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We will 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 (Section 2.1). Then we set aside the traditional methodological worry that cosmology cannot be a science, because, it is alleged, there cannot be laws of cosmology (Section 2.2). Finally, we review some limitations on ascertaining the structure of any universe described by general relativity (Section 2.3).

2.1. Scientific realism, and how cosmology bears on it

We take scientific realism to be the doctrine that most of the statements of the mature scientific theories that we accept are true, or approximately true, whether the statement is about observable or unobservable states of affairs. Here, "true" is to be understood in a straightforward correspondence sense, as given by classical referential semantics. And, accordingly, scientific realism holds our acceptance of these theories to involve believing (most of) these statements - i.e. believing them to be true in a straightforward correspondence sense. This characterization goes back, of course, to van Fraassen (1980: 7-9). It is not the only characterization: judicious discussions of alternatives include Stanford (2006: 3-25, 141f.) and Chakravartty (2011: Section 1). But it is a widely adopted characterization-and will do for our purposes.

We are scientific realists in this sense. We concede that to defend this position in general requires precision about the vague words "mature", "accept", "observable", "true" and (perhaps especially) "approximately true". But we will leave this general defense to more competent philosophers (the other Chapters in this volume, and e.g. Psillos (1999, 2009)). Our theme is, rather, the relations between scientific realism and cosmology; and our main claims about them, in particular that cosmology gives no trouble to scientific realism, will not need such precision.

At first sight, this theme can seem unpromising, or at least limited. For scientific realism is a general philosophical doctrine; so one naturally expects to assess it by distinctively philosophical arguments. And at first sight, this suggests that cosmology, or indeed any science, cannot be expected to help in the assessment: a science's results, theoretical and observational, can hardly be expected to determine what our attitude to these very results (or other scientific results) should be. So it can seem that our theme is merely a matter of cosmology providing examples of scientific claims and theories that illustrate the philosophical theses of scientific realists - or perhaps, of their various opponents: in short, a matter of cosmology providing case-studies for philosophy of science.

We think there are two main replies to this skepticism. In short, they are as follows. (1): Cosmology providing case-studies can be a rich theme, not a limited one. (2): The distinction between the philosophical and the empirical is not as sharp and straightforward as this skepticism assumes; and in fact cosmology raises various issues that bear on scientific realism - not by cosmology's results straightforwardly illustrating it (or threatening it), but by cosmology prompting a general philosophical question (or a whole line of thought) about it. We shall first say a little about (1); and then turn to (2) - to which most of the paper is devoted.

(1): Obviously, a case-study can be rich in its philosophical morals. But modern cosmology, with its truly stupendous knowledge claims, prompts a more specific point. Cosmologists nowadays claim to have established, for example, that a second after the Big Bang, the entire material contents of the universe we now see were confined in a dense fireball, with a temperature of about 1010 K and a density of about 2000 kilograms per cubic centimeter. Hearing this, surely every philosopher (whether a scientific realist or not!) feels a school-child's thrill - quickly followed by worrying how we could ever know such a proposition?

Our own view is that the cosmologists are right. That is: this particular claim, and countless other claims about the overall history of the universe from about the one-second epoch onwards, are now, and will forever remain, as well established as countless other scientific facts, e.g. that plants photosynthesize and that insulin has fifty-one amino acids.

In Section 3, we will briefly defend this scientific realist view of the results of modern cosmology. But we admit that the general task of assessing how scientific realism fares in today's cosmological theories would be very ambitious: by no means, an unpromising or limited endeavor. Indeed, it would be too ambitious for us: we will duck out of a general defence of our form of scientific realism for today's cosmological theories. For it would involve two major projects. One would have to first define what parts of these theories are indeed "mature and accepted". Then one would have to argue that most of these parts are "true, or approximately true" in a correspondence sense, whether they are about observable or unobservable states of affairs. These projects outstrip both our knowledge of cosmology, and (a rather different matter) our knowledge of what is the state of play in cosmology: i.e. what the community of cosmologists regards as accepted.

