Re-Evaluating Our Cosmological Models: Why Now?

In my 1964 Science Fair project, entitled 'The Structure of the Universe'  (which was given a feature look in the Miami Herald) I got many things wrong. The reason wasn't to do with errors, but in using the existing base of cosmological data and information to construct my model. Chief among these was the theory of continual creation which had been proposed by Fred Hoyle and Hermann Bondi.. It proposed that a hydrogen atom was ‘created’ in the universe on the basis of the perfect cosmological principle. A quantitative rate for the input-creation advanced by Jayant Narlikar ('The Structure of the Universe', Oxford Univ. Press, 1977) was:

4.5 x 10^-45  kg m^-3 s^-1

This was taken to be the rate of new matter created per second within a cube - which is expanding at the rate H, where H is Hubble's constant. Then, one second later the side dimension of the cube will have increased by (1 + H)  and its volume will have increased to (1 + H)³ .  In this way, new matter is created within the 1 s interval with new mass: M = 3H r.

 And so,  though the universe was indeed expanding, it didn’t change its appearance. So its density must remain the same.  (The additional space created by the expansion must therefore have the same density of matter, r )   In addition, because of the principle of “continual creation”, the universe had no beginning and no end.  Thereby I was able to construct a model based on a matter and anti-matter universe (one with positive curvature the other, negative)  in a state of "equilibrium" with matter destroyed via annihilation equal to the new matter created via continuous creation.

It was a beautiful model which garnered top awards, but alas only months away from becoming passé.  This transpired when the first  evidence for the Big Bang emerged. This was thanks to Nobel-winning work by Arno Penzias and Robert Wilson. The experience showed me (as it did Fred Hoyle and Hermann Bondi) that our perspective on the universe and especially models, can change with just one major new discovery.

I based a lot of my model on the validity of the perfect cosmological principle which maintained that the universe was the same in space as well as time, and the same physical laws that apply on Earth applied everywhere else. In other words, our solar system and planet are nowhere special. Two sub-assumptions of the principle are that: 1)  the universe is homogeneous, i.e. looks the same for all locations, and 2) the universe is isotropic, appearing the same in all directions.

But back in the 1960s we still didn't know of the existence of cosmic voids. Those had to wait five decades for their discovery. Voids have roughly 1/10 the matter density of galaxy clusters (like our Local Group) but account for nearly 60 percent of the volume of the visible universe, thereby introducing inhomogeneity.

Even before the void discovery, there was the discovery of relic structures of the Big Bang by George Smoot and his collaborators at the University of California at Berkeley, in 1992. The investigation made use of data obtained from NASA's Cosmic Background Explorer (COBE) satellite. The data exposed very small temperature differentials (dT), from which density variations could be deduced. (In principle the temperature variations of the form dT/T are taken as a proxy for density fluctuations (dr / r)  in the early universe). These variations were also  found consistent with the postulated characteristics of an inflationary cosmos, as opposed to an always uniformly expanding cosmos. Indeed, an inflationary phase would feature an exponential rate of expansion by way of doublings over very small time periods.

What is the problem? It has remained trying to model a homogeneous universe despite data and findings that show the universe is inhomogeneous.  To quote astrophysicist Thomas Buchert (New Scientist, June, p. 33):

"To model such a complex structure with a homogeneous solution is a bold idealization."

Of course, cosmologists haven't been deterred. They merely resort to what's called modeling via  "statistical homogeneity" which means upping the scale for examining the cosmos to one wherein the inhomogeneities are radically reduced or vanish.  For example, on the scale of 400 million light years, voids and galaxy clusters average out into uniformity. But is this 'kosher'? Probably not because we have no real visualization of the cosmos on such scales.

Not yet mentioned are dark matter and dark energy, especially how the latter overturns our conceptions of cosmic order, see e.g.

http://brane-space.blogspot.com/2008/10/dark-energy-evidence-for-new-law-of.html

Dark energy has also been found to be linked to the accelerated expansion of the cosmos, e.g.

http://brane-space.blogspot.com/2011/10/three-share-physics-nobel-for.html

Even more interesting, the cosmos' inhomogeneity contributes separately to the acceleration. Thus as more mass has clumped into galaxy clusters, the cosmic voids have grown causing the universe to expand more rapidly in those regions. The result is an accelerating effect similar to that attributed to dark energy but without any remote hint of it. (See e.g. The Journal of Cosmology and Astroparticle Physics, Vol. 10, p. 043).

What does all this mean for our cosmic perspective and cosmological models? Headaches! It means we may have to ditch the simplistic idealizations that pander to order, uniformity and aesthetics and instead come up with some ugly alternatives that violate our temperaments. For example, the whole Einsteinian notion of space-time is predicated on a continuum in which the entities are conjoined. But....if space expands at much faster rates in certain places then one must accept that clocks will tick at different speeds too.

