Expert: Philip A. Stahl - 7/1/2010

Question
QUESTION: Hi,
I dont know if this is the proper venue, but I wanted to post a theory I have about the big bang.  I am a novice, so I hope this is not too elementary a question.
Has anyone ever thought about the big bang as part of a cycle of the universe, similar to most other things we observe such as the seasons?
The easiest way to explain my theory is
1) It is based on curved space.

2) It explains what I have heard about the expansion speeding up.

The easiest way to explain it is first in 2D.  Imagine an explosion on the surface of the earth.  If all of the particles travel east, west, north and south, they should all impact on the other side of the planet with as much force as the original explosion.  
Now imagine the same hypothesis in 3D.  If space is curved, it does not matter which way you go... up, down, left, right etc... you will eventually come across the same point (much like traveling along the surface of the earth).  Maybe the big bang is just another cycle in an endless cycle.  
Maybe the galaxies have passed the half way point and are starting to feel the effects of the other galaxies pulling it faster to the next big bang point(what went west, is now starting to feel the gravity of what went east around the curve of space).
Well, this is my theory, I hope I have not asked too basic a question that has been asked by every first year freshman.

Thank you for your time,
Patrick McLaughlin


ANSWER:
(This is sent as a "revised answer" because the All experts "image sender" only allows one image to send sent per question. So, the 2nd image I referenced below - the graph to do with the Type 1a supernova data, can't be sent unless you send a short follow-up. You could even just write: 'I didn't see the graph for the supernova data showing acceleration, could you send that?')

Hello,


Actually, physicist John Wheeler, in his "reprocessed universe" - articulated a cyclic model more than 3 decades ago. I append a sketch showing the basic concept, from an article I did in 'The Bajan' (now defunct) magazine, in 1982.

In Wheeler's "oscillating model" recurring big bangs usher in a new expansion each time, then - when the cosmic density is large enough, the universe collapses ('big crunch') leading to a new big bang and different cycle. These cycles also can portend distinct universes with perhaps different values of constants such as G, alpha (fine structure constant), e(electronic charge, h - Planck's constant, etc. and obviously, some may feature life and others no life.

Wheeler himself pointed out most cycles wouldn't be favorable to life based on changes in 'alpha'. He showed that a star's luminosity (power output) varies as the 20th power of this constant. In effect, if the value of alpha varied (in a new cycle) by as little as 1%, nearly all stars would be very hot blue stars with a lifespan of 10-20 million yrs. This is too short for life as we know it to evolve.

So, what happened and why did the recycled-reprocessed universe go out of favor? Basically, because the observations related to the cosmic density parameter (carried out largely in the 90s) showed the cosmos simply lacks the density for recollapse, and also- its curvature is essentially 'flat'.


First, note that universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called in turn: 'closed' (can have curvature k = +1); 'critical' or flat (k=0) or 'open' (can be k = -1), respectively.

Most critical of these is the middle one for k= 0 (why it's also called "critical") because if we observe the universe endlessly expanding with nothing to break it, it must have curvature k=0.


Now, to determine whether any cosmological template leads to deceleration or not, we need to find the cosmic density parameter:

OMEGA =  rho / rho_c

where the denominator refers to the critical density. Thus if:

rho >   rho_c

(c = critical)

then the cosmic density is able to reverse the expansion (e.g. decelerate it) and conceivably usher in a new cycle. (New Big bang etc.) The observations that help determine how large rho is, come mainly from observing galaxy clusters in different directions in space and obtaining a density estimate from them.

In addition the late 90s observations that have disclosed the presence of "dark energy" have also helped. That data, e.g. from Boomerang balloon,  and other satellite detectors shows that  rho ~ 0.3 or that:

rho = 0.3 (rho_c)

I.e. that  rho <  rho_c so there is no danger of the cosmos decelerating.

Indeed, our observations of type 1a supernovae disclose the expansion to be *accelerating*. (Refer to 2nd diagram which is a graph showing how the type 1a supernovae occur in the accelerating region. (One entry shown with error bars).

If you make a plot of absolute magnitude (vertical axis) against redshfit (z, for the galaxies they occur in) then type Ia supernovae will be distributed in a particular way, as shown.

In the above graph,  we find the scattered points emanating from the origin up to the upper right.  In terms of the real data, the type Ia data points all fall to the LEFT of the dotted line, or in what we call the 'accelerating universe' region. On the other side of the diagonal is the "decelerating region". (See, also: 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53.)

Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have also provided further evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS).

