The standard Friedmann models are considered by many as being the best approximation for the observed large scale distribution of galaxies, since the results predicted by these models are usually quite good approximations to the observations (Peebles 1993). However, although no observational evidence was so far found to severely contradict this widespread belief, the question remains of whether or not other cosmological models could also provide theoretical predictions in line with observations. This is obviously an important aspect in the general acceptance of the standard Friedmannian models as good approximations to the observed Universe, inasmuch as we can only have a direct response to the question of how good the Friedmann models really are, if we are able to test the data against the predictions of other non-standard cosmological models.
Nevertheless, cosmography is presently dominated by observational relations derived only within the Friedmannian context (Weinberg 1972; Sandage 1988, 1995; Peebles 1993), and obviously those relations do not allow comparisons between standard and non-standard cosmologies. Therefore, in pratice we have a situation nowadays where the observational test of non-standard models is quite difficult due to the absence of detailed and observationally based relations derived with that purpose.
There are exceptions, however, and the basis of a general theory for observations of cosmological sources was presented by Ellis (1971), but later, in a series of papers (Ellis & Perry 1979; Ellis, Perry & Sievers 1984; Sievers, Perry & Ellis 1985) the theory was further developed, with the presentation of detailed calculations of observational relations from where cosmological effects can be identified and separated from the brightness profile evolution of the sources.
Although such study was a step forward in the possibility of direct observational test of non-standard cosmological models, the detailed theory of Ellis, Perry and Sievers equally demands detailed observations of the sources, a task usually not feasible when dealing with large scale redshift surveys, where the total number of observed objects varies from hundreds to thousands of galaxies. (1)
The approach of this work differs from those quoted above because in here cosmological sources are considered point sources, and therefore observables like flux and colour are integrated over the whole object. This is a reasonable approximation for the objects included in these surveys, since they are usually so faint that observation of their structure is very difficult with the presently available techniques. Therefore, by treating galaxies as point sources we can, at least in principle, apply the methods presented in this paper to the large and deep galaxy surveys presently available.
The observational relations presented here were derived with the aim of eventually using them to compare with this set of data, that is, the redshift surveys of galaxies. As a consequence, the theory used here could offer the possibility of comparing the predictions of different cosmological models with the need of much less real data than demanded by the theory of Ellis, Perry and Sievers. Besides, this simpler view of the problem creates the option of a first order test of cosmological models against observations without the imediate need of detailed data, which in turn would demand a more complex and demanding analysis. However, in order to be able to obtain observational relations capable of being compared with observations, to a certain extent we need to depart from Ellis' (1971) approach and discuss in detail some specific observations in cosmology within some specific bandwidth, since this is the way astronomers deal with their data.
This paper is the first of a series where it is carried out a program for investigating whether or not other, non-standard, cosmological models could also explain the data obtained from the large-scale redshift surveys of galaxies. Here I shall discuss the basic theory for observational relations in limited frequency bandwidth, the quantities which are mostly used by observers, and some pitfalls regarding their connection to the underlying geometry and practical astronomical observations. In Section 2 I present some basic definitions and equations, and in Section 3 the approach, method and observational relations apropriate for this program are discussed. The paper ends with a concluding section.
1 Actually, often it is not even desirable to obtain such detailed observations since what is being frequently sought are data for doing statistics of the distribution of galaxies. Back.