The Emergence of Spacetime in Quantum Gravity Big Bang Models

Can spacetime have a beginning, or an end? Spacelike curvature singularities, like those of the big bang or big crunch of cosmology, or that inside a black hole, strongly suggest that the semiclassical description of spacetime breaks down, and it isn't clear at present whether or not quantum cosmology is up to the task of making sense of these singularities. This talk will survey some thoughts that have been put forth on the subject.

Georges Lemaître was the first to take seriously physical cosmology of the expanding universe, as well as the first to speculate on what quantum theory could possibly have to say about the this. I shall begin with a look at his amazing, 1931 paper in Nature, `The beginning of the world from the point of view of quantum theory'. The paper is very brief --- just a couple of paragraphs --- but contains profound thoughts about the quantum origin of structure in the universe, as well as the origin of time itself, starting from a unique quantum state. It has striking parallels with modern concepts of cosmology such as inflation and the Hartle-Hawking no-boundary wave function of the universe (Hartle and Hawking 1983).

Next I'll sketch Hartle and Hawking's proposal for the beginning of the universe from nothing. Time becomes meaningless before a certain time, or rather, time is emergent. There is no complete theory realizing this notion. It's a rather tentative proposal that has yet to be fully understood, and it may require a generalization or modification of quantum theory to accommodate it, if it makes sense at all.

Something like the time reverse of the Hartle-Hawking picture could be happening inside black holes. As the singularity is approached, time may cease to be meaningful, so that, in a sense, there is an internal boundary to spacetime. The alternative, that there is a baby universe inside, is disfavored by holographic duality.

I'll end with a description of a very different scenario for a smooth `beginning' for the universe, imagined by Gott and Li (1998): the universe could create itself by virtue of being non time-orientable. They illustrated the idea using antipodally identified de Sitter spacetime. While it isn't clear whether the rest of physics could be formulated in such a time non-orientable spacetime, this is an intriguing possibility.

Many theoretical arguments indicate that, at the fundamental level, spacetime `dissolves' into a new set of quantum entities, of no direct gravitational, spatiotemporal or geometric interpretation, and from which it has to emerge (alongside the usual notion of geometry and gravity), in suitable approximations (Oriti 2014). This emergence can be understood in terms of different `levels', depending on which aspect of standard spacetime is recovered, on the nature of the fundamental entities, and on various new epistemological tasks posed by such emergence (Oriti forthcoming).

Within such scenario, we argue that cosmology should be understood as the hydrodynamic regime of fundamental quantum gravity, since in this regime spacetime emerges from non-spatiotemporal quantum gravity structures. We also suggest that this emergence may also involve a cosmological phase transition, dubbed `geometrogenesis'. This view on cosmology presents itself a number of novel conceptual and technical challenges, with respect to both classical relativistic cosmology and traditional quantum cosmology, concerning in particular the notion of time and cosmic evolution. We discuss these conceptual and physical implications within a modern approach to quantum gravity: group field theory (GFT).

Recently, we have studied GFT condensate states, showing that: (1) they describe continuum homogeneous geometries, apt to describe the universe at cosmological scales; (2) an effective cosmological dynamics can be extracted from the fundamental quantum dynamics, as an hydrodynamic approximation, and it reproduces a modified Friedmann equation; (3) the modifications coming from quantum gravity replace the big bang singularity with a quantum bounce. This effective cosmological dynamics may also allow for an accelerated inflation-like phase of expansion of purely quantum gravity origin. This constitutes a derivation of cosmological dynamics from first principles, and it offers a general template for the emergence of continuum spacetime from fundamental quantum gravity. These recent developments are reviewed in Oriti (2017).

As an important part of the general picture, we illustrate results, possibilities and expectations concerning the fate of cosmological singularities, emphasizing their conceptual implications.

In the context of group field theory hydrodynamics, if an inflationary-like paradigm is shown to be consistent at very high energies, the existence of cosmological singularities may be practically irrelevant. If we have a bouncing scenario, then singularities are resolved by quantum effects, without breaking an effective hydrodynamic description in terms of continuum spacetime. If the hydrodynamic approximation breaks down around the would-be singularity or around the cosmic bounce, then we may have a consistent primordial cosmological dynamics without spacetime. If this breakdown is due to the fundamental GFT system approaching a phase transition, then we have an emergent universe scenario, with a degenerate phase followed by an expanding phase with proper semi-classical limit: geometrogenesis replaces the cosmological singularity.

