The poorly understood behaviour of the universe

Klaas de Boer, Univ. of Bonn

Many people wonder about the nature of the universe. Where do we come from and what does it all mean? One general aspect is fascinating, the fact that all galaxies in the universe move away from us. Soon questions arise about the fate of the universe. Where will it end? And how certain are we about it all?

Contents:   Receeding galaxies   Expansion   Fate of the universe   Figure expansion behaviour   Acceleration and Supernovae Ia   Nobelprize 2011    Where will it end?    Uncertainties and questions  

Receeding galaxies

A surprising aspect of the behaviour of the universe is known for about a century. In the 1920s it was observed that all galaxies seem to flee from us, the farther away they are, the faster. This motion is visible through the Dopler effect, the shift of features in the spectrum due to velocity (in km/s). Galaxies recede from us in all directions. One claim astronomers then made was that the universe must be "homogeneous", one sees galaxies in all directions. The other claim was that, when all galaxies receede, this can only be understood as due to an expanding universe.

Hubble (1929) showed that all his galaxies receede from us (receeding velocity on vertical axis, distance horizontally). His data suggest H = 500 km/s /Mpc. Since then, the distance scale was thoroughly recalibrated: H for here and now is H0 ≅ 70 km/s /Mpc.

If the universe is expanding, then the galaxies are not really racing away from us. It rather is "the fabric of the universe", or the geometric grid, that is expanding and the galaxies just go with the stretching of that fabric. Then it is, actually, incorrect to say that the galaxies have large speeds away from us. Since we measure this receeding in the light of galaxies using the shift in wavelength (towards the red) of well recognisable spectral lines, this shift is labelled red-shift.  [ Again, the earthly shift discovered by Dopler is the one due to motion and is called the Dopler effect; the larger the velocity, the larger the Dopler shift. ]

The rate of expansion is defined by a constant which is in units of km/sec per Mpc. This expansion rate was soon named after Hubble, the Hubble Constant H, Hubble being the first to make a diagram of speed versus distance (see figure).  [ The parsec (pc) is the yardstick of astronomers; Mpc is megaparsec, a million pc ; so H is in velocity/distance. ]  H gives the recession velocity of galaxies versus the distance of those galaxies. This rate can, of course, only be determined over the distance we can cover with our measurements. The most difficult part of the determination is to get accurate distances. This involves recognizing in those galaxies special stars of which the intrinsic brightness is well calibrated. If one has enough measurements, one gets an accurate value for H. But before the era of astronomical satellites the distance covered was too small for a good judgement. Actually, the satellite built specifically with the purpose to make more detailed measurements in distant galaxies to find such special stars was therefore named after Hubble!


Do the galaxies move or does the universe (its fabric) expand? Understanding the difference means shifting your point of view: either you see things as simple humans (and then all galaxies speed away), or one takes the grand perspective and sees that the universe expands and earthlings measure a shift and interpret that as velocity of the galaxies, which is not really correct; it is the speed difference of two points in the fabric, the one were we are and the one at the location of the galaxy we look at. The redshift it is larger over larger distances, there is more path length being stretched.

If the universe expands, does perhaps everything expand? The determined rate of expansion is, actually, very small, that small, that our Milky Way galaxy does not expand in a measurable way (if we were able to measure it in our galaxy at all). The expansion is noticeable only on the vast scales of the universe.

All galaxies appear to move away from us, and from each other, the expanding universe. Therefore, in the very distant past they must have been quite close to each other. This led to the idea of the "Big Bang" (a term coined by Fred Hoyle), the moment where all this racing away from each other started.

Two aspects of this expanding are quite noteworthy.
- Galaxies at very large distances have sent out their light quite long ago, and that light needed time to reach us. What we therefore see is light from a galaxy in the past. We can, as it were, do astro-archaeology by investigating the redshifted light from very distant galaxies. There appears to be hardly any indication that the universe in the very distant past was different from what we see in our local environment today.
- Because the light from those very distant galaxies comes to us quite redshifted (due to the expansion of the universe), light from that galaxy appears quite red. If the distance is extreemely large, the light is exceedingly redshifted, and at some point we have no way of detecting such light any more. We then reach the limit of the observable universe. But that does not meean that this is the limit of the universe. Imagine someone in that far-away galaxy, looking forward, thus in the same direction we are looking. That observer can see forward over the same distance as backward to us, and in his forward there again are plenty of galaxies!

Fate of the universe

Now to the essential part of the questions about the universe, the equations describing it and the question of its fate.

Around the turn of the 19th to 20th century, astronomers (de Sitter, Einstein, Robertson, Walker, and others) derived a set of rather simple equations for the state of the universe. At that time, one just thought the universe was static (why would it have been else?) and the scientists looked for a mathemathical description of a stationary universe, in which galaxies just moved a bit hither and thither. Some scientists doubted, however, that such a stationary universe could exist. They asked: What about the gravitational forces that galaxies exert on each other? The galaxies surely must all move toward each other.

