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 *H*_{0} claimed by the
ΛCDM-model (cf. section 3.3)
and the much lower value *H*_{0} = 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 ⋅ 10^{6} 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.

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) 10^{6} y by help of ^{10}Be / ^{9}Be-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} ×
10^{6} 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.