Spacetime singularities---broadly construed as 'rips' in spacetime where general relativity breaks down---are often held to be pathologies which need to be resolved. Researchers working on the foundations of physics, both physicists and philosophers, often pin their hopes on the elusive quantum theory of gravity (QG) to offer a way to rid spacetime of these rips. What is less agreed upon is what precisely counts as singularity resolution: what criteria would a QG have to fulfill to resolve spacetime singularities? In this talk, I critically analyse a proposed criterion for the resolution of the big bang singularity to draw philosophical lessons about how to interpret such criteria, and how they might influence our understanding of spacetime.
I start with the Wheeler-DeWitt equation (WDW). WDW governs the dynamics of the quantised gravitational field, and while generally not well-defined, in the cases of drastically reduced models of certain cosmologies, called 'minisuperspace models', it can be. Its solutions (which are wavefunctions) in such cases encode all information about the geometries and the matter present in the corresponding universes. 
The criterion for singularity resolution that I focus on was initially proposed by DeWitt and more recently explicated by Kiefer: that the solutions to WDW vanish at the singularity. Kiefer illustrates the criterion using a two-dimensional minisuperspace model of a Friedmann-Lemaître-Robertson-Walker universe---a homogeneous, isotropic and expanding/contracting universe---filled with a hypothetical perfect fluid. His results suggest that in this model, as the universe gets closer to zero towards the big bang singularity, the value of its wavefunction also approaches zero.
This talk addresses questions about the model which have been mentioned by physicists, but not widely acknowledged by philosophers. For one, does the minisuperspace model approximate reality in a way that the things we learn about singularity resolution from the model would apply just as well to universes with more realistic numbers of degrees of freedom? For another, how does one interpret the 'DeWitt criterion'? It looks promising as a condition for singularity resolution because heuristically, it makes the probability amplitudes of singular spaces zero at the QG level. But this is only assuming that wavefunctions and probability amplitudes are related in the same way in QG as they are in ordinary quantum mechanics, and that they are in the timeless context of the WDW is not clear. Hence, for the criterion to even qualify as a sufficient criterion for singularity resolution, we either need a satisfactory probability interpretation at the QG level or a different interpretation of the criterion that amounts to singularity resolution. 
Clarifying the meaning of the DeWitt criterion will also let us ask questions about the nature of spacetime at the big bang and how it relates to our notion of classical spacetime. Finally, I discuss how the criterion compares to other criteria for resolving other kinds of singularities than the big bang, and whether such comparisons might shed any light on the overarching question of what it even means to resolve a singularity. 

The concepts of law, retro/prediction, and explanation are centrally spatiotemporal, describing dynamics and underwriting scientific inference. So in a theory in which time (or space) are not fundamental, they will need to be re-examined. In this talk we probe this line of thought, by considering the possible breakdown of spacetime in quantum gravity (QG) models of the big bang.

One can envision different ways to represent a `transition' from non-spatiotemporal to spatiotemporal epochs: for instance as a wavefunction over configuration space with support in regions in which spacetime was and was not effectively definable. But that picture requires knowledge of the non-spatiotemporal degrees of freedom and equations governing them. The current understanding is instead generally semi-classical, in which (a) only the effectively spatiotemporal region is known (described using classical degrees of freedom with QG corrections), and (b) the non-spatiotemporal region is typically represented by a boundary condition expressing its effect on the spatiotemporal epoch. Although the investigation we propose is thus limited by the current state of physics, we aim to show how such `boundaries' to spacetime can still illuminate the philosophical issues.

String cosmology (Gasperini 2007) models the universe through the relativistic field equations imposed by Weyl symmetry: at lowest order, the Einstein field equations. As discussed in our (2018), one solution is an expanding universe divided into accelerating and decelerating epochs, separated by a Big Bang curvature singularity. It is not known how the singularity is resolved, or whether unknown, perhaps non-spatial, `M-theory' degrees of freedom are involved: hence a `wavefunction picture' does not exist in string theory. However, scenarios in which the singular region probes M-theory with corrections in powers either of string coupling or length have been studied: for instance, string gas and ekpyrotic models.

Standard loop quantum cosmology studies symmetry-reduced systems with just one degree of freedom---the scale factor (Bojowald 2011). The resulting dynamical equation is easily amenable to scientific analysis, even affording a straightforward interpretation of a continuous evolution in time, right through the big bang from a pre-big-bang epoch. Looking beyond this simplistic case at generic states in loop quantum gravity, we find that these do not in general admit a spatiotemporal interpretation. One would expect the cosmological case to fit a semi-classical framework in which the two epochs are separated by a boundary where the effective spatiotemporality breaks down. In the canonical version of the theory, the wavefunction picture is mathematically intractable, and only a semi-classical analysis can be attempted. In the alternative covariant framework, the dynamics is expressed as transition amplitudes between kinematical spin networks states, and there is at least the promise of the fuller wavefunction picture.

We will argue that in either string theory or loop quantum gravity, one can meaningfully study such a universe in our `semi-classical' framework, asking for instance: how parameters describing the singular region are determined by earlier or later epochs, or offer clues to more fundamental, perhaps non-spatiotemporal, degrees of freedom?