The Large Scale of the Universe
in Space and Time.
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The problems arising from the uniqueness of the universe are compounded by its vast scale in both space and time,
which poses major problems for observational cosmology. We therefore need to introduce various principles in addition to the observations in order to develop working models that will support theories that may interpret the current observations and predict the future ones with a reasonable degree of accuracy.
In order to get an idea about observations on the large scale of the universe, let’s have a look at the distances we are dealing with. The distance to Andromeda, the nearest large galaxy, is such that it takes the light about two million years to travel to earth. The speed of light is about 300,000 km per second, which means that if you send a very powerful light signal from earth, it will not reach Andromeda for a couple of million years. The present size of the visible universe is about five thousand times bigger than the distance to Andromeda. This huge size relative to our own physical scale places major constraints on our ability to observe distant regions (and certainly prevents us experimenting with them). The uniqueness of cosmology in this respect is that it deals with this scale: the largest with which we can have causal or observational contact.
Astronomical observations are confined to the past null cone, fading with distance.
We can effectively only observe the universe, considered on a cosmological scale, in one space-time event[1] in terms of “there and then”. Visual observations are possible only on our past light cone, so we are inevitably looking back into the past as we see to greater distances. Uncertainty grows with distance and time.
On the other hand, the vast scale of the universe implies that we can effectively only view it from another spacetime event “here and now”. If we were to move away from this spatial position at almost the speed of light for say 10,000 years, we would not succeed in leaving our own galaxy, much less in reaching another one; and if we were to start a long-term astronomical experiment that would store data for say 20,000 years and then analyze it, the time at which we observe the universe would be essentially unchanged (because its age is now believed to be about 13.7 billion years and the extra time would make a negligible difference). This is quite unlike other geographic sciences: We can travel everywhere on earth and see what is there. The situation would be quite different if the universe were much smaller. Given its actual scale, such that we are now seeing galaxies whose present distance from us is about 10 billion light years, the effect is as if we were only able to observe the earth from the top of one mountain, and had to deduce its nature from those observations alone.
Because we can only observe by means of particles and electromagnetic radiation coming to us at a speed limited by the speed of light[2], and we can run astronomical observations of distant sources and background radiation by telescopes operating at all wavelengths (optical, infrared, ultraviolet, radio, X-ray, Gamma Rays) but all of them are constrained to rays lying in our past light cone. These allow detailed observations (including visual pictures, spectral information, and polarization measurements) of matter as it intersects our past light cone. In observing distant regions, we can also aspire to use in the future neutrino and gravitational wave telescopes, and perhaps some sort of cosmic ray observations representing information coming to us at the speed of light or less. However all our detailed data about distant regions is gathered along our past light cone.
As a consequence, we encounter the following problems in interpretation of the astronomical observations.
First of all, because we cannot travel considerable distances from Earth and therefore cannot change the point from which we observe the Universe, we can obtain only 2-dimensional projection on the sky, which gives us only partial information about real 3-dimensional distribution of matter in the universe. Many stars which appear in close positions in the sky are in fact separated by great distances along the axes of our observation, and only their projections 2-dimensional plane make us view them as close counterparts. Constellations, those groups of stars that for millennia were considered parts of one stellar structure, have nothing to do with each other apart the fact that they only appear in close proximity on the 2-dimensional plane. Lets have a look at constellation Ursa Minor (Little Dipper).
The well-known bright star Polaris, which shows us the direction to the North Pole, is 432 light years from us, while the next star in the constellation, Delta Ursae Minoris, is 183 light years away, which makes it twice closer to us than the more luminous star Polaris. Why does Polaris appear brighter if it is farther away? This is because Delta Ursae Minoris is a main sequence star (like our sun) while Polaris is a giant. The things in sky are not as they appear!
It is obvious that we need reliable methods to measure the distances in order to obtain the true picture of the Universe. Even though we have succeeded in using different objects as “standard candles”, this method of measurement is not quite reliable. Some distances are measured with precision as low as 50%, which is like if you were asked the distance to next gas station and you replied between 50 and 100 miles. Well, it’s a big difference even on earth scale, saying nothing of possible mistakes of thousands of light years. There are many stars the distance to which is unknown.
