The Cosmological Principles

7.01. How many cosmological principles are known?

In the first six chapters of this book, the six major cosmological principles were presented; some of them have many different formulations, and sometimes substantially different, even separately designated, versions. Thus, along with the six main principles, several minor ones were presented too, but only those closely related to them. In this short chapter I would like to introduce some of the other, less known principles. There have been many attempts to classify all the known or even all the plausible cosmological principles (e.g. Ellis 1975, 1984; Ellis, Harrison 1974). In this book I made use of the systematic review by Tadeusz Sierotowicz (1990) as a check list for ascertaining that any principle of interest had not been omitted. However, the order of the following presentation is not too systematic, just starting from the most particular and ending with the most general. Of course, it is debatable what is more and what less general.

7.02. The Lucretian Cosmological Principle

Titus Lucretius Carus (95-ca. 55 B.C.) was a poet rather than a philosopher or astronomer, but in his poetic works, particularly in his poem De Rerum Natura, he recapitulated and popularized the views of the Greek philosopher Epicurus (341-270 B.C.), providing a general view of the Universe, which is as follows.

In this and similar statements Lucretius maintains that the Universe is infinite in space and time and that there is no center of the Universe. All this is concordant with the Ancient Indian Cosmological Principle, but there is a new element, the proposition that the total amount of matter as well as of energy within the Universe does not change with time. The Ancient Indians believed that everything is subject to permanent change. Some cosmologists consider Lucretius a precursor of Copernicus (cf.: Jaakkola 1989) and his theses an anticipation of the Perfect Cosmological Principle, while others give his propositions the rank of an independent principle, the Lucretian Cosmological Principle.

It should be left to historians to clear up to what extent the propositions of Lucretius were original, what he had just repeated from Epicurus and his other predecessors, and what impact he had on his successors. From the point of view of cosmological principles, his is a variant of the Perfect Cosmological Principle with Hubble's constant equal to zero, as discussed in 5.7. As a matter of fact, the Perfect Principle produces only one model with three variants (according to the respective values of Hubble's constant: positive, zero, or negative). Since the Lucretian Principle corresponds to just one of the variants, it is a matter of individual opinion whether it is more proper to call it the Lucretian Cosmological Principle or the cosmological model of Lucretius, which happens to fit into the frames of one of the modern cosmological principles.

There can be found in historical treatises as well as in modern non-professional publications of astronomy some other pictures (models) of the "world system" (Universe) built upon personal views. Hardly ever are such philosophical views regarded as cosmological principles and named after their authors. This fact should not be taken as a depreciation of their work. I do not want to underestimate the impact of non-astronomers on the development of astronomy.

7.03. Weyl's postulate as a cosmological principle

Weyl's postulate concerns a particular geometric property of space-time noted in General Relativity, that the world lines of the substratum form a normal congruence of time geodetics. To express the same idea in non-mathematical terms: the lines representing individual histories of substratum particles in four-dimensional space-time look, in three-dimensional space, like hair that has just been brushed. Though the postulate can be applied in other theories using the concept of space-time, it is used primarily in relativistic models.

As a cosmological principle, it is broader than the Copernican Principle when applied to constructing relativistic models but narrower when considered in general, since it cannot be applied to theories not involving the notion of world lines (e.g. to some quantum theories). In fact, the majority of relativistic models conform to Weyl's postulate, but it is rather seldom referred to as a cosmological principle.

7.04. Principle of Verification

Sometimes it is required that a model of the Universe be verified in the observable part of the Universe (in the local environment of the human abode). This requirement as a categorical demand is, of course, contradictory to the very essence of a cosmological principle. A cosmological principle is by no means to be verified by astronomical observations. If it were possible, then instead of forming theories or constructing models of the Universe, we could just describe what it looks like. Of course, one can assume that the Universe is the same in every place as it is around us (this is the meaning of the Copernican Principle), but this assumption cannot be tested observationally in the observable region.

Thus, if we understand this principle to mean that the entire Universe should look like our environment, it would become tantamount to the Copernican Principle. If, however, the Principle of Verification is to have any cosmological meaning different from the above, it has to be interpreted that cosmological models should describe the observable (as well as the unobservable) region of the Universe, and this description should be consistent with the observations. It requires very little indeed. All cosmological models constructed not just for their own sakes or for methodological purposes conform to this principle. Otherwise they would not have been taken seriously. Even the models which presume various physical laws and various dimensionalities in different parts of the Universe describe exactly what we do observe within the observable part.

So indeed this postulate (principle) as a cosmological principle is either contradictory or equipollent to the Copernican Principle, or it can be meant as an appeal: "You should not construct cosmological models just for their own sake." Models constructed only for methodological purposes often, contrary to the Verification Principle, do not depict reality as observed around us and thus can be readily discriminated from the "actual" models.

