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The last fifty years have seen the triumphant rise of observational cosmology as a precision science. Looking back, the discovery in 1964 of the cosmic background radiation (CMB) was an iconic initial event. But at least as important was the subsequent use of satellites to make precise observations about parts of the electromagnetic spectrum that we cannot observe on earth: i.e. neither optical nor radio wavelengths. This of course includes the microwave wavelengths of the CMB itself: whose properties have been measured with ever-greater precision, probing ever more finely the early universe, by a succession of satellites: COBE, WMAP and Planck. This has also of course depended on inventing and developing sensitive yet robust instruments that can be reliably operated remotely, i.e. by radio signals: an extraordinary collaborative achievement of diverse disciplines, ranging from quantum optics to software engineering. And quite apart from the CMB, the last fifty years has witnessed various large and detailed observational programs, both terrestrial and by satellite. The eventual upshot of these observations, building up from countless precise measurements of many diverse quantities - relating not just to the cosmos as a whole but to the structure of stars and of galaxies - has been to give us a detailed overall history, not just of the evolution of the universe as a whole, but also of the formation of galaxies and the life-cycles of stars. Undoubtedly, we live in a golden age of cosmology!

This is not the place for a detailed review of these developments aimed at philosophers, fascinating though they are: both as regards the scientific methods used and the stupendous cosmic history thus inferred. We have already, in (1) of Section 2.1, ducked out of the attempt to say exactly which results of modern cosmology - which chapters of the overall story just mentioned - should count as "mature and accepted" and so, for we scientific realists, as approximately true in a correspondence sense. 6

But to set the scene for later Sections' discussions, we need to cite a few `bare bones' of the overall thermal history of the universe (Section 3.1). This will lead in to a brief defense of scientific realism in relation to cosmology (Section 3.2).

3.1. Four snapshots of the early universe ...

We have already mentioned that the properties of the CMB confirmed the idea of a primordial fireball described by the Big Bang theory. More precisely, the idea is that all the matter in the entire universe we can observe today was once, about 13.8 billion years ago, confined to a much smaller volume, at energies, temperatures and densities so high that atomic structure breaks down, and there is instead a "soup" of subatomic particles. This idea has been worked out in detail and with great quantitative precision, by combining various parts of established physics: the physics of how subatomic particles interact (comprising both the standard model of elementary particle physics, and nuclear physics); the general relativistic description of spacetime; and (relativistic) thermodynamics and hydrodynamics.

Agreed: as one considers earlier times, the energies (and temperatures and densities) get so high that discussion needs must go beyond established physics. But amazingly, established physics suffices to describe the fireball right back to about 10−4 seconds after the Big Bang! 7

We now spell this out a bit. Two preliminary points: in effect, the first is about space, and the second about time.

(1): We referred to "the entire universe we can observe today". Bearing in mind that light has a finite speed, so that we see more distant objects as they were at earlier times, the appropriate meaning of this phrase, and similar phrases like "the observable universe" is: the past light-cone of Earth-now. So the idea of a primordial fireball is that all the matter and radiation content of the past light-cone of Earth-now was once confined to a much smaller volume. 8

(2): It will be helpful (though difficult!) to think logarithmically, not arithmetically: to think, for example, that since the present time is about 1017 seconds after the Big Bang, the time t = 10−17 seconds before the Big Bang is as much before t = 1 second, as we are after it. Though this sounds blatantly wrong, the rationale for it is that, as every physicist knows, physics is a matter of scales, i.e. orders of magnitude. That is: if you change the object, or topic, or regime, you wish to describe by an order of magnitude, i.e. by a factor of about 10, you are liable to need a very different description: and even more likely if you change by two orders of magnitude, i.e. by a factor of about 100. This trend holds whether the quantity whose value you change is time, or distance, or energy or temperature: (indeed in quantum theory and relativity theory, these quantities are intimately related, so that changing one involves changing others). In particular, this means that when cosmologists puzzle over what was the state of (the matter and radiation now comprising) the observable universe, at say t = 10−6 seconds, or how physical processes changed as a result of the cooling between, say, t = 10−11 and t = 10−6 seconds, we should not accuse them of straining at gnats, i.e. of myopically concentrating on very transient matters which cannot matter very much. For, agreed: the universe was changing unbelievably rapidly (arithmetically speaking!); but the relevant processes change-and so our description must change-in crucial ways, depending logarithmically on the earlier time considered.

