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2.1. The universe: a well defined physical system?

Sciences or branches of science are classified by the subject investigated, or by the methods of investigation used. Thus, cosmology could be called "cosmophysics" in parallel with geophysics or solid state physics because its subject is the cosmos. In this spirit, in dictionaries, cosmology is defined as the general science of the universe [2], the science of the physical laws of the universe [3] or, as the Oxford Companion has it: "the study of the entire Universe" ([4], p. 61). A textbook tells us: "In cosmology we try to investigate the world as a whole and not to restrict our interest to closed subsystems (laboratory, Earth, solar system etc.)" [5]. The world as a whole, though, is not readily accessible, empirically. Whether bootstrap definitions like the universe is "the largest set of objects (events) to which physical laws can be applied consistently and successfully" [6], or formulations as "the universe means all that exists in a physical sense" ([7], p. 1) are more helpful, is a matter of taste. Once in a while, even a religious flavour is added when the universe is "usually taken to mean the totatility of creation." ([8], p. XV).

In this situation, scientists provide qualifying attributes, and point to subfields of cosmology linked with them [7]): the observable universe, the visible universe, the physical universe, the astronomical universe [9], the astrophysical universe [10]. Although, at present the biosphere is not included in cosmology, by some of these attributes it is not strictly ruled out. In order to be able to do physics, an idealized subsystem of "all that exists" must be selected. A preliminary definition, i.e., "we understand the universe to be the largest presently observable gravitationally interacting system", would satisfy the needs of the practizing cosmologist. 3 From the point of view of epistemology, such a definition is hardly acceptable, though. The observable universe changes permanently, because the domain of nature observable to us depends on the power of the available measuring instruments. Consequently, a further definition of the "observable universe" reads as "what in principle we can observe" ([4], p. 314). Cautious authors have avoided the word "universe" altogether in favor of expressions like "the metagalaxy" [11], "distribution of matter on the largest scale" [12], or "structure on a large scale" (cf. [7]).

In spite of this situation, most cosmologists seem not to worry about the domain of application of their theories: in the wake of time they expect to find out. They take it for granted that the physical system "universe" is as meaningful as the alterable and touchable physical systems investigated in the laboratory. 4 Possibly, the cosmos is definable only in the sense of a mathematical limit process. Or, as an ontological construct: "the largest inextendible entity". Progress of research seems not to be hampered by this attitude. 5 In comparison, the concept of elementary particle is accepted in the sense of the smallest indivisible entity. At first, it should have been the atom, then the nucleus and, presently, it is the quark - with no end of further subdivisions in sight. An approximative definition of the universe as a physical system may well be the only one allowed to physicists; however, there is the danger that the epistemological background gets out of sight. In fact, particularly in quantum cosmology and in approaches related to string theory, the universe is treated as an entity resembling more a particle among other particles than the totality of gravitationally interacting masses on the largest scale (Cf. also sections 2.1.1 and 5.3). In a way, methodologically, cosmophysics is opposite to phenomenological thermodynamics. There, valid laws are formulated without the need of knowing the detailed microscopical structure of matter. In cosmophysics, until recently (dark energy!) we were dealing with the detailed knowledge of structured parts of a system unknown in its totality.

If cosmology were just a branch of applied mathematics we could define it as the study of the global properties of "cosmological solutions" of certain field equations, notably Einstein's (cf. [14]). We would then include singularities (e.g., at the big bang) as boundary points of the Riemannian manifold representing the universe. However, the qualification of an exact solution as a model for the cosmos still would have to be made by borrowing ideas from physics; for example, by the kind of isometry group to be assumed. Possibly then, homogeneous and isotropic cosmological models with compact space sections of negative curvature would have to be discarded because they admit only a 3-parameter isometry group, globally [17]. 6 The cosmological models of applied mathematics which, by careless use of language sometimes were called "cosmologies" ([22], [23], [24]) or "universes" ([25], [26]), need not have any relation to the world outside of our brains. This point is not a side issue: in the "multiverse scenario" no distinction is made between what is a mental construct and what, by its relation to empirical data, can be accepted as some kind of "reality" external to our mind, cf. section 5.3.

