quantum cosmology (quantum mechanics applied to the entire universe, and in particular to its space-time structure) essentially began with a small number of foundational papers by Bryce DeWitt, Charles Misner, [...]

Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime. [ABSTRACT FROM AUTHOR]

Abstract: Using a pair of linear invariant operators satisfying the Liouville–von Neumann equation, we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum. [Copyright &y& Elsevier]

Normally one thinks of the motion of the planets around the Sun as a highly classical phenomenon, so that one can neglect quantum gravity in the solar system. However, classical chaos in the planetary motion amplifies quantum uncertainties so that they become very large, giving huge quantum gravity effects. For example, evidence suggests that Uranus may eventually be ejected from the solar system, but quantum uncertainties would make the direction at which it leaves almost entirely uncertain, and the time of its exit uncertain by about one quadrillion years. For a time a quadrillion years from now, there are huge quantum uncertainties whether Uranus will be within the solar system, within the galaxy, or even within causal contact of the galaxy. [ABSTRACT FROM AUTHOR]

Abstract: It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities. This is the measure problem of cosmology. [Copyright &y& Elsevier]

Abstract: By combining a renormalization group argument relating the charge e and mass of the proton by (in Planck units) with the Carter–Carr–Rees anthropic argument that gives an independent approximate relation between these two constants, both can be crudely estimated. These equations have the factor of 0.1π and the exponent of 20 which depend upon known discrete parameters (e.g., the number of generations of quarks and leptons, and the number of spatial dimensions), but they contain no continuous observed parameters. Their solution gives the charge of the proton correct to within about 8%, though the mass estimate is off by a factor of about 1000 (16% error on a logarithmic scale). When one adds a fudge factor of 10 previously given by Carr and Rees, the agreement for the charge is within about 2%, and the mass is off by a factor of about 3 (2.4% error on a logarithmic scale). If this 10 were replaced by 15, the charge agrees within 1.1% and the mass itself agrees within 0.7%. [Copyright &y& Elsevier]

Abstract: Unless our universe is decaying at an astronomical rate (i.e., on the present cosmological timescale of Gigayears, rather than on the quantum recurrence timescale of googolplexes), it would apparently produce an infinite number of observers per comoving volume by thermal or vacuum fluctuations (Boltzmann brains). If the number of ordinary observers per comoving volume is finite, this scenario seems to imply zero likelihood for us to be ordinary observers and minuscule likelihoods for our actual observations. Hence, our observations suggest that this scenario is incorrect and that perhaps our universe is decaying at an astronomical rate. [Copyright &y& Elsevier]

We construct new complete, compact, inhomogeneous Einstein metrics on Sm+2 sphere bundles over 2n-dimensional Einstein–Kähler spaces K2n, for all n⩾1 and all m⩾1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of Sm with S2 bundles over K2n, for m>1. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies Sm times R2 bundles over K2n that generalise the higher-dimensional Taub-BOLT metrics, and with topologies Sm×R2n+2 that generalise the higher-dimensional Taub-NUT metrics, again for m>1. [Copyright &y& Elsevier]

One may perform a local field redefinition to transform between gravity minimally coupled to a free scalar field and gravity conformally coupled. However, the allowed field values differ in the two cases. For a minisuperspace consisting of a Friedman–Robertson–Walker geometry and a homogeneous scalar field, the conformal coupling allows a more general class of solutions of the Wheeler–DeWitt equation than does the minimal coupling. Nevertheless, there is a one-to-one correspondence between the bounded solutions in the two cases for k=1. This correspondence exploits an isomorphism between harmonic oscillator wavefunctions and solutions of the massive Klein–Gordon equation in the 1+1 dimensional Rindler wedge. [ABSTRACT FROM AUTHOR]

Abstract: If the initial quantum state of the universe is a multiverse superposition over many different sets of values of the effective coupling ‘constants’ of physics, and if this quantum state collapses to an eigenstate of the set of coupling ‘constants’ with a probability purely proportional to the absolute square of the amplitude (with no additional factor for something like life or consciousness), then one should not expect that the coupling ‘constants’ would be so biophilic as they are observed to be. Therefore, the observed biophilic values (apparent fine tuning) of the coupling ‘constants’ is statistical evidence against such simple forms of wavefunction collapse. [Copyright &y& Elsevier]