So here are some snapshots from the thermal history of the observable universe: four snapshots, in reverse chronological order, all corresponding to established physics. 9

(A). t = 1013 seconds: which is about 380,000 years after Big Bang. This is an important time: for at about this time, the universe first became transparent to radiation (by free electrons combining with nuclei to form atoms). So our direct observations by light, and other electromagnetic radiation, can go back only to this decoupling time tdec. (It is also known as the time of recombination: though all agree that combination would be a much better name, since the electrons and nuclei were not stably combined at any earlier time.) The temperature is about 3000 K (corresponding to an energy of ∼ 0.3 eV). (By way of comparison, the temperature at the surface of the Sun is about 6000 K). The size of the universe relative to its size today (as given by the appropriate ratio of the scale factor) is ∼ 10−3, and the mass density is ∼ 10−21 g/cm3.

(B). t = 10−2 seconds after the Big Bang. Temperature ∼ 1011 K (corresponding to an energy of ∼ 10 MeV). Nuclei form: i.e. at higher temperatures, they "melt" into their constituent protons and neutrons. The size of the universe relative to its size today is ∼ 10−11, and the mass density is ∼ 109 g/cm3.

(C). t = 10−6 seconds after the Big Bang. Temperature ∼ 1013 K (corresponding to an energy of ∼ 1 GeV). Protons and neutrons form: i.e. at higher temperatures, they "melt" into their constituent quarks.The size of the universe relative to its size today is ∼ 10−12, and the mass density is ∼ 1017 g/cm3.

(D). t = 10−11 seconds after the Big Bang. Temperature ∼ 1015 K (corresponding to an energy of ∼ 100 GeV). This is the temperature/energy above which the electromagnetic and weak forces are in a sense unified in the electro-weak force (viz. by the effective potential being SU(2)-symmetric), and below which they are distinguished by the Higgs mechanism. That is: this is the temperature/energy at which the Higgs mechanism works, producing an electro-weak phase transition. Since the discovery of the Higgs particle in 2012, this can be taken as the upper end of the confirmed energy range for the standard model of particle physics. That is: before t = 10−11 seconds, the energies are too high for us to be confident that the standard model applies. The size of the universe relative to its size today is ∼ 10−15, and the mass density is ∼ 1027 g/cm3.

We emphasize that this thermal history is by no means the only main claim of modern cosmology that is now firmly established. Other examples include our theories of stars and galaxies: for which one could, as in footnote 9, cite authoritative descriptions over several decades which largely agree with each other. But more relevant to us is the way in which the CMB, though very homogeneous and isotropic, has tiny irregularities whose structure (especially how their size depends on angle) gives detailed evidence about the interplay before the decoupling time, between gravitation tending to clump the matter, and radiation pressure opposing the clumping. This interplay links directly to parameters describing the universe as a whole, such as whether the average density is large enough for gravitational attraction to eventually overcome the expansion, so that the universe ends in a Big Crunch instead of expanding forever. In the last fifteen years, data about these irregularities gathered mostly by satellite projects like WMAP and Planck have been used to estimate these cosmological parameters, resulting in a striking concordance with estimates obtained by completely different methods. We will return to this topic in Section 4.

So much by way of citing some of modern cosmology's stupendous claims about the very early universe. Let us return to our warrant for believing them, and thus our defense of scientific realism.

3.2. ... as viewed by a scientific realist

Our main view is (as we said in (1) of Section 2.1) that indeed, cosmology has definitively established such stupendous claims as those cited at the end of Section 3.1. But we should add three clarifications to this realist credo. They expand on our basic point in Section 1, that while scientific realism claims, roughly speaking, "we can know, indeed do know, about the unobservable", it does not claim that "all the unobservable is known"; or even, "all the unobservable is knowable". 10

(1): A spectrum of reasonable credence: - Scientific realism enjoins us to believe propositions about the unobservable only when the evidence is sufficiently plentiful and varied. Of course, there can be no general statement of what would be "sufficient". And for cosmology, all parties admit that the evidence gets thinner as we consider earlier and earlier times, corresponding to ever-higher energies, temperatures and densities. As we mentioned in Section 3.1 (footnote 7 and snapshot (D)), it is common nowadays to take the boundary between known and speculative physics to be at about 10−11 seconds after the Big Bang (this time corresponding to the electro-weak phase transition). So for earlier times, observational data are so lacking and theory is accordingly so speculative, that one has to be agnostic.