2.1.1. A mathematized historical science?

With astronomy, cosmological research shares the situation that its object, the universe, or parts of it of cosmic relevance, have to be observed at a space-time distance, measured on and inside the past lightcone from a tiny part of the Earth's (or the solar-system's) worldline. Experiments cannot be carried out for observing effects. Observational cosmology may be compared to geological, palaeontological or archeological field work: deeper and deeper strata of the past are excavated, with the difference to palaeontology and archeology being that the present state of the objects observed is unknown. Cosmological theory does not describe a museum of relics but a dynamical system. Also, for cosmology, better mathematical models exist.

This historical aspect is not the full story, but it shows up in many ways; one of them being the transformation of the concept "prediction". In cosmology, without exception, prediction is a conclusion from present observations to past times or, vice versa, after hypothetical input for past times, to consequences for the present. In slightly altering a statement of Friedrich Schlegel (who directed it toward historians): cosmologists are prophets for the past. In physics proper, prediction means the foretelling of a future state from conditions given now. The social usefulness of natural science (and technology) rests on this regular meaning of prediction. Certainly, cosmological models can be used to make exact calculations toward the future [27], [28]. For cosmological time scales these calculations are pointless, however, because they cannot be validated by observational tests: Will any of them be preserved for a test in ~ 106 years? Even if cosmological theory could provide us with a reliable description of the past, its validity for the future cannot be probed; it is a consequence of continuity assumptions for the mathematical equations of theoretical cosmology. If the precision of, say, spectroscopic measurements could be increased to the extent that the changes in redshift of distant objects can be monitored over a time-span within our lifetime, then extrapolations applicable to the motion of the objects, for the near future only, will become possible. In "make-believe cosmology", the "ultimate fate of the Universe" is broadly discussed with future events timed with little reservation (cf. 5.3).

A sober physical and philosophical assessment of a "lack of predictability in the real universe" is given by ([29], p. 61).

Nowadays, the word "prediction" is used by most physicists working in cosmology as meaning "a consequence of" without any implication of linking the present to the future. This can become rather quixotic as in: "[..], a fundamental discreteness of spacetime at the Planck scale of 10-33 cm seems to be a prediction of the theory [..]."

2.1.2. Other features peculiar to cosmology

A characteristic feature of the universe, once believed to be important, is its uniqueness: one and only one such physical system ("the world as a whole") can be thought of as given to us. Unfortunately, with the advent of quantum cosmology and superstring theory, a semantical erosion of the word "universe" has begun. Already two decades ago, we had been asked "How many universes are there?", when authors investigated "a dilute gas of universes" or a "single parent universe ... in a plasma of baby universes" [30]. We were approached to "suppose universes are emitted from t = 0 like photons from an antenna" [31]. At the time, it remained a miracle, though, what kind of tangible receptacle could house or receive multiple universes. By now, this problem seemingly has been fixed by the introduction of the concept "multiverse" (Cf. section 5.3).

If the uniqueness of the universe is accepted, why then is this system so special? Isn't the Earth unique, too? True, as far as its individuality is concerned. But the Earth is just one of the planets in the solar system and one of billions more conjectured around other stars (exoplanets). 7 It gets its individuality by comparison with other planets. In contradistinction, is there an empirical or a conceptual way of comparing "our" universe to "others"? 8 In speculations of past years, statistical methods were applied to a set of "universes" residing in the mind in order to get a handle on the values of fundamental constants of nature [32].

As a consequence of the uniqueness of the universe, specific cosmic laws cannot obtain [33]. It is not excluded that new physical laws will be discovered while we try to scientifically describe the cosmos. Such laws, however, will refer to properties of parts (subsystems) of the universe and to relations among them.

Can theories applying to a single object be falsified? The example of the steady-state cosmological model seems to show that falsification is possible for statements of cosmological theory, because observations made now are observations of past states of the universe. Yet, as the complex attempt at a revival of the steady-state model shows [34], some caution is in order. This, again, indicates that cosmology could be interpreted as kind of a mathematized historical science: with falsification meaning nothing more than that our interpretation of the historical record has been mistaken and must be revised.