The second problem in the interpretation of astronomical observations arises with the realization of the fact that we can see distant galaxies only at earlier times in their history. There is no way for us to know what’s going on in these galaxies now, because light coming from them left its source millions – and for more distant galaxies billions – of years ago.
It is the same if we could learn about geography of what now constitutes the continent of Africa only by observing it as it used to look in the era of dinosaurs. This gives some advantages by making cosmology a geographic and a historical science combined into one, although the science is curses with ultimate disadvantages. Because we are looking at the past appearance of the object of our observation, we have to consider the evolution of this object in order to determine the distances. In practice it is one of the unknowns we are challenged to determine.
The third problem arises when we face the fact that distant sources appear very small and very faint, both because of their physical distance, and because their light is highly red shifted (as suggested by main-stream cosmology due to the expansion of the universe)[3].
It is difficult to detect the light that comes from the great distances, let alone determine characteristics of the objects that emit it. Moreover, there is the problem of absorption by intervening matter that can interfere with light from distant objects. The farther away we look, the worse these problems get. Therefore the certainty of our knowledge of the Universe decreases rapidly with distances.
A certain solution to these problems comes from the availability of geological-type data; that is, the present-day status of rocks, planets, star clusters, galaxies, and so on, which contains much information on the past history of the matter comprising those objects. Reviewing this data allows us to obtain detailed information on conditions near our past world-line in space-time at very early times if we can interpret this data correctly. “Geological” type observations can probe the region in our immediate vicinity in the very distant past. Physical and astrophysical observations tell us about conditions of the far distant past of more distant objects.
This constitutes the basis of physical cosmology, which is the study of the evolution of structures in the universe, tested by comparison with astronomical observations.
We have also an opportunity to measure the abundance of elements in our region of space and confirm it in distant regions, which can serve at some degree our better understanding of nucleosynthesis in the Hot Big Bang.[4]
If we can obtain adequate quality data of this kind for objects at high redshifts, we can use this to probe conditions very early on in their histories at some distance from our past worldline.
One of the main challenges of observational cosmology is determining the large-scale geometry of the universe.
The obvious way to approach this problem is to try to determine the geometry of the universe directly from observations (assuming that the nature of objects observed is properly understood). This approach is based on Observational Cosmology Theorem, which states that the data in principle available on our past null cone from astronomical observations is just necessary and sufficient to determine the space-time geometry on that null cone.
Even if these assumptions are right and there is sufficient data available to determine the space-time geometry on that null cone, it is possible that the observable universe is only a small fraction of a bigger universe that may always stay beyond our observational abilities, especially if one believes in the newly-found acceleration of the universe, which may separate different parts of the universe at a such pace that the light from these sources will never be able to reach our telescopes.
The size of the observable universe has grown one thousand times larger in the last one hundred years as our observational equipment has improved. Maybe it is worth waiting until we are able to observe an even bigger part of the universe before we jump to any conclusions about its geometry? The currently observable universe appears flat, which may not be the case as the size of the observable universe increases. Analogously, from a terrestrial point of view the earth appears flat, but when seen from space, it appears round.
It is a good question, whether there is a need to research areas that obviously lack sufficient data to obtain conclusive results, or if it is better to leave these areas alone until other methods that may prompt us to reconsider the questions researched are developed. Alas, this is not the approach in modern science. What was the point of losing lives in order to reach North and South Pole when in half of a century it was reachable by flight? The flight was developed for independent purposes but later was available to satisfy the thrust of geographers to learn what the earth’s poles for centauries were concealing from them. It turned out not much
We already mentioned the allegory that describes the cosmologist as a man standing on the top of the hill in desert and trying to make meaningful conclusions about the earth as a whole, with no ability to see the oceans.