But of course, there is a spectrum here: of credence, as well as times and energies. The standard model has indeed passed every test that experimental high energy physicists have subjected it to, in the forty years since its formulation in the mid-1970s; (culminating in the discovery of the Higgs boson in 2012). And the theories of nuclear physics, that describe the synthesis of nuclei from protons and neutrons (a lower-energy process occurring at about 10−2 seconds after the Big Bang) are even better confirmed than the standard model. But of course not every aspect of the standard model (or even of nuclear physical theories) has been confirmed: especially, its description of phenomena at the upper end of its (impressively wide) energy range. So a scientific realist might be cautious, and not believe the standard model's description of the very early universe, for times earlier than some cut-off time that is later than 10−11 seconds. For example, they might have a cut-off time as late as 10−2 seconds, or one second: thus being more cautious than we reported in footnote 7.

On the other hand, a less cautious attitude is also reasonable. Aspects of the standard model involved in `snapshots' (C) and (D) above, i.e. for t = 10−6 and t = 10−11 seconds, have been confirmed in recent terrestrial experiments.

(i): Corresponding to snapshot (C): in the RHIC (Relativistic Heavy Ion Collider) at Brookhaven, USA, protons in gold nuclei have been "melted" to produce a (very short-lived!) quark-gluon plasma; (for an experimental review, cf. e.g. Shuryak 2005). This means the quarks were liberated from their confinement inside a proton, after some 13 ×109 years: indeed, a long prison sentence!

(ii): Corresponding to snapshot (D): at the LHC (Large Hadron Collider) at CERN in 2012, the discovery of the Higgs particle lent credence to the mechanism, proposed in the standard model, whereby interactions with the Higgs field gives elementary particles their mass. Thus it would also be reasonable to take the standard model, even at the energies obtaining at t = 10−11 seconds, to be confirmed by terrestrial experiments: and to be a "mature and accepted" theory that earns our belief. So a scientific realist could take t = 10−11 seconds as the cut-off for credence.

To sum up: in the last forty years, we have been very fortunate, as regards both: (a) confirming the standard model in particle accelerators; and (b) successfully applying it to the early universe-whose enormous density makes it a very different regime from the near-perfect vacuum of an accelerator. 11

(2): Towards terra incognita: - But it is also reasonable to fear that this good fortune cannot continue! More precisely: we should expect that, however fortunate we may be in the future, as regards both (a) making observations and (b) developing theories, we shall never know all, or even much, about arbitrarily high energies and thus about arbitrarily early times. There are really three points in play here: two about high-energy physics, and one about cosmology.

(i): As regards making observations, we cannot expect to-we cannot afford to!-build particle accelerators that achieve arbitrarily high energies: or even energies much above those now attainable. (But we should also note, in a more optimistic tone, the power of human ingenuity and tenacity to make quantitative observations of the most arcane kind. The obvious current example is again the recent detection, culminating forty years of effort, of gravitational waves (Abbott et al. 2016): that is, the detection of distortions of spacetime on a length-scale of a thousandth of the diameter of a proton!)

(ii): As regards developing theories, we now realize (largely as a result of our modern understanding of renormalization, led by Wilson's work from the mid-1960s) that by and large, the most we can hope for is effective theories: i.e. theories that accurately describe phenomena that occur in a certain energy range, but are inaccurate for higher energies.

(iii): As regards cosmology, recall that "the Big Bang" is really a label for terra incognita. Formally, it labels a singularity of our theoretical descriptions, both the general relativistic description of spacetime (infinite curvature etc.) and the quantum description of matter and radiation (infinite energy, density etc.). But these infinities surely represent breakdowns of our theories, not physical realities. And as we consider higher and higher scales, of curvature, or of energy or density etc., we have no guarantee that we are capable of formulating an accurate theory for phenomena at those scales - or even that our basic concepts such as spacetime, and physical quantities like energy and momentum, apply at those scales. And bearing in mind that we need to think logarithmically: it is no solace to be told that this cognitive lacuna is over in a minuscule fraction of a second! 12

(3): Conceptual change: - Our realist credo is not intended to deny major epistemic ruptures, such as are often dubbed `conceptual change' and-or `meaning variance'. Progress in cosmology has of course involved such ruptures, in the process of establishing the present consensus about the universe's history after about a thousandth of a second: the outstanding example from twentieth-century cosmology is, no doubt, general relativity's description of spacetime as dynamical, and of the universe beginning in a singularity. And future research about that history will presumably again involve such ruptures. Looking ahead, the obvious putative examples are dark matter and dark energy. They are a major causal and structural aspect of the cosmic history revealed by modern cosmology: indeed, they dominate the mass-energy content of the universe. But their nature is not understood: and gaining that understanding may involve some kind of epistemic rupture. So agreed: we still have a lot to learn.