To illustrate the substantial questions that arise here, we mention the obvious topics: dark matter, and dark energy. (Ruiz-Lapuente (2010) is a fine collection, including both observational and theoretical perspectives; Massimi and Peacock (2015) is an introduction for philosophers.) We would say-along with most cosmologists, of course - that:

(i) both of these are known to exist, and indeed known to dominate the matter-energy content of the universe; but

(ii) they are not observable (at least: not yet!), and their nature is wholly unknown.

Both (i) and (ii) obviously raise questions of both physics and philosophy. Thus: in what sense are dark matter and dark energy known to exist, yet unobservable (at least: not yet "directly observable")? And does our present evidence for them warrant taking our present statements about them to be true, in a correspondence sense-even while we admit, à la (ii), that their nature is wholly unknown?

(2): But even without undertaking (1)'s ambitious task of assessing how scientific realism fares in today's cosmological theories, there is much to discuss under the theme of "scientific realism and cosmology". For the distinction between the philosophical and the empirical is not crisp or straightforward - as is obvious from all modern philosophy of science. (Here it is usual to cite Quine (1953). But we maintain that Quine was unfair to Carnap, and that there are much more nuanced treatments of the relation between the philosophical and the empirical, and between the analytic and the synthetic; cf. Putnam (1962), Stein (1992, 1994).)

And indeed, there are various issues in cosmology, that - rather than straightforwardly supporting or threatening scientific realism - instead prompt a question (or a whole theme) about it. We will first (Section 2.2) set aside one such theme, about the role of laws in cosmology, since we think that nowadays it is a non-issue - as do most cosmologists, and philosophers of cosmology. Then we will review some theorems in general relativity suggesting we cannot know the global structure of spacetime (Section 2.3). As we will see, this gives a different perspective on the familiar philosophical theme of under-determination of theory by data, viz. by emphasizing the need, not just to obtain data, but to gather it together. Then in Section 3f., we will see how cosmology threatens the usual philosophical distinction between (i) under-determination by all data one could in principle obtain, and (ii) under-determination by all data obtainable in practice, or up to a certain stage of enquiry. (Following Sklar (1975: 380f.), (ii) is often called `transient under-determination'.) For data about the early universe is so hard to get that what is not obtainable in practice looks very much unobtainable in principle!

2.2. No laws of cosmology? No worries

There is an obvious "one-liner" objection one might raise about the idea that cosmology is a science: as follows. Since there is, by definition, only one universe, any putative laws of cosmology could have only one instance. 1 But laws are usually taken to be, or at least to imply, suitable true generalizations: where what counts as `suitable' is disputed, but is usually taken to imply having many more instances than just one! 2 So if a science aims to formulate laws, it seems that cosmology cannot be a science.

The answer to this objection is clear. It is that cosmology can perfectly well be a science, without formulating, or aiming to formulate, even one law whose instances are universes. We say this, not because (as some philosophers maintain, e.g. Giere (1999)) science in general does not need to formulate laws, and need only formulate models: but because the laws of cosmology can just be the laws of the various physical theories that describe parts of the universe. Thus there is an ambiguity in a phrase like "a law governing a universe", and similarly, in claims like "cosmology formulates laws governing universes". This can mean: either "a law whose instances are universes", in which case we reject the claim; or "a law whose instances are (as in other sciences) parts of the universe (i.e. objects, events, states of affairs), but which is called "a law governing a universe" because it is important in describing and-or explaining the spatially and temporally very large-scale features of the universe, which are the business of cosmology" - in which case we accept the claim. In short: the fact that cosmology has the whole universe as its subject-matter - since it aims to describe and explain the very large-scale features of the whole universe - is perfectly compatible with its laws being the laws of the various local physical theories: such as, in present-day cosmology, the laws of the various quantum field theories, the various theories of statistical mechanics and hydrodynamics, and special and general relativity.

