Re: What happens if the rate of expansion of the universe becomes infinite?

Hi Howard,

Your question concerns a topic of current active research. Firstly, it may be useful to define some terms. From measurements of the cosmic microwave background anisotropies we know that the universe is (very close to) spatially flat. We know that matter accounts for only 30% of the energy density needed to make the Universe spatially flat. The remaining 70% is generally called dark energy. One candidate for dark energy is vacuum energy (energy associated with the virtual particles that populate the quantum vacuum). Vacuum energy is also called the cosmological constant. There are other candidates for dark energy besides vacuum energy, with quintessence being the most popular at the moment.

If dark energy is indeed the cosmological constant, then the expansion rate of the Universe will keep increasing, and the universe will become less and less dense with time. There is nothing paradoxical or troubling about this, as the expansion rate will always be finite at finite time. Eventually, quantum gravitational effects will take over. For example, fluctuations of the scalar field producing the cosmological constant can lead to a curvature space-like singularity. Such a scenario is highly improbable, but given enough time can happen. Another effect that can lead to a curvature singularity is quantum fluctuations in the gravitational field itself. At present, nobody knows what happens to the parts of the Universe that return to singularity.

The above is only possibility - the expansion of the Universe does not have to keep accelerating. If the dark energy is quintessence, a scalar field slowly rolling down it's potential, then the future of the Universe can involve a recollapse, decelerating expansion, or other behavior depending on the details of the potential.

Recently, other models (alternative to the standard big bang + inflation) have been proposed that attempt to incorporate the current acceleration phase of the Universe, but with an eventual recollapse, e.g., the "cyclic model".

Vit