As incredible as that sounds, it doesn't come near the ultimate conclusion: that if this is so it means the very age of the universe (which we now give as 13.8 billion years) is not a constant and instead will depend upon where the measurement is made. If you measure within a void you will get one answer, and in a galaxy cluster another. (According to one recent theory, it implies the age of the universe would be measured to be up to 18.6b years old where the low density of matter "means the clock has ticked particularly fast", New Scientist, op. cit. )

But which is better? To live with our idealistic fantasies of order and uniformity of space-time, or to live in reality and know the actual truth of how the universe operates?   Bear in mind the entire history of our science has been overturning sundry pet concepts of the universe, and especially our place within it.

Now may be the time for cosmologists to put on their big boy pants and devise theories which, although they may try the orderly temperament, are much closer to reality!

Three Share Physics Nobel for Accelerated Cosmic Expansion Discovery

The recently announced awards for the Nobel Prize in Physics should come as no surprise to those who've been following events in cosmology the past two decades or so. That is, the universe has been found to be undergoing an accelerated rate of cosmic expansion. To put it into colloquial terms, the universe has been found to be not only stretching but stretching at a faster and faster rate.

The Prize itself was shared between Saul Perlmutter, of the Supernova Cosmology Project of the University of California Berkeley, who received half (see photo) and Brian Schmidt of the High-Z Supernova Search team at the Australian National Observatory, and Adam Riess of the Space Telescope Science Institute in Baltimore, MD. Both Riess and Schmidt shared the other half of the Nobel. All three worked in competition with each other.

Perlmutter's basic data graph, with the absolute magnitude (M) plotted against redshift (z) is shown in the graph adjacent to his picture above. Type Ia supernovae were selected because they all have a similar amount of mass so release energy at about the same rate ("luminosity") hence exhibit the same brightnesses. Thus, difference in brightness (as we saw with the distance modulus exercises in 'Tackling Simple Astronomy Problems') enables one to compute the distances.

In addition, by measuring the extent of the red shift, e.g.:

[L' - L]/ L = v/c

where L' denotes red-shifted wavelength, L the normal wavelength, c, the speed of light, it is possible to estimate how fast the supernova is receding (v).

In Perlmutter's case, it took four months of checking and re-checking his results before he accepted that, indeed, the rate of expansion was accelerating. In terms of the real data points, those associated with the Type Ia supernovae all fall to the LEFT and above the dotted line (see graph), or in what we call the 'accelerating universe' region. On the other side of the diagonal dotted line is the "decelerating region".

In his beautifully done summary presenting his work (See, e.g. 'Supernovae, Dark Energy and the Accelerating Universe', Physics Today, April, 2003, p. 53) Perlmutter not only shows the accelerating data but also provides an explanation in terms of dark energy. Thus, Perlmutter proposes dark energy as the primary agency for the ongoing increased rate of accelerated expansion.

He does this (ibid.) by first associating the "accelerating region" with what he calls "vacuum energy". He then invokes a cosmological "equation of state" (think of something like the equation of state for an ideal gas, e.g. P = nkT) for this vacuum energy, as:

w = (p/ rho) = -1

where p denotes pressure and rho energy density.

If: p less than (rho /3) we have gravity that repels

Or (If we set: 0 = (rho + 3p))

p = (- rho)/3


This is consistent with Einstein's theory of general relativity - which one could say approaches the status of a 'basic law of physics'. In this case, the existence of a negative pressure is consistent with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts.

Of course, simple algebra applied to the above also shows that the energy density would have to be negative, e.g. energy density = - (pressure).

These results all tossed the orthodox expectation that the universe would eventually re-collapse onto its head. Obviously, it can't re-collapse if it is forever accelerating with outwermost galaxy clusters growing further and further apart. For gauging this one uses the Omega parameter:

OMEGA = rho/ rho(c)

where rho(c) denotes a critical energy density.

If then rho > rho (c)

the universe would be able to re-collapse, else not.

Current data, e.g. from Boomerang and other satellite detectors shows that :

rho = 0.3 (rho (c))

I.e. that rho less than rho(c)

so there is no danger of the cosmos decelerating.

When the predictions of the different theoretical models are combined with the best measurements of the cosmic microwave background, galaxy clustering and supernova distances, we find that the proportion of the dark energy component of OMEGA:

0.62 < OMEGA_dark < 0.76,

where OMEGA_dark = rho_dark/ rho(c), and -1.3 < w < -0.9

Or to put in into the words of the Royal Swedish Academy of Sciences:

"If the expansion will continue to speed up the universe will end in ice"

Indeed!