The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case? In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not (...) valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete. After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views. -/- DOI: 10.58679/TW62329. (shrink)

Over time, the general theory of relativity has accumulated several anomalies and discrepancies, indicating the need for a better theory about gravity or other approaches. The ad-hoc hypotheses introduced in general relativity to explain gravitational singularities based on energy conditions are not very efficient. More detailed assumptions on the content of the subject are needed. Many scientists and philosophers have come to the conclusion that singularities must be associated with reaching the limits of the physical validity of general relativity, and (...) a new theory of quantum gravity needs to be developed. DOI: 10.13140/RG.2.2.32579.55848. (shrink)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the problems faced in the search for a theory of quantum gravity. I find that none of them shows any defect (...) in our comprehension of general relativity as a physical theory. I conclude by comparing general relativity with quantum mechanics, a theory that manifestly does stand in need of an interpretation in an important sense. Although many aspects of the conceptual structure of general relativity remain poorly understood, it suffers no incoherence in its formulation as a physical theory that only an ‘interpretation’ could resolve. *Received November 2007; revised February 2009. †To contact the author, please write to: Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected] . When science starts to be interpretive it is more unscientific even than mysticism. (D. H. Lawrence, “Self‐Protection”). (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

This essay aims to provide a self-contained introduction to time in relativistic cosmology that clarifies both how questions about the nature of time should be posed in this setting and the extent to which they have been or can be answered empirically. The first section below recounts the loss of Newtonian absolute time with the advent of special and general relativity, and the partial recovery of absolute time in the form of cosmic time in some cosmological models. Section II considers (...) the beginning and end of time in a broader class of models in which there is not an analog of Newtonian absolute time. As we will see, reasonable physical assumptions imply that the universe is finite to the past, and Section III turns to consideration of the “beginning” itself. We critically review conventional wisdom that a “singularity” reveals flaws in general relativity and briefly assess ways of avoiding the singularity. (shrink)

Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is to achieve. Here, we first evaluate how particular types of singularities may suggest an incompleteness of current theories. We then classify four different 'attitudes' towards singularities in the search for QG, and show, through examples in the physics literature, that these lead to (...) different scenarios for the new theory. Two of the attitudes prompt singularity resolution, but only one suggests the need for a theory of QG. Rather than evaluate the different attitudes, we close with some suggestions of factors that influence the choice between them. (shrink)

I discuss singular space-times in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

Traditional debates, such as those regarding whether the universe is finite in spatial or temporal extent, exemplified, according to Kant, the inherent tendency of pure reason to lead us astray. Although various aspects of Kant’s arguments fail to find a footing in modern cosmology, Kant’s objections to the search for a complete objective description of the cosmos are related to three intertwined issues that are still of central importance: the applicability of universal laws, the status of distinctively cosmological laws, and (...) the explanatory sufficiency of laws. We will advocate a broadly Kantian position on these three issues as part of a critical response to a prevalent strain of Leibnizian rationalism in contemporary cosmology. (shrink)

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

Intuitively, the totality of physical reality—the Cosmos—has a beginning only if (i) all parts of the Cosmos agree on the direction of time (the Direction Condition) and (ii) there is a boundary to the past of all non-initial spacetime points such that there are no spacetime points to the past of the boundary (the Boundary Condition). Following a distinction previously introduced by J. Brian Pitts, the Boundary Condition can be conceived of in two distinct ways: either topologically, i.e., in terms (...) of a closed boundary, or metrically, i.e., in terms of the Cosmos having a finite past. This article proposes that the Boundary Condition should be posed disjunctively, modifies and improves upon the metrical conception of the Cosmos’s beginning in light of a series of surprising yet simple thought experiments, and suggests that the Direction and Boundary Conditions should be thought of as more fundamental to the concept of the Cosmos’s beginning than classical Big Bang cosmology. (shrink)

Many physicists have thought that absolute time became otiose with the introduction of Special Relativity. William Lane Craig disagrees. Craig argues that although relativity is empirically adequate within a domain of application, relativity is literally false and should be supplanted by a Neo-Lorentzian alternative that allows for absolute time. Meanwhile, Craig and co-author James Sinclair have argued that physical cosmology supports the conclusion that physical reality began to exist at a finite time in the past. However, on their view, the (...) beginning of physical reality requires the objective passage of absolute time, so that the beginning of physical reality stands or falls with Craig's Neo-Lorentzian metaphysics. Here, I raise doubts about whether, given Craig's NeoLorentzian metaphysics, physical cosmology could adequately support a beginning of physical reality within the finite past. Craig and Sinclair's conception of the beginning of the universe requires a past boundary to the universe. A past boundary to the universe cannot be directly observed and so must be inferred from the observed matter-energy distribution in conjunction with auxilary hypotheses drawn from a substantive physical theory. Craig's brand of Neo Lorentzianism has not been sufficiently well specified so as to infer either that there is a past boundary or that the boundary is located in the finite past. Consequently, Neo Lorentzianism implicitly introduces a form of skepticism that removes the ability that we might have otherwise had to infer a beginning of the universe. Furthermore, in analyzing traditional big bang models, I develop criteria that Neo-Lorentzians should deploy in thinking about the direction and duration of time in cosmological models generally. For my last task, I apply the same criteria to bounce cosmologies and show that Craig and Sinclair have been wrong to interpret bounce cosmologies as including a beginning of physical reality. (shrink)