But a great deal is now established. In particular: we can be confident (albeit not certain!) about the thermal history of universe, as sketched in the four snapshots above. For we have very good physical reasons to believe that this history is robust (especially at times from about a thousandth of a second onwards) to whatever the dark matter and dark energy turn out to be.

6 So we here must set aside several topics that, independent of the general effort to assess how scientific realism fares in cosmology, would form excellent case-studies. For example: (i) the life-cycles of stars, for which cf. e.g. Chandrasekhar (1939), Kaler (2006), Ryan and Norton (2010); (ii) the sophisticated methods and instruments used e.g. to establish astronomical and cosmological distances, for which cf. e.g. Pasaschoff (1994), Rowan-Robinson (2011: Chapter 3) and Longair (2003: Chapter 18, 478-98; 2006, Chapters 7, 11, 13). Back.

7 We here take "about 10−4 seconds" as the "cut-off for credence", not because of a specific problem or controversy, but simply because reason and evidence do not dictate a unique cut-off: recall the discussion in (1) of Section 2.1. Certainly, 10−4 seconds is endorsed by some authorities; e.g. Rowan-Robinson (2011: 100), and forty years ago, Weinberg endorsed 10−2 seconds (1977: 5). But as we discuss below: it is also reasonable to be less cautious, since it is common nowadays to take the boundary between known and speculative physics to be at about 10−11 seconds (!) after the Big Bang as the cut-off (e.g. Earman and Mosterin 1999: 2). Agreed: it is also reasonable to be more cautious, even taking one second. Anyway, for the interests and purposes of philosophers, the scientific story is equally amazing when one is more cautious: say, withholding credence for times earlier than one second. And certainly it is not reckless for a scientific realist to endorse the story from about this time: one renowned expert says he is 99% confident of the story from one second onwards (Rees: 1997: 65, 17; 2003: 24, 31). Back.

8 Notice that on this usage, "observable" in "the observable universe" does not connote being macroscopic: the observable universe includes all physical objects and events in the past light-cone of Earth-now, no matter how microscopic. This usage was of course also in play in Section 2.3's idealization that an observer at p could "observe" metric structure on arbitrarily fine length-scales, albeit only within her past light-cone. Back.

9 Agreed, only the first two concern times later than t = 10−4 seconds: which in footnote 7, we took as the cut-off for credence. But recall that this choice was in the middle of the reasonable spectrum, from 10−11 seconds to one second: cf. also the ensuing discussion in the main text.

Another indicator of how well-established is this thermal history is the fact that authoritative textbook descriptions of it, written over the last forty years, largely agree with each other. Cf. for example: Sciama (1971: Chapters 8, 12-14), Weinberg (1972: Chapter 15.6, pp. 528-545), Wald (1984: 107-117), Barrow and Tipler (1988: 367-408, Sections 6.1-6.7), Lawrie (1990: 315-326), Longair (2006: 394-399), Weinberg (2008: 101-113, 149-173; Sections 2.1, 2.2, 3.1, 3.2). For fine popular accounts, cf. Weinberg (1977, Chapters 5,7), Silk (1989: Chapters 6 to 8), Rowan-Robinson (1999: Chapter 5), Silk (2006: 112-128). Back.

10 For a complementary discussion, cf. Butterfield (2012: Section 2.2). Back.

11 Our success in (b) depends on a striking feature of the theory of quarks and gluons, viz. asymptotic freedom: roughly, the strength of their interactions decreases at high density. Back.

12 For some more details, for philosophers, about point (ii), cf. e.g. Butterfield (2014a), Butterfield and Bouatta (2015). Point (iii) broaches the vast topic of our search for a quantum theory of gravity: for introductions aimed at philosophers, cf. e.g. Butterfield and Isham (2001), Rovelli (2007), Rickles (2008), and Dawid, this volume.

Point (iii) also broaches two more specific topics: (a) the need to scrutinize whether our concepts of space and time apply; cf. issue (2) in the list at the end of Section 1, and the work of Rugh and Zinkernagel: (b) the need to scrutinize the definition of, and the occurrence of!, singularities in general relativity. For (b) we recommend Curiel (1999). We also thank him for emphasizing that one should not blithely claim that quantum effects will efface singularities, or that singularities will not appear in an ultimate theory of quantum gravity. For notice that Wall (2013) shows that if the Generalized Second Law is valid, then there will necessarily be singularities even in regimes where quantum effects make themselves felt. Back.

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