There is a good analogy here between cosmology and geology. Both have a special subject-matter - the universe and the Earth, respectively - about which they aim to describe and explain, not every feature, but certain large-scale features. To do this, they only need laws governing the parts of their subject-matter relevant to their descriptive and explanatory aims: they do not need laws whose instances are universes, or Earths. Thus cosmology is no more impugned as a science by the existence of only one universe, than geology is by the existence of only one planet Earth (Cleland 2002, Butterfield 2012: 4-7). (Agreed: with the discovery of exoplanets, `geology' might come to mean the science of all planets, or of all Earth-like planets. But the analogy remains good, with the current meaning of `geology'.)

We said that this answer to the objection is clear. But we should note that some sixty years ago, the objection was actively discussed. This was because it was entangled with another more specific debate, about whether laws could describe a putative origin of the universe (cosmogony); and this debate was vivid, and involved cosmologists, because it related to the rival claims of the Big Bang and steady-state theories-the latter of course denying that there was such an origin. Thus if you held both that laws could not describe an origin of the universe, and that science aimed to formulate laws, then you would be minded to favor the steady-state theory, since it side-stepped this apparent limitation on science.

Besides, this debate involved other questions, which again relate to the nature and role of laws in cosmology. One question, more philosophical than physical, concerned cosmogony in general: is the idea of an origin of the universe, i.e. a beginning of time, coherent? This had of course long been struggled with by philosophers, including Aristotle and Kant. A second question was closer to physics: how if at all could we justify the powerful, simplifying symmetry principles that were imposed on our cosmological models? This second question was closely related to the Big Bang vs. steady-state debate, since it took two more specific forms, one for each side of the debate. Namely:

(1): How could an advocate of the Big Bang justify the cosmological principle (CP) of the Big Bang (Friedmann-Robertson-Walker: FRW) models? (The CP requires that on sufficiently large length scales, the universe is spatially isotropic and homogeneous.) And:

(2): How could a steady-state theorist justify strengthening the CP's requirements, by imposing the perfect cosmological principle (PCP): which added to spatial isotropy and homogeneity, the requirement of time-constancy-and so forbad an origin of the universe?

Obviously, if one is faced with trying to justify such symmetry principles, it is tempting to seek a general argument: for example, along the lines that: (i) the aims of science, or the formulation of laws of nature, or some similar general goal, require or presuppose that "Nature is uniform"; and (ii) this last requires spatial and-or temporal "uniformity", in a precise sense such as spatial isotropy, and spatial and-or temporal homogeneity.

So much by way of sketching the scientific, and philosophical, debates in cosmology some sixty years ago. To close this discussion, it suffices to note that these debates died away after the mid-1960s, owing to the refutation of the steady-state theory by the discovery in 1964 of the cosmic background radiation (CMB), the "echo" of the primordial fireball described by the Big Bang theory. Accordingly, the original objection above, that cosmology cannot be a science, also died away. Indeed, the fact that the CMB should still be detectable was deduced already in 1948 by Big Bang theorists in their model of early-universe nuclear physics-but the prediction was forgotten about. Besides, this now-famous episode is itself a striking case of this Subsection's main point: that cosmology can manage perfectly well as a science, while invoking only the laws of local physical theories. 3

2.3. Ascertaining the global structure of spacetime?

We turn to reviewing some theorems (by Manchak (2009, 2011), building on ideas by Malament (1977) and Glymour (1977)) to the effect that, according to general relativity, one cannot know the global structure of space-time, even if one knew, as completely as one could, the local facts about the structure of spacetime (and also, the local facts about the state of matter and radiation).

Our review is brief, for two reasons. (1): These theorems have already been discussed from a philosophical viewpoint (e.g. Beisbart (2009: 181), Norton (2011: Sections 5,6), Smeenk (2013: Section 5, 628-33) and Butterfield (2014: Section 2, 59-60). (2): These theorems - despite their foundational interest - have not influenced the theoretical cosmology community. This is presumably because they are proved by a stupendous "cut-and-paste" construction on a given spacetime model: a construction which looks unphysical. 4