Anyway, from the data available it is possible, in principle, to determine the space-time in the past of the null cone and, if there is no interference, in its future. However in practice this is difficult to carry out both because of the problem of estimating distances for all observed sources, which requires a knowledge of the nature of the sources, and because of the serious difficulty in obtaining some of the needed data (which include apparent distortions of all distant objects and the transverse velocities of all observed matter). The further we observe down the past light cone, the larger the uncertainty becomes.
This direct observational approach, where no prior model is assumed for the space-time geometry, has been pursued to some degree. In essence, this approach underlies the observational studies that discovered large-scale structures[5] such as the great walls and voids.
Nevertheless it is not widely adopted as an overall approach to cosmology, both because of these observational difficulties, and because it has little explanatory value. The direct observational approach simply tells us what the geometry and matter distribution is, but not the nature of it.
It is accepted in mainstream cosmology to use a theory-based approach: We assume a priori a model based on a space-time geometry with high symmetry and then determine its essential free parameters from the comparison of theoretical relations with astronomical observations.
There is always a need for the link between observations and theoretical models. Such standard models of cosmology are the Friedmann-Lemaitre (FL) family of universe models. Their metric describes a homogeneous and isotropic universe, which has the same uniform composition throughout, independent of the direction in which we look. These models are easy to comprehend and they have good explanatory power. Moreover, the physical predictions of these models (the existence of blackbody cosmic microwave background radiation[6] and specific light element production in the early universe) seem to be confirmed by observations.
The problem is, to what degree do observational data confirm these universe models for the expanding universe geometry?
According to current astronomical observations, the observed region of space is nearly isotropic about us. It is true regarding the distribution of galaxies on a large scale, and it is also true regarding observed cosmic microwave background radiation.
Indeed, background radiation is spectacularly isotropic, with a slight anisotropy, which is understood to result from our motion relative to the rest frame of the universe.
The fact that on a large cosmological scale no major matter concentrations in any particular region of observable universe were found signifies that the space-time structure and the matter distribution are isotropic about us.
This allows us to design exact spherically symmetric universe models that would be supported – or at least not contradicted – by current observations. In general, such models will be spatially inhomogeneous, with our Galaxy located at or near the center. Philosophically speaking this won’t be a very popular theory, because of the previous failures of Geocentric and Heliocentric models.
Nevertheless, it is certainly possible, though not probable.
In order to supply convincing observational evidence for spatial homogeneity in addition to the spherical symmetry we may employ various arguments.
One of such arguments is the cosmological principle: Just assume spatial homogeneity because it is the simplest case and you don’t need anything more complex on the basis of current observations. We may simply adopt a philosophical principle as the basis of argument. This is essentially an a priori prescription for the initial conditions of the universe. It means a universe that initially has an isotopic geometry will have that geometry at later times, because the symmetries of the initial data are usually preserved.
Another argument is Friedmann-Lemaitre (FL) observational relations. If we could show that the source observational relations had the unique FL form as a function of distance, this would establish spatial homogeneity in addition to isotropy.
However, the observational problems mentioned earlier – specifically that we cannot measure distances reliably enough do not allow us to carrying this through. Astrophysical cosmology could resolve this in principle, but is unable to do so in practice.
In the face of this, the usual procedure is to assume that spatial homogeneity is known in some other way. But attempts to prove spatial homogeneity observationally fail. Even though the alternative interpretation would be that these observational data are evidence of spatial inhomogeneity, i.e. that we live in a spherically symmetric inhomogeneous universe in which we are situated somewhere near the centre, with the cosmological redshift[7] being partly gravitational.
Similarly, the supernova data usually are understood to imply the existence of a cosmological constant. This could also be interpreted as evidence of inhomogeneity, without the need for “dark energy”. Most cosmologists regard such proposals as very unappealing, but that does not prove they are incorrect. It just proves the fact that there is an uncertainty in this question and obtaining the hard evidence of homogeneity is not as easy as it might look.
