## Did the universe have a beginning?

**Audrey Mithani, Alexander Vilenkin**

*We discuss three candidate scenarios which seem to allow the possibility that the universe could have existed forever with no initial singularity: eternal infation, cyclic evolution, and the emergent universe. The first two of these scenarios are geodesically incomplete to the past, and thus cannot describe a universe without a beginning. The third, although it is stable with respect to classical perturbations, can collapse quantum mechanically, and therefore cannot have an eternal past.*

**1 Introduction**

One of the most basic questions in cosmology is whether the universe had a beginning or has simply existed forever. It was addressed in the singularity theorems of Penrose and Hawking [1], with the conclusion that the initial singularity is not avoidable.

These theorems rely on the strong energy condition and on certain assumptions about the global structure of spacetime.

There are, however, three popular scenarios which circumvent these theorems: eternal inflation, a cyclic universe, and an “emergent” universe which exists for eternity as a static seed before expanding. Here we shall argue that none of these scenarios can actually be past-eternal.

Inflation violates the strong energy condition, so the singularity theorems of Penrose and Hawking do not apply. Indeed, quantum fluctuations during inflation violate even the weak energy condition, so that singularity theorems assuming only the weak energy condition [2] do not apply either. A more general incompleteness theorem was proved recently [3] that does not rely on energy conditions or Einstein’s equations.

Instead, it states simply that past geodesics are incomplete provided that the expansion rate averaged along the geodesic is positive: H_{αυ} > 0. This is a much weaker condition, and should certainly apply to the past of any inflating region of spacetime. Therefore, although inflation may be eternal in the future, it cannot be extended indefinitely to the past.

Another possibility could be a universe which cycles through an infinite series of big bang followed by expansion, contraction into a crunch that transitions into the next big bang [4]. A potential problem with such a cyclic universe is that the entropy must continue to increase through each cycle, leading to a “thermal death” of the universe. This can be avoided if the volume of the universe increases through each cycle as well, allowing the ratio S=V to remain nite [5]. But if the volume continues to increase over each cycle, H_{αυ} > 0, meaning that the universe is past-incomplete. We now turn to the emergent universe scenario, which will be our main focus in this paper ….

Read more: http://arxiv.org/pdf/1204.4658v1.pdf

Read also:

**1. ****Mathematics of Eternity Prove The Universe Must Have Had A Beginning**

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