These theorems provide a different perspective on the familiar theme of the under-determination of theory by data: the idea that all possible observations might fail to decide which of a set of alternative theories is correct. For most philosophical discussions take "all possible observations" to mean the observations made by all observers, wherever situated in space and time, without regard to bringing the data together at some single point (or small spacetime region). But, on the other hand, cosmologists are continually confronted with the limits of our observational perspective on the universe: for example, that we can only now observe the past light-cone of Earth-now; and that direct observations by light, and other electromagnetic radiation, can go back only to the time (about 380,000 years after the Big Bang) when the universe first became transparent to radiation, i.e. to the last scattering surface, from which the CMB originates. (On the other hand, we should note, indeed celebrate, examples where we break previous limits to our observational perspective: the obvious current example being the recent detection of gravitational waves (Abbott et al. 2016).) Thus cosmologists will tend to be amenable to a definition of "all possible observations" which reflects such limitations - and these theorems work with just such a definition, albeit an idealized one.

Thus Manchak envisages that an observer at a point p in a spacetime M might ascertain, by suitable observations, the metric structure of the past light-cone I(p) of p: after all, information, such as measurement results, from within I(p) can reach p by a signal slower than light. But Manchak goes on to prove that such an observer cannot know much about the global structure of her spacetime, since many different spacetimes, with widely varying global properties, have a region isometric to I(p) (where "isometric" means "has the same metric structure as"). 5

More precisely: let us take a spacetime to be a manifold M equipped with a metric g, written (M, g). Then Manchak defines a spacetime (M, g) to be observationally indistinguishable from (M′, g′) iff for all points pM, there is a point p′ ∈ M′ such that I(p) and I(p′) are isometric. (The fact that this notion is asymmetric will not matter.) Then he proves that almost every spacetime is observationally indistinguishable from another, i.e. a non-isometric spacetime.

More precisely, the theorems incorporate (i) a mild limitation; and two significant generalizations ((ii) and (iii)).

  1. The theorems set aside spacetimes (M, g) that are causally bizarre in the sense that there is a point pM such that I(p) = M. (This last condition implies various causal pathologies, in particular that there are closed timelike curves.)
  2. But the theorems accommodate any further conditions you might wish to put on spacetimes, provided they are local, in the sense that any two spacetimes (M, g) and (M′, g′) that are locally isometric (i.e. any pM is in a neighborhood UM that is isometric to a neighborhood U′ ⊂ M′, and vice versa) either both satisfy the condition, or both violate it. (This means the theorems can probably be adapted to allow assumptions about the observer at p ascertaining facts about matter and radiation in I(p).)
  3. The theorems also prevent an observer's ascertaining some significant global properties of her spacetime. Manchak lists four such properties (2011: 413-414). (Three are "good causal behavior" properties: viz. that the spacetime be globally hyperbolic, inextendible and hole-free. We will not need their definitions. But it is worth noting the fourth property, spatial isotropy: there being, at every spacetime point, no preferred spatial direction. For this is crucial to the cosmological principle mentioned in (1) at the end of Section 2.2.) Thus the theorems imply: given a spacetime (M, g) with any or all of these properties, there is an observationally indistinguishable spacetime with none of them.

Thus Manchak's theorems (2009: Theorem, p. 55; 2011: Proposition 2) amount to the following.

Let (M, g) be a spacetime that is not causally bizarre, that satisfies any set Γ of local conditions, and that has any or all of the four listed global properties. Then there is a non-isometric spacetime (M′, g′) such that:
(a): (M′, g′) satisfies Γ, but has none of the four listed global properties; and
(b): (M, g) is observationally indistinguishable from (M′, g′).

What should we make of this endemic under-determination of global spacetime structure, even by perfect knowledge of the metric structure of the observer's past light-cone?

Though we cannot discuss this at length, we stress that previous philosophical commentators (cf. the references at the start of this Subsection) are skeptical of the obvious realist strategy, viz. condemning some of the observationally indistinguishable alternatives as unphysical. In particular, there seems no good general reason to break the under-determination by imposing the cosmological principle (CP: cf. (1) at the end of Section 2.2). For many models that violate CP are physically reasonable (Beisbart and Jung 2006: 245-250; Beisbart 2009: Section 5, 189f.; Butterfield 2014: Section 3, 60-65). More generally, on the topic of justifying cosmological models' symmetry principles, we recommend: (i) for a conceptual introduction, Ellis (1975); (ii) for recent work on the prospects for showing the universe to be homogeneous, Clarkson and Maartens (2010) and Maartens (2011).