The problem of motion in general relativity is about how exactly the gravitational field equations, the Einstein equations, are related to the equations of motion of material bodies subject to gravitational fields. This article compares two approaches to derive the geodesic motion of matter from the field equations: the ‘T approach’ and the ‘vacuum approach’. The latter approach has been dismissed by philosophers of physics because it apparently represents material bodies by singularities. I argue that a careful interpretation of the (...) approach shows that it does not depend on introducing singularities at all and that it holds at least as much promise as the T approach. (shrink)

We consider to what extent the fundamental question of spacetime singularities is relevant for the philosophical debate about the nature of spacetime. After reviewing some basic aspects of the spacetime singularities within general relativity, we argue that the well known difficulty to localize them in a meaningful way may challenge the received metaphysical view of spacetime as a set of points possessing some intrinsic properties together with some spatiotemporal relations. Considering the algebraic formulation of general relativity, we argue that the (...) spacetime singularities highlight the philosophically misleading dependence on the standard geometric representation of spacetime. †To contact the author, please write to: Department of Philosophy, University of Lausanne, CH-1015 Lausanne, Switzerland; e-mail: [email protected]. (shrink)

Radical ontic structural realism (ROSR) asserts an ontological commitment to ‘free-standing’ physical structures understood solely in terms of fundamental relations, without any recourse to relata that stand in these relations. Bain ([2013], pp.1621–35) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category theory (...) does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalizations of general relativity do not warrant the claim that these theories describe ‘object-free’ structures. We conclude that category theory offers little if any comfort to ROSR. 1 Introduction: Ridding Structures of Objects2 The Set-theoretic Peril for Radical Ontic Structural Realism3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism4 Throwing out the Relations with the Relata5 Categorial and Set-theoretical Structures6 Radical Suggestions from Topological Quantum Field Theory?7 Sheaves of Einstein Algebras as Radical Structures?8 Conclusions. (shrink)

Determinism fails easily if spacetimes with points removed from the spacetime manifold are taken to be physically reasonable representations of a way the world could be according to classical general relativity. I discuss a recently proposed condition for determining which spacetimes have holes—epistemic hole freeness—and show that epistemic hole freeness gives the correct verdict in some non-globally hyperbolic spacetimes with a closed subset removed, certain spacetimes with genuinely indeterministic features count as having an epistemic hole, which implies that the requirement (...) of epistemic hole freeness enforces a form of determinism, and there is a large class of spacetimes that intuitively are radically indeterministic and unphysical due to containing a hole, but are free from epistemic holes. I show that a few natural ways of remedying are not satisfactory. (shrink)

This exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as `time travel' and `holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a `physically reasonable' spacetime structure (...) in modern physics is far from clear. (shrink)