Another argument is physical arguments. It states that physical processes such as inflation make the existence of isotopic regions highly likely, indeed much more probable than spherically symmetric inhomogeneous regions. Even though it is a viable argument, we must be clear that we are merely replacing an observational test with a theoretical argument based on a physical process that may or may not have happened. It may seem to many mainstream cosmologists there is no definitive
observational proof that inflation took place.
The inflationary universe theory is popular because of its predictions of the detailed pattern of Cosmic Background Radiation anisotropy on a small scale. That argument would only become rigorous if it is shown that spherically symmetric inhomogeneous models (with or without inflation) cannot produce similar patterns of anisotropy. As a matter of fact, however, such models can produce similar patterns of anisotropy, because the acoustic oscillations that lead to the characteristic predicted anisotropy patterns take place after inflation and can plausibly happen if suitable initial conditions occur without a previous inflationary phase. Doesn’t that mean that before we attempt to explain inflation by a cosmological constant or quintessence (or any other form of “dark energy”), we need to obtain more substantial proof that inflation has really taken place?
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[1] This means that we cannot see what is going on in Andromeda galaxy right now, we can observe the space-time events attributed to this region of space as they would appear for local observers about two million years ago.
[2] According to Albert Einstein’s theory, so far proved to be correct, nothing can travel faster than the speed of light.
[3] Red Shift occurs when the visible light from an object is shifted towards the red end of the spectrum. (Spectrum is the range of colors observed when white light is dispersed through a prism. Spectrum is referred to a plot of light intensity as a function of frequency or wavelength. ) More generally, red shift is defined as an increase in the wavelength of electromagnetic radiation (in this case light) received by a detector compared with the wavelength emitted by the source. This increase in wavelength corresponds to a decrease in the frequency of the electromagnetic radiation. Conversely, a decrease in wavelength is called blue shift. So, expansion of the universe is explained by main-stream science by Doppler effect, the apparent change in frequency and wavelength of a wave that is perceived by an observer when the source of the waves is moving relative to him.
[4] Nucleosynthesis is the process of creating new atomic nuclei from preexisting nucleons (protons and neutrons). The primordial preexisting nucleons were formed from the quark-gluon plasma of the Big Bang as it cooled below ten million degrees. This first process may be called nucleogenesis, the genesis of nucleons in the universe. The subsequent nucleosynthesis of the elements (including all carbon, all oxygen, etc.) occurs primarily in stars by nuclear fusion. Using the Big Bang model it is possible to calculate the concentration of helium-4, helium-3, deuterium and lithium-7 in the universe as ratios to the amount of ordinary hydrogen, H.
The measured abundances all agree with those predicted. The agreement is relatively poor for 7Li and 4He, the two elements for which the systematic uncertainties are least understood. This is considered strong evidence for the Big Bang, as the theory is the only currently available explanation for the relative abundances of light elements.
[5] In physical cosmology, the term large-scale structure refers to the characterization of observable distributions of matter and light on the largest scales (typically on the order of billions of light years). Sky surveys and mappings of the various wavelength bands of electromagnetic radiation have yielded much information on the content and character of the universe’s structure. The organization of structure appears to follow as a hierarchical model with organization up to the scale of superclusters and filaments. “Great Wall” is a sheet of galaxies more than 500 million light years long and 200 million wide, but only 15 million light years thick. The existence of this structure escaped notice for so long because it requires locating the position of galaxies in three dimensions, which involves combining location information about the galaxies with distance information from redshifts.
[6] Cosmic microwave background radiation, also referred as relic radiation, is a form of electromagnetic radiation discovered in 1965 that fills the entire universe. It has a thermal 2.725 kelvin black body spectrum which peaks in the microwave range at a frequency of 160.4 GHz, corresponding to a wavelength of 1.9 mm. Most cosmologists consider this radiation to be the best evidence for the hot big bang model of the universe.
[7] In physics, light loses energy when it moves away from a massive body such as a star or a black hole; this effect reveals itself as a gravitational redshift in the frequency of the light, and is observable as a shift of spectral lines towards the red end of the spectrum.