However, as we also said: these theorems seem to have had no impact on cosmologists. As we will discuss in Section 3, cosmologists take themselves to have established, during the last fifty years, a detailed account of the evolution of the universe, from less than a thousandth of a second after the Big Bang onwards. (Here, "the universe" can be understood as the past light-cone of Earth-now; or better: as the future light-cone of the past light-cone of Earth-now.) This is an account which endorses CP, by using a FRW model for spacetime. While many details of this account remain to be understood (for example: the nature of dark matter and dark energy), there is a strong consensus about what has already been established: which we will describe in more detail in the next Section. Thus for cosmologists today, the live issues about under-determination relate - not to the global structure of the universe in the above sense (in particular, not to the rationale for CP), but - to:

(i) ill-understood aspects of the account after the first thousandth of a second, e.g. our present evidence not settling the nature of dark matter and dark energy; and

(ii) the history of the universe much (logarithmically!) before one second, especially the nature of the putative inflationary epoch, and the idea of a multiverse: i.e. issues about primordial cosmology: to which we will turn in Sections 4 and 5.

As mentioned at the end of Section 2.1, these issues will threaten the usual distinction between under-determination by all data one could in principle obtain, vs. by all data obtainable in practice.

1 Here and in the rest of this Subsection, "universe" can be taken as broadly as possible, so that the discussion also covers a cosmology that posits a multiverse: i.e. for such a cosmology, please read "universe" as "multiverse". Back.

2 As recounted in countless discussions of laws of nature: the dispute mostly concerns distinguishing laws from "accidents", i.e. merely accidentally true generalizations; and one tempting way to make the distinction is to say that in a law, the universal quantifier "all" is unrestricted in scope-which is meant to make for having many instances. Back.

3 For a history of the 1950s debate about laws in cosmology, cf. Kragh (1996: Section 5.2 219-51), who refers to philosophers such as Dingle, Harre, Munitz and Whitrow, as well as physicists. Massimi and Peacock (2015a) is a philosophical introduction. The prediction of the CMB was by Alpher and Herman (1948). For the history, cf. Kragh (1996: 132-5), Longair (2006: 319-23) and (more popular), Barrow (2011: 139-47), Singh (2004: 326-36, 428-37). Durrer (2015) is a technical review of (i) the history of investigating the CMB and (ii) the significance of the results, over the last fifty years. For a fine philosophical discussion of laws in cosmology, cf. Smeenk (2013: Section 4).

Note that nowadays `Big Bang' is ambiguous between three ideas: (i) the Big Bang theory, a very well confirmed theory of the evolution of the observable universe; (ii) the Big Bang fireball, i.e. the early conditions according to the Big Bang theory; and (iii) the Big Bang singularity, a hypothetical beginning of time which, as we will see in Section 5, is even more hypothetical in the context of eternal inflation. (Thanks to Anthony Aguirre for this point.)

Although we have no truck, and a scientific realist need have no truck, with Section 2.2's original objection: its second, more scientific, question-how can we justify cosmological models' symmetry principles?-is undoubtedly important. For the CP, we will return to this briefly in Section 2.3. Back.

4 But this lack of influence may well be unfortunate. As discussed in the references in (1), and in Manchak (2011): our defining a model by a cut-and-paste construction is no evidence at all that its features are not generic among general relativity's models. Back.

5 It is usual to write M for the spacetime, to indicate that it has the structure of manifold; and the minus-sign superscript in I(p) indicates the past, rather than future, light-cone. One might object that an observer could surely not ascertain so much as the metric structure of her entire past light-cone. But in reply: (i) this idealization only makes the theorem stronger, along the lines "even if you knew the metric structure of your entire past light-cone, you could not know the global structure"; (ii) there are theorems that support this idealization, e.g. about how to deduce the metric structure of the interior of the light-cone from information about its boundary (Ellis et al. 1985: Section 12). Back.

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