The full implications of the mentioned equations became apparent only after the work of Hubble. Here it is of importance to know that these equations could be derived and shown in graphic form only when assuming a "homogeneous" universe;

Behaviour of a homogeneous universe: time t versus size R(t). Note the point of "here and now" and the directions of past and future. Three special behaviours are shown (labelled with k and q): case E (ever expanding), case C ( critical case ), and case R (eventually contracting). Intermediate cases are possible, too.

for a non-homogenous universe the mathematics is exceedingly complicated. If such a homogeneous universe expands, then the crucial question is: will it continue to expand, will it just stop, or will it eventually start to contract? With each new kind of relevant measurement these question were again debated.

To understand this aspect one has to use a diagram. In it, the vertical axis gives the "size of the universe", the horizontal axis gives the time. Since we are here and now in our universe, we are on the indicated location in the diagram. When we observe space, we by definition look back in time, all that has happened sends light in all directions and we can pick up the light coming to us. Thus what we can "see" of the universe is to the lower left of the "here and now" point. Since the expansion of the universe is measured in km/s /Mpc, this rate appears as the slope of a line from "here and now" to the past, the slope equals the Hubble constant as measured now: H0= 71 km/s /Mpc.

The mentioned equations have, in addition to H0, two important parameters. One is the nature of the geometry, given by k, the other parameter, q, has to do with the deceleration, the way the mass in the universe counteracts the expansion. There are three possibilities for k, each implying a range of values for q: k=0 means the universe has euclidian geometry (geometry as we know it and q=0.5), k=−1 means it has hyperbolic geometry (and q is between 0 and 0.5), or k=+1 means it has spherical geometry (and q is larger than 0.5). Let us not dwell long on the theoretical background of these two parameters, building with H and R a simplified form of the Friedmann-Lemaître equations. There is a further parameter, the mean density of matter in the universe, which astronomers think they can estimate. This mean density is in the mathematics related with q (and thus k). For a homogeneous universe the essential aspect of the outcome of the equations can be given as based on this mean density.

  • case C.  At the so-called Critical density (and q = 0.5), the universe will expand further but expansion will slow down ever more without coming to a halt; it is the "limiting case" of the behaviour between the two other possibilities.

  • case E.  At smaller density than in Case C (so when q < 0.5) the expansion hardly will slow down and the universe will Expand forever.

  • case R.  At larger density than Case C (so when q > 0.5), the mass in the universe exerts a considerable gravitational pull which will, eventually, brake the expansion and will bring the universe to Reverse.

- In case E, expansion will continue forever, which is unappealing. However, the density of matter in the universe is really too low to gravitationally halt the expansion.
- In case C, the mean density should be just right. This is the favoured solution. Still, the universe must contain more matter than known. That problem is solved by postulating the existence of extra matter, which is not seen and therefore called "Dark Matter", DM. This is a contentious topic all by itself.
- In case R, the density needs to be large, while the amount of matter one can document is way too little; so this is unlikely. One would need even more of the hypothised DM than in case C.

Whichever case applies, the formulae (or the diagram) can now be used to plot the behaviour. And the crossing of the development (backwards) with the line of zero extent of the universe gives the time elapsed since the beginnings of the expansion, for that model. Depending on the model one so finds (again, see the figure above) for the age of the universe (time since the "big bang" in billions of years, Gyr):

  case E: age larger than 13.7 Gyr  
(shown is the case for 18 Gyr)

    case C: 13.7 Gyr    
(see the figure)

  case R: age less than 13.7 Gyr  
  (shown is the case for 7.5 Gyr)

Since we know that the oldest stars are as old as 13 Gyrs, case Reverse is unlikely to describe the actual universe. Which leaves us with case Critical or case Expansion..... Case C then requires that DM exists. But nobody knows what DM is! These things are much debated aspects of the models of the universe. But nobody has a real solution. And each case has its fanatic believers (yes, scientists are human, too).

Acceleration and Supernovae Ia

Supernovae, stars exploding with a bright flash, come in different types. One type, the supernova type Ia (SNIa), is important for the study of the universe because it is (on fairly good grounds) thought to be the explosion of a well defined star type, thus the flash should be for all these of intrinsically equal brightness, always. But the larger the distance to such a supernova, the see less light we see. Exactly that aspect is used to calculate the distance of that object. The SNIa are the only objects available of which the distance can be derived accurately over very large distances. In a seperate essay one finds more about the nature of SNIa. Most important is, that one can fairly easily measure the Dopler shift in the spectrum (the recession velocity of the grid point at the location of the SNIa), so that one has again information about the expansion of the universe, over large distances.