This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause (...) for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist. -/- Friends of the KCA have sought to defend their view that physical reality began to exist in two distinct ways. As I discuss in chapter 2, the first way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a priori arguments meant to show that, as a matter of metaphysical necessity, the past must be finite. If the past is necessarily finite, then the past history of physical reality is necessarily finite. And if having a finite past suffices for having a beginning, then, since the past history of physical reality is necessarily finite, physical reality necessarily began to exist. I show that the arguments which have been offered thus far for the view that the past is necessarily finite do not succeed. Moreover, as I elaborate on in chapter 5, having a finite past does not suffice for having a beginning. -/- As I discuss in chapter 3, the second way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a posteriori arguments meant to show that we have empirical evidence that physical reality has a finite past history. For example, the big bang is sometimes claimed to have been the beginning of physical reality and, since we have excellent empirical evidence for the big bang, we have excellent empirical evidence for the beginning of physical reality. The big bang can be understood in two ways. On the one hand, the big bang can be understood as a theory about the history and development of the observable universe. Understood in that sense, then I agree that the big bang is supported by excellent empirical evidence and by a scientific consensus. On the other hand, some authors (particularly science popularizers, science journalists, and religious apologists) have wrongly interpreted big bang theory as a theory about the beginning of the whole of physical reality. As I argue, while a beginning of physical reality may be consistent with classical big bang theory, classical big bang theory does not provide good reason for thinking that physical reality began to exist. -/- In part II, I turn to discussing three necessary, but not necessarily sufficient, conditions for physical reality to have a beginning. Before discussing the three conditions, in chapter 4, I introduce three metaphysical accounts of the nature of time (A-theory, B-theory, and C-theory) as well as some formal machinery that will subsequently become useful in the dissertation. I introduce the first of the three conditions in chapter 5. According to the Modal Condition, physical reality began to exist only if, at the closest possible worlds without time, physical reality does not exist. I show that this condition helps us to make sense of various views in both theology and philosophy of physics. In chapter 6}, I introduce the second of my three conditions, the Direction Condition, according to which, roughly, physical reality began to exist only if all space-time points agree about the direction of time, so that all space-time points can agree that physical reality's putative beginning took place in their objective past. In chapter 7, I discuss the third condition, the Boundary Condition, according to which physical reality began to exist only if there is a past temporal boundary such that physical reality did not exist before the boundary. I show that there are two senses in which physical reality could be said to have had a past temporal boundary. Lastly, in chapter 8, I show that there is a relationship between my three conditions and classical big bang theory, even though the relationship is not the one usually identified in the literature. -/- In part III, I present four arguments for the view that, at the present stage of philosophical and scientific inquiry, we cannot know whether physical reality satisfies the three necessary conditions to have had a beginning and, consequently, we cannot know whether physical reality had a beginning. As I will prove in chapter 9, no set of observations that we currently have, when conjoined with General Relativity, entails that physical reality satisfies the Direction or Boundary Conditions. As I show in chapter 10, considerations in the philosophical foundations of statistical mechanics entail either that the Cosmos violates the Modal Condition or else that there is a transcendental condition on the possibility of our knowledge of the past that prevents our access to data we would need to gather to determine whether physical reality satisfies the Boundary Condition. In chapter 11, I show that there are a number of live cosmological models according to which physical reality does not satisfy the Boundary Condition. As long as we don't know whether any of those cosmological models are correct, we do not know whether physical reality satisfies the Boundary Condition. Lastly, I turn to confirmation theory and show that, at our present stage of inquiry, ampliative inferences for the conclusion that physical reality satisfies the Modal, Direction, and Boundary Conditions are not successful. (shrink)

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal structure".

The evolution of gravitational tests from an epistemological perspective framed in the concept of rational reconstruction of Imre Lakatos, based on his methodology of research programmes. Unlike other works on the same subject, the evaluated period is very extensive, starting with Newton's natural philosophy and up to the quantum gravity theories of today. In order to explain in a more rational way the complex evolution of the gravity concept of the last century, I propose a natural extension of the methodology (...) of the research programmes of Lakatos that I then use during the paper. I believe that this approach offers a new perspective on how evolved over time the concept of gravity and the methods of testing each theory of gravity, through observations and experiments. I argue, based on the methodology of the research programmes and the studies of scientists and philosophers, that the current theories of quantum gravity are degenerative, due to the lack of experimental evidence over a long period of time and of self-immunization against the possibility of falsification. Moreover, a methodological current is being developed that assigns a secondary, unimportant role to verification through observations and/or experiments. For this reason, it will not be possible to have a complete theory of quantum gravity in its current form, which to include to the limit the general relativity, since physical theories have always been adjusted, during their evolution, based on observational or experimental tests, and verified by the predictions made. Also, contrary to a widespread opinion and current active programs regarding the unification of all the fundamental forces of physics in a single final theory, based on string theory, I argue that this unification is generally unlikely, and it is not possible anyway for a unification to be developed based on current theories of quantum gravity, including string theory. In addition, I support the views of some scientists and philosophers that currently too much resources are being consumed on the idea of developing quantum gravity theories, and in particular string theory, to include general relativity and to unify gravity with other forces, as long as science does not impose such research programs. -/- DOI: 10.13140/RG.2.2.35350.70724 . (shrink)