7.05. The Uniformity Principle

This principle requires that the laws of physics be the same all over the Universe (i.e. the same as those valid in terrestrial laboratories). This requirement amounts to less than the Generalized Copernican Principle. Copernicus considered the planets as physical bodies. He said expressis verbis that other planets produce gravity [1] like our Earth. If, instead of the laws of gravity, we take the laws underlying all physical interactions and, instead of the planetary bodies, all matter contained in the Universe, then we obtain another generalization of the Genuine Copernican Principle: the Universe at every point is governed by the same physical laws. Thus we have obtained a universe which can be very much diversified, but still the same physics is valid everywhere. The Generalized Copernican Principle is a special case of the Homogeneity Principle. All models based on the former must necessarily conform also to the latter. Hierarchical models of the Universe (cf.: 4.15) satisfy the latter only.

7.06. The Probability Principle

This principle makes us choose from all plausible cosmological models those which are most probable in the sense of probability calculus. This criterion of selection is in fact used by many cosmologists as an auxiliary principle. For example, in contemporary relativistic models one looks for a development of the Universe that is independent as much as possible from the initial conditions. The probability of such an evolutionary line is greater than that of a line involving some specific initial conditions. This principle cannot be reconciled with the Anthropic Principle in most of its versions. The Anthropic Principle does not claim that the Universe should be the most probable one but, rather, calls for an explanation of why it is so improbable.

7.07. The Stability Principle

This principle advises the selection of such models which are, as much as possible, not sensitive to perturbations. In fact, all models conforming to the Probability Principle also satisfy the Stability Principle and the other way around. The difference is that the former is formulated in mathematical terms, while the latter rather in physical ones.

7.08. The Uncertainty Principle

Heisenberg's quantum principle of uncertainty is nowadays almost always assumed in all cosmological discussions. However, cosmology can also have an uncertainty principle of its own. When we claim something about the unobservable parts of the Universe, even "nearby" regions placed just beyond the horizon, then our claim is uncertain. The same is the case when we express any opinion or make any calculations concerning distant cosmological epochs.

It is rather difficult to count this principle as a cosmological one. It does belong to cosmology, but it does not tell how to imagine the physically unperceivable parts of the Universe. Rather, it prevents us from making hasty conclusions about them.

7.09. The Simplicity Principle and the Principle of Aesthetic Appeal

In fact, the Simplicity Principle was conceived after the old and good rule of Ockham's razor; it claims that one should avoid superfluous entities. This principle had already caused much harm in astronomy (cf.: Rudnicki 1984). At the turn of the 19th century, astronomers were at the point of accepting the "elliptical and spiral nebulae" as other galaxies. But the zone of avoidance along the Milky Way was discovered. To avoid the anti-Copernican conclusion that our Galaxy is situated in the center of the Universe, it was natural to assume the existence of galaxies also in the zone of avoidance, as well as the existence of dark matter of some kind, screening them from us. However, the invisible galaxies and (also invisible) screening matter were considered, following Ockham's razor rule, to be merely "superfluous entities." Therefore, for about 100 years, the preferred interpretation was that those "elliptical and spiral nebulae" are but dusty or gaseous nebulae situated within the Galaxy; the central position of our Galaxy could not be accepted without violating Copernican views (the term 'Copernican Cosmological Principle' was not in use yet). Extragalactic astronomy was thus brought to a standstill for a century, until eventually everyone became convinced that the two "superfluous entities" actually exist. Thus, in a science like cosmology, appealing to a principle like Ockham's razor would be outright indecent.

However, simplicity can be also understood as something that is modest and aesthetic. Since we know very little about the unobservable parts of the Universe, the appeal that we should represent them in as simple and as smooth a way as possible is certainly reasonable. A hypothesis or a picture of the Universe should not avoid multiplying entities when needed, but should be simple in the aesthetic sense of the word. Usually the Principle of Aesthetic Appeal is considered a separate one. 'Cosmos' is a Greek word for something ordered, that is, something beautiful, aesthetic and not too complicated. When we comprehend the etymology of the word 'cosmos', then the principle of aesthetic appeal is inherent in the very name 'cosmological principle'. One should keep it in mind.

7.10. The Principle of Unity

This principle can be formulated as follows: cosmology must be concordant with physics. When taken in the most primitive sense, this principle is, in fact, always fulfilled. More sophisticated cosmological models involve more sophisticated physical theories, more fantastic models more fantastic theories. No individual physical theory is accepted by all physicists or by all cosmologists. Every, even the most exotic cosmological idea bases itself on some physical considerations.

This principle should not be wrongly connected to the Homogeneity Principle. Here the laws of physics may be different in various domains of the Universe, but every domain must be based on solid physical principles. The only question remains - what is and what is not a solid physical principle?

This principle can be regarded as an appeal for a closer collaboration of physicists with cosmologists. In this form, it is the most general principle, requiring that any considerations concerning the unobservable parts of the Universe be performed only by people with a background in physics. As a cosmological principle it requires very little indeed. Therefore, I have mentioned it last.