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We have seen that cosmology shows features of descriptive astronomy, explicatory astrophysics, palaeontology, history, mathematics, physics, and natural philosophy. As long as it is handled as cosmophysics, i.e., as an extension of physics from the galactic through the extragalactic realm to ever larger massive gravitating structures, it is part and parcel of physics proper. Questions relating to parts of the cosmic picture are debated like those in other branches of physics; an example would be given by the three methods for determining baryonic acoustic oscillations [62]. The evolution in (past) time is more problematic. As soon as a description of the universe ("the world as a whole") by a cosmological model is attempted, knowledge gained is of a "softer" character than knowledge from astrophysics and planetary science research. Synge's statement of the mid 60s, i.e., that "of all branches of modern science, cosmological theory is the least disciplined by observation" [178]), must be shifted nowadays to the inflationary model, quantum cosmology and to string theory, though. To what degree can we trust in cosmological modeling, to its more than merely descriptive imaging of the universe? In view of the necessary correction of the distance scale which occured in the 1960s, and of the sudden change from Λ = 0 to a non-vanishing contribution of the cosmological constant in the 1990s, it should come not as a surprise when scientists from other quarters will keep reserved, a little. This applies especially to the concept of dark energy.

6.1. The epistemic value of cosmology

The most characteristic feature of research in the natural sciences is the collection of precise empirical data and their connection by self-consistent theories. In consequence, technical applications, possible derivation of novel relations among the empirical data ("new effects") obtain as well as models of explanation and understanding for the systems investigated. It is essential that such explicatory models map, with a minimum of hypotheses, a larger piece of the network of relationships found in the external world into percepts of our mind. It is particularly important that we are lead, by such understanding, to new possibilities of qualitative or, better, quantitative experimentation/observation. In view of such demands, is cosmological theory represented by the ΛCDM-model simple, empirically well based and conceptually clear? It may be too simple as we will discuss in section 6.2.2. Parts of it, among them the large scale structure and cosmic background radiation, are empirically extremely well supported. Other parts are only very indirectly, e.g., the inflationary scenario. The part concerned with the era right after the big bang (quantum cosmology) has not yet come near an empirical foundation. Although the range of their validity is unknown, Einstein's equations, their homogeneous and isotropic solutions, the methods to deviate from them (perturbation theory), and the quest for initial conditions are conceptually very clear. This cannot be said of the big bang concept (origin of space and time?) or, rather, of the whole Planck era which is neither conceptually nor methodically under control. The concept of inflation is very clear, in principle, but hazy in its technical details, e.g., during reheating. An application of cosmology, beneficial for society, is the development of technology for the improvement of observational tools. Another very important one is the emergence of an understanding of the world ("Weltbild") independent of a particular society and its cultural background; it is owed to the disciplining force of the laws of nature.

6.2. The explanatory value of cosmology

Nevertheless, one might still worry about the significance of knowledge produced by cosmological theory, in particular, about the "explanatory power" of the standard model. The concept is used here in the sense of a convincing reduction to, or a link with simpler established facts. Have we now understood, beyond a mere description, why, in the modeled evolution of the cosmos, first an extreme global thinning of matter against gravitational attraction had to occur while, subsequently, massive superstructures arose from local condensations against global expansion? Is it clear why the expansion of the universe after an explosive phase with deceleration parameter q = -1 slowed down to q ≃ 1/2 and then steped up again to today's q = -0.7 ± 0.1 from type Ia supernovae? Playing it all back to stochastic perturbations of a quantized scalar field of unknown origin and uncertain dynamics compensating gravitational attraction by its negative pressure does not explain enough. The more so as the initial values have to be put in by hand as long as no convincing theory for the era before inflation is available.

It is difficult, from the theoretical point of view, to make transparent the web of assumptions, logical deductions, and empirical input spun by cosmologists if the explanatory value of the cosmological model is to be evaluated. Hypotheses of differing weight are intermingled as, for example, the classical, relativistic, nonlinear theory of gravitation, nonrelativistic thermodynamics and kinetic theory for massive particles in perturbation theory, the relativistic Einstein-Boltzmann equation for the fluctuations of photon and neutrino fields, the linear theory of density fluctuations with non-linear complements, quantum field theory in curved space (during inflation), quantization of gravitation, nuclear physics (primordial nucleosynthesis) and high energy physics (baryogenesis). Approximations are made whenever they are needed for a calculation with the aim of connecting theory and data.

Special case studies could bring more light. A presentation from which one might try to get an impression of the explanatory value of cosmological modeling are lecture notes by N. Straumann [179], although not written under this aspect. In them, all calculational steps from primordial quantum fluctuations until how they show up in the acoustic peaks of oscillating matter describing the anisotropy of CMB are taken. An 8-parameter description for density-, velocity- and metric perturbations is used within two different 2-fluid-models before (electrons, baryons, photons plus dark matter) and after recombination (electrons, baryons, dark matter plus photons). 41

The reliability of the empirical data also has to placed under scrutiny. There are ambiguities in the interpretation of observations of the large scale structure (redshift surveys) due to selection effects and the evolution of objects. 42 There still is a discrepancy between the value of the Hubble constant H0 claimed by the ΛCDM-model (cf. section 3.3) and the much lower value H0 = 62.3 ± 1.3 (± 4.0) based on the high-accuracy distance indicators of the astronomers [64]. Similar problems arise for the large angle scale in CMB, or temperature and noise fluctuations [181].