Evoluția testelor gravitaționale dintr-o perspectivă epistemologică încadrată în conceputul de reconstrucție rațională al lui Imre Lakatos, pe baza metodologiei acestuia a programelor de cercetare. Perioada evaluată este foarte vastă, începând cu filosofia naturală a lui Newton și până la teoriile gravitației cuantice din zilele noastre. Pentru a explica mai rațional evoluția complexă a conceptului de gravitație din ultimul secol, propun o extindere naturală a metodologiei programelor de cercetare pe care o folosesc apoi pe parcursul lucrării. Consider că această abordare oferă (...) o nouă perspectivă asupra modului în care au evaluat în timp conceptul de gravitație și metodele de testare a fiecărei teorii a gravitației, prin observații și experimente. Argumentez, pe baza metodologiei programelor de cercetare și a studiilor oamenilor de știință și filosofilor, că actualele teorii ale gravitației cuantice sunt degenerative, datorită lipsei dovezilor experimentale pe o perioadă îndelungată de timp și a auto-imunizării împotriva posibilității falsificării. Mai mult, în prezent este în curs de dezvoltare un curent metodologic care atribuie un rol secundar, neimportant, verificărilor prin observații și/sau experimente. Din această cauză, nu va fi posibilă o teorie completă a gravitației cuantice în forma actuală care să includă la limită relativitatea generală, întrucât teoriile fizice au fost dintotdeauna ajustate, în decursul evoluției lor, pe baza testelor observaționale sau experimentale, și verificate prin predicțiile făcute. De asemenea, contrar unei opinii răspândite și a unor programe active actuale privind unificarea tuturor forțelor fundamentale ale fizicii într-o singură teorie finală, pe baza teoriei corzilor, argumentez că este puțin probabil în general să se realizeze această unificare, și nu este posibil oricum ca unificarea să se elaboreze pe baza teoriilor actuale ale gravitației cuantice, inclusiv prin teoria corzilor. În plus, susțin punctele de vedere ale unor oameni de știință și filosofi că în prezent se consumă mult prea multe resurse pe ideea dezvoltării teoriilor gravitației cuantice, și în special teoria corzilor, care să includă relativitatea generală și să unifice gravitația cu celelalte forțe, în condițiile în care știința nu impune astfel de programe de cercetare. -/- DOI: 10.13140/RG.2.2.14582.75842 . (shrink)

We discuss scientific realism from the perspective of modern cosmology, especially primordial cosmology: i.e. the cosmological investigation of the very early universe. We first state our allegiance to scientific realism, and discuss what insights about it cosmology might yield, as against "just" supplying scientific claims that philosophers can then evaluate. In particular, we discuss: the idea of laws of cosmology, and limitations on ascertaining the global structure of spacetime. Then we review some of what is now known about the early (...) universe : meaning, roughly, from a thousandth of a second after the Big Bang onwards. The rest of the paper takes up two issues about primordial cosmology, i.e. the very early universe, where "very early" means, roughly, much earlier than one second after the Big Bang: say, less than 10^{-11} seconds. Both issues illustrate that familiar philosophical threat to scientific realism, the under-determination of theory by data---on a cosmic scale. The first issue concerns the difficulty of observationally probing the very early universe. More specifically, the difficulty is to ascertain details of the putative inflationary epoch. The second issue concerns difficulties about confirming a cosmological theory that postulates a multiverse, i.e. a set of domains each of whose inhabitants cannot directly observe, or otherwise causally interact with, other domains. This again concerns inflation, since many inflationary models postulate a multiverse. For all these issues, it will be clear that much remains unsettled, as regards both physics and philosophy. But we will maintain that these remaining controversies do not threaten scientific realism. (shrink)

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...) novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions---by no means meant to be canonical or exhaustive---one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory. (shrink)

We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the cosmological constant. This possibility leads to a finite, bouncing unitary cosmology. Whereas the usual Wheeler–DeWitt cosmology generically displays pathological behaviour in terms of non-finite expectation values and non-unitary dynamics, the finiteness and unitarity of our model are formally guaranteed. For classically singular models (...) with a massless scalar field and cosmological constant, we show that well-behaved quantum observables can be constructed and generic solutions to the universal Schrodinger equation are singularity-free. Key features of the solutions of our model include a cosmic bounce due to quantum gravitational effects, a well-defined FLRW limit far from the bounce, and a super-inflationary epoch in the intermediate region. Furthermore, our model displays novel features including: i) superpositions of values of the cosmological constant; ii) a non-zero scattering length around the big bounce; and iii) bound ‘Efimov universe’ states for negative cosmological constant. The last feature provides a new platform for quantum simulation of the early universe. A companion paper provides detailed interpretation and analysis of particular cosmological solutions. (shrink)

I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects living in infinite-dimensional spaces, working through many examples from cosmology. I focus on the relation of topological to measure-theoretic notions of and relating to probability, how they diverge in unpleasant ways in the infinite-dimensional case, and are even difficult to work with on their own. Even in cases where an appropriate family of spacetimes (...) is finite-dimensional, and so admits a measure of the relevant sort, however, it is always the case that the family is not a compact topological space, and so does not admit a physically significant, well behaved probability measure. Problems of a different but still deeply troubling sort plague arguments about likelihood in that context, which I also discuss. I conclude that most standard forms of argument used in cosmology to estimate the likelihood of the occurrence of various properties or behaviors of spacetimes have serious mathematical, physical and conceptual problems. (shrink)