Did the universe have a beginning?

Abstract: 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.

• The paper shows that current models like eternal inflation and cyclic evolution are fundamentally incomplete in the past due to constraints from quantum mechanics and expansion rates.
• It methodically evaluates each model using a generalized incompleteness theorem, establishing that any spacetime with a positive average expansion cannot be geodesically complete.
• The analysis of the emergent universe model reveals that quantum instabilities, modeled via the Wheeler-DeWitt equation, lead to inevitable collapse, negating a timeless cosmos.

Evaluating the Beginning of the Universe in Cosmological Models

The exploration of whether the universe had a definitively identifiable beginning or has existed indefinitely is a critical inquiry in cosmological research. In the paper "Did the Universe Have a Beginning?" by Audrey Mithani and Alexander Vilenkin, three cosmological models that deviate from the predictions of the classical singularity theorems established by Penrose and Hawking are evaluated regarding their potential to describe a past-eternal universe. The models considered include eternal inflation, cyclic evolution, and the emergent universe scenario. This paper methodically assesses these models and refutes their capability to account for a universe without a beginning.

Eternal Inflation and Cyclic Evolution

Eternal inflation and cyclic evolution are prominent cosmological models, often suggested as frameworks to avoid an initial singularity. Eternal inflation posits that quantum fluctuations can cause inflationary expansion to restart repeatedly in various regions of spacetime, implying a potentially eternal inflating multiverse. However, the paper utilizes a generalized incompleteness theorem, which shows that any spacetime undergoing inflationary expansion cannot be geodesically complete in the past if the expansion rate $H_{av}$ is positive. The cyclic evolution model describes a universe that experiences an infinite cycle of big bangs, expansions, and contractions. However, as with eternal inflation, the paper asserts that cyclic universes still entail $H_{av} > 0$, leading to the same conclusion of past incompleteness due to entropy considerations.

The Emergent Universe Model

The emergent universe scenario proposes a static "cosmic seed" that initiates expansion without a preceding singularity. This model theoretically offers a static solution stable with respect to classical perturbations. Nonetheless, Vilenkin and Mithani examine the quantum mechanical implications for the universes suggested by this model. They demonstrate that quantum instabilities are significant in this context, leading to an inevitable quantum collapse. Specifically, the analysis employs the Wheeler-DeWitt equation to mimic the behavior of quantum harmonic oscillators, showing a nonzero probability for a collapsing state. Therefore, even if classically stable, the emergent universe scenario cannot withstand quantum effects, invalidating its bid for an infinite past.

Implications and Speculation on Future Research

The evaluations within this paper underscore significant implications for theoretical and observational cosmology. By dismissing these models as past-eternal, the research emphasizes an unavoidable singularity or inception of time — a conclusion aligning cosmology more closely with singularity theorems, albeit with modern interpretive frameworks. Furthermore, the incorporation of quantum mechanical assessment underlines the intersecting roles of quantum physics in understanding cosmological phenomena.

Looking forward, advancing cosmological theories must consider quantum principles alongside relativistic dynamics to reconcile these findings with potentially new models. Future investigations might explore alternative formulations of emergent universes or entirely novel models that might offer pathways to articulate a beginningless cosmological scenario. Integrating comprehensive observations with theoretical advancements — especially in quantum gravity and the study of dark energy — might yield progressive insights into whether further refinements can sustain these or new models against the implications of quantum mechanics.