Such measurements seem to indicate that the rate of expansion in the past (as seen from the objects very far away) was a little slower than the expansion nearer to us, thus more recent. This finding led to all kinds of (wild) speculations proposing all kinds of new effects in physics, like an "accelerating universe" and the hypothesis of "dark ernergy" (to propell this excess expansion). But there does not seem to be a better explanation. Still, one feels uneasy with yet another "dark" parameter.

For more on the supernovae and the acceleration idea see Nobelprize for Physics 2011.

Where will the universe end?

The ultimate question remains unanswered. It is not known how the universe really behaves. And therefore we cannot say how it will end.

What is well established is that all galaxies receede from us, as measured by the redshift. It is understood to be a change in the geometric grid of the universe. The rate of expansion is given by the Hubble constant. The models currently en vogue give no indication for the behaviour of the universe in the future. Either the universe will have eternal expansion, making the universe ever larger and ever less bright, leading to a cold "end". Or it will slow down followed by contraction, but this means the "dark matter" must exist somehow and nobody has a clue. And then there is this "elegant" critical case, expansion but slowly approching a steady state, also requiring DM. For this case all parameters must be just right

The universe is as it is, has neither a "centre", nor an "edge" and an "outside". We, as observers, whichever vantage point we assume to have, are inside this universe and cannot see this universe from outside, there is no outside. The geometric grid of the universe was in the past substantially more compact than it is now but it existed all the time. That long ago, the universe was filled with a hot glowing plasma, of which we still see the "afterglow" at much expanded wavelengths; this is the infrared cosmic background. It should be clear that H0 did not have the same value all the time. In the past it must have been larger. But note that H0 as measured is the value for the entire universe NOW.

Something can be said about the time since the "beginning". If we try to see objects very far away, we run into the problem that at some very large distance the stretching of the grid is so large that wavelengths become infinitely long. That distance is the one where the speed of the recession of its grid point from us approaches the speed of light. In other words, at a distance r0=c/H0. Putting H0= 70 km/s /Mpc one finds a distance of about 4200 Mpc which is equivalent to about 14 Gyr light travel time. In short, we can see objects only out to a distance that is equivalent to the total travel time of signals (since the beginning of expansion). But this does not mean that there is noting beyond that distance; in fact, the universe just continues, only we cannot see that any more, as mentioned above.

One aspect is clear. Before any change toward the end of the universe would be visible, mankind will long be gone or mankind will have found the answer. Let us continue to be impressed by the beautiful night sky as can be seen in the few remaining dark places on Earth.


Uncertainties and questions

How certain is this all? Let us address a few problem areas.

Age of oldest stars. The determination of the age of stars relies on models for the stars which include also the enrichment in heavy elements. However, the simplest determination comes from groups of stars, called star clusters, in which the stars were born together and aged together. They form a "population" for which the age can be well determined based on the length of the phase of hydrogen burning. The mass of the stars which aparently still burn hydrogen sets the age based on the life-expectancy of each star related with the initial mass. Of several of the oldest clusters the age is found to be close to 13 Gyr, sometimes older, sometimes somewhat younger, depending on the models for the stars emplyoed. This age is uncomfortably close to the age of the universe from expansion, since it would leave the universe too little time to come to the first star formation at all.

No need for the hypothetical dark matter? Recent investigations of small galaxies have made clear that in most such small galaxies (if not in all of them) there is no discrepancy between velocities and mass in terms of the Virial Theorem. The problem with earlier investigations was that (in hindsight) the interpretation of the measurements was "quick and dirty". The total mass of a galaxy is thought to be related with the width of the distribution of the velocities of its objects: a wider distribution means more "agitation" and thus that more mass is needed to keep the system together. In the mean time one has also recognised that there are systematic motions in many such galaxies, violating the assumption (tacitly made) that all motions are random. With these recognitions it was possible to understand such small galaxies whithout the additional hypothetical DM, even eliminating the need for initial blobs of DM thought to be required to form such galaxies at all.

Homogeneity of the universe. Even if DM is not needed to understand small galaxies, there still was the need to have DM to "fix" the model of the universe of the Critical case, of a homogeneous universe..... By and large the universe seems to be homogeneous, i.e., looks much the same in all directions. But it has become clear that there are regions in which density of matter (number of galaxies) differs considerably from the average, in fact is very low, the so-called "voids". A theoretician in Christchurch (NZ) has made a "toy universe" consisting of regions with above average and with below average density. In this toy universe the expansion is not monotonous, the effect of redshift is not cumulative and the age of the universe can be quite larger than the 13.4 Gyr as derived for the homogeneous case. Already the first attempt to make the models for the universe more realistic shows that the unexplained aspects like the age conflicting with stellar ages need not be conflicting (at all).

There are more problem areas, which are not detailed here. It suffices to note there is much to do and much to reconsider!

../~deboer/expuniv/expuniv.html   2017.08.12   (first version 2011.08.31)