6.2.1. Comparison with other natural sciences

A juxtaposition of cosmology with other branches of natural science with the aim to compare their relative explicative strengths is meaningful only in part. Of special interest are disciplines with historical aspects like geology, geophysics and paleontology. There, the evolution of systems is also modeled, if only on shorter time scales than the cosmological ones. One could become inclined to believe that knowlegde about the Earth must be easier to obtain and be more secure than knowledge about past eras of the universe. Yet, this seems not to be the case. An example is the enigmatic solid inner core of the Earth, thought to be formed from small nickel-iron crystals. Apparently, it is not homogeneous as one might assume, but shows large scale structures and anisotropy found through seismic waves [182]. Explanations are still debated (existence of layers etc) but, unlike the anisotropies of CMB, it seems unlikely that those in the inner core can be explained by small perturbations to an isotropic Earth [183]. Scenarios about the making of an inner planetary core seemingly have not yet converged to an accepted standard one as the inflationary scenario has in cosmological theory.

Why is it that the physics of the Earth`s innermost core cannot be described as precisely (in terms of error bars) as the physics of the universe reflected by the concordance model? A tentative answer would be that the physics of the universe gets simpler the further we look back into the past. Simpler than solid state physics applied to the Earth with its many-body interactions, collective phenomena, phenomenological interactions, complicated phase transitions. This view is supported by the fact that the inner core of the gaseous Sun apparently is known much better. But, is it exluded that the apparent simplicity of the universe is due to the simplifying assumptions underlying the cosmological model and not an intrinsic feature of the cosmos? In fact, the ΛCDM-model including inflation is built in such a way that the imprints of inflation may be seen in CMB, but that the microwave background cannot show traces of the ensuing eras before the last scattering surface. A weaker argument might be that the rate of change in the cosmos, after the formation of large structure, is smaller than in geology. In the inner core of the Earth "one might expect to see changes on a human scale" [183].

A similar situation prevails in palaeontology, in which, as in cosmology, many disciplines like physics, geology, anatomy, technical mechanics, and biology work together. Here, the evolutionary history of the Earth including its biosphere is studied. As an example, fossils, say of feathered dinosaurs of various periods (in the range of million years duration), are compared. Phylogenetic trees are constructed with the help of mathematics. The discovery of an iridium-rich layer at the Cretaceous-Tertiary boundary [184] and the ensuing suggestion of an asteroid impact as its cause, were tentatively combined to unravel the mystery of the observed event of mass extinction (of the dinosaurs), ca. 65 ⋅ 106 y before the present. 43 Does this idea have an assimilable explicatory power as the idea of an inflationary period of the universe, even if it cannot be expressed within a mathematical model? Aren't the "standard candles" used in observational cosmology comparable to fossils? Perhaps, the success with solar nucleosynthesis led us to believe that we know more of the physics of supernovae millions of light years away than what is known about the touchable fossils of palaeontology.

6.2.2. Error bars

The statistical errors of a few percent given by "precision cosmology" are amazing (Cf. 3.3). These numbers are reliably calculated by the best methods available (after filtering and averaging of the primary data). Thus, on the one hand, they stand for the progress made in assessing the data. In this context, the increased use of methods of Bayesian statistics is notable [185]. On the other hand, how significant then is the uncertainty of ~ 1% for the age of the universe? It is roughly the same uncertainty as presented for the age of the Earth [186] or, for the material from which it was formed [187]. Should't the absolute dating become more and more precise, the less we go back in time? Yet, absolute (chronometric) dating in palaeo-anthropology tends to be no better than dating in cosmology: the first appearance of hominids is claimed to be (7.0 ± 0.2) 106 y by help of 10Be / 9Be-dating of the surrounding sediments [188]. An answer could be that the limits in accuracy are set by nuclear physics (radiometric dating), i.e., by a precise knowledge of half-lives and decay constants. The errors vary from 0.1%-1% (uranium) to ≤ 10% (potassium-argon). In addition, uncertainties from geochemistry (distribution of isotopes) and from isotope-chronostratography (changes in the environment needed for the calibration of radioactivity data) must be added. Dating errors in palaeo-anthropology thus cannot be much better than dating in primordial or stellar nucleosynthesis. For uncertainties in big bang nucleosynthesis cf. 3.1.1.

There is a discrepancy between the precision presently ascribed to cosmological parameters (errors of 1% to 10%) and the lack of qualitative knowledge. Quantitatively, the time of (photon) decoupling (via CMB) is set at 380081-5841+5843 y after the big bang (cf. [82], Hinshaw, G, Weiland, J.L. et al., p. 45, table 7). Can this compensate the fact that we know less about the much later formation-details of luminous galaxies near to us? Although it is widely believed that their nuclei house massive black holes, neither by theory nor by simulations, an understanding of black hole galaxy seeds has been reached [189]. The same holds for spiral galaxies with thin disks. The ΛCDM-model can give only a relatively crude picture of structure formation and evolution. But perhaps, this is the domain of astrophysics, not of cosmology. Simulations of galaxy formation and evolution have met with great success, cf. [190]. Similarly, the age at reionization is given to be 432-67+90 × 106 y. The hope is that plasma physics at that time has been understood well enough and that its consequences for CMB have been taken into account (cf. [191], [13], p. 407-409). For the cognitive value of a physical model numerical precision does not play the decisive role. However, numerical precision has to be taken dead serious for predictions into the future. The precise numbers produced by CMB within the ΛCDM-model are very relevant if alterations of the cosmological model will be attempted. However, they are as irrelevant to society with regard to the future as are the ages related to palaeontology. Progress of precision cosmology reflected by the narrowing of error bars may be of an intra-theoretical value, only.

41 In this work, it is assumed that dark energy does not contribute to the formation of large scale structures. Other authors wish to include dark energy perturbations during the matter dominated era [180]. Back.

42 It is notoriously difficult to get reliable distance measurements beyond redshift z = 1. Back.

43 This dating remains virtually unchanged since the 1960s. Back.

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