2.1.3. Initial conditions

The Einstein-field equations for the cosmological model being hyperbolic partial differential equations, a Cauchy initial value problem with given initial data must be solved in order that we may arrive at a unique solution. An additional chain of argumentation or even a theory must be developed by which the initial data actually in effect for the universe as we observe it are picked out from among the imagined set of all possible initial data. Thus cosmogony, the theory of what brought the cosmos into being, and cosmology are inseparable 9. The rise of quantum cosmology indicates an attempt of bringing cosmogony into the reach of science (Cf. 5.2).

Already within classical theory, attempts had been made to understand homogeneity and isotropy near the big bang [37], [38]. R. Penrose suggested to assume homogeneity of space - corresponding to a low value of entropy - as an initial condition. He tentatively used the Weyl tensor as a measure of the entropy and required it to vanish at singularities in the past [39], [40], ([41], p. 344). Moreover, in this context, various anthropic principles ([42], [43] have been invoked since their first formulation, and are used even heavier, today. 10 In fact, within make-believe cosmology, the search for a rationale for the initial data required for the universe to be as it appears to be, seems to be a main motivation.

As an aside: a related question is whether observation of the physical system "universe" will permit, in principle, a reconstruction of its initial state. Even for as simple a system as the solar system such a task is rather difficult. From what can be learned from deterministic chaos and, in view of the possibility that the Einstein field equations need not be an ever-lasting foundation of cosmophysics, particularly for what happened right after the big bang, we should remain reserved in this matter. Fortunately, for the standard cosmological model, initial data for the very beginning of the universe (at the big bang) are not needed. Nevertheless, initial data are required at the beginning of the inflationary phase. These may be guessed and validated in the sense of being consistent with what is derived theoretically and then observed (cf. 4.2).

The fact that we need initial, not final conditions reflects the open problem of the arrow of time: how to derive the unidirection of time when the basic equations are time-symmetric? Is it linked to the "collapse of the quantum wave function"? ([29], p. 76; cf. however [44].)

2.2. Cosmological questionaire

With the beginning of research in cosmology a list of general questions arose:
- Is space (defined by the distance range between gravitating bodies) of finite or infinite extension? 11

- Is time (defined by the duration of certain systems as compared to others) of finite or infinite duration in the future, in the past?

- How does cosmic dynamics look (phases of accelerated and/or decelerated expansion, structure formation, etc.)?

- What is the matter content of the universe? In the form of baryons, of radiation (zero mass particles), of dark matter? What is dark matter made from?

- Is a non-vanishing cosmological constant needed?

If the system were finite in space and in past time, we might ask for the total mass (energy), angular momentum, electric charge, etc and the age of the universe. The last concept is reasonable only if all parts of the cosmos can be parametrized by one single time parameter. In case there is a dynamics, the initial state of the universe and its evolution in time are of interest. Numerous further questions will arise within the three pieces of cosmological modeling to be briefly discussed below. Some believe that, by the presently accepted cosmological model (ΛCDM), many of these questions have been brought nearer to an answer (Cf. section 3.3).

3 Gravitation is the dominant interaction on the largest scales. On smaller scales, all other interactions come into play. Back.

4 Untouchable physical systems as the Sun, a star, a galaxy exert direct sensorial reactions on us. The universe does not. Back.

5 In this spirit, in recent monographs the physical system "universe" remains undefined (cf. [13]). Back.

6 Cf. also, cosmological models with multiply connected space sections ([18], [19], [20], [21] Back.

7 The search for exoplanets with parameters close to those of the Earth may form a link to the biosphere. Back.

8 Of course, cosmological models can be compared with each other - on paper, though. Back.

9 The assumption of temporal closedness of the universe is one escape route in sight. With its painful consequences for causality and pre-(retro-) dictability, the idea has not yet been taken seriously. The idea of a cyclic universe with multiple beginnings and ends also has been proposed since antiquity. For recents proponents with very different suggestions, cf. [35], [36]. Back.

10 The debate is still going on whether anthropic principles are useful as a selection principle with an exploratory value, or just express a demand for self-consistency of the cosmological model. Back.

11 The property of being infinite refers to the mathematical model. It has no observational meaning. Back.

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