The best assay we have of the cosmos' components, based on all these measurements is:

1) The matter component is only ~ 7%

2) The dark matter component is ~ 23%

3) The dark energy component is ~ 70%

The "kicker" (or "closer" if you will) is that the type 1a results, the 2DF -SDSS results and the WMAP results are all also firmly backed up by earlier Boomerang (balloon) data that – when plotted on a power spectrum- discloses two adjacent ‘humps’ one a bit higher than the other. The “first acoustic peak” and the “second acoustic peak” fit uncannily to the sort of spherical harmonic function that describes a particular plasma condition. In this case, one that conforms to the supernova-derived values of OMEGA_ (d, m). (Where Omega_d is at least 0.65, i.e. the universe is at least 65% dark energy)

The problem, since the results have come out, has been that most of the critics don't have enough plasma physics or mathematics to make a case *against* the findings. In particular, most of them have are not familiar with the nature of the spherical harmonic function and how it applies to the plasma condition or state revealed.

I grant a lot of this is esoteric, but don't feel bad, since it also has many cosmologists and astrophysicists confounded! Many still question the very existence of dark energy or that the cosmos is accelerating like it is, which suggests a *repulsive* aspect to gravity. But the data are hard to refute, and no one has succeeded yet.

Added (technical)  footnote on the repulsive aspect of dark energy:

Most astrophysicists now believe the dark energy is associated with something called *vacuum energy* which has a particular "equation of state". (Think of something like the equation of state for an ideal gas, e.g. P = nkT).

For this vacuum energy:

w = (Pressure/ energy density) = -1

This is actually consistent with Einstein's general theory of 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.  

Specifically the term (rho + 3p) acts as a source of gravity in general relativity, (where rho = energy density).

If we set:  0 = (rho + 3p) then:

p =  -rho /3   (or  rho  = - 3p)

and if:  p <  (rho /3) we have gravity that repels.



---------- FOLLOW-UP ----------

QUESTION: Thank you for your response.  If I understand your answer, you addressed a cosmos that slows down and then pulls back in.  
In my model, after slowing, it would actually start accellerating, never having to change directions.  The example of an explosion happening on one side of the earth with gravity holding the particles on the surface would travel around the earth and meet again on the other side.  As the particles made it past the "half way around the earth" point, they would start to feel the attraction of the other particles (what particles that went "west" would feel the pull of particles that went "east" when they get closer on the other side of the "ball")due to curved space.

Answer
Hello,

The problem is that your "model" is inapplicable because it's predicated on Newtonian gravitation (based on the analogy you gave) and not on general relativity. All credible theories of cosmic origin, or putative explanations - say of the expansion, have to use general relativity. The first sign of a "crank" (e.g. "crackpot") theory is when it doesn't. Indeed, the whole basis of geometry for the cosmos - what curvature it has, is predicated upon general relativity. (Note: I am not insinuating *you* are a crank or crackpot, since you already acknowledged being a freshman and "novice". So "naive" perhaps but not a crackpot. That appellation I reserve for more mature, trained physicists- or mathematicians-  who always insist they've "overturned Einstein" or some such rubbish, and come up with a whole new "theory". In most cases, when they send these treatises out, they just end up in someone's dumpster.)

Let's look at the applicable equation that would apply here (and by the way, I've also appended the 2nd diagram - showing the type Ia supernova data in a rough sketch form. Any credible theory of HOW the cosmos is accelerating has to be able to account for this. It's no use invoking analogies to Earth and how particles behave in its gravity field, since this is all to do with Newtonian dynamics!)


We have (cf. Perlmutter, previous citation):

R’’/R = - 4pi/ 3  G rho (1  +  3 w)

Here R is a cosmic scale factor, R’’ is the acceleration (e.g. second derivative of R with respect to time t), G is the Newtonian gravitational constant, rho the mass-energy density. We inquire what value w must have for there to be no acceleration or deceleration.
(Note here the General relativity enters via the R" and (1 + 3w) factors.)

Basic algebra shows that when w = -1/3 the whole right side becomes zero. The supernovae plot data constrain w such that it cannot have a value > (-1/2). Most plausibly, w – the ratio of pressure to density is (Perlmutter, ibid.) (called the cosmological equation of state)

w = (p / rho) = -1

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

I think the core problem with your "model" is the supposition that the universe is implicitly spherically curved and hence it "matters not which way you go". The problem is that this (k= +1) curvature is not supported by the existing data. What we have then is a flat continually expanding universe that in no part is "slowing down".

It is good you have a keen interest in cosmology, but I'd suggest holding your model until you're exposed to much more relevant course work (including at least the completion of an astrophysics course) and much more math, such as differential equations and maybe some tensor calculus.

Then, later, you can return to what you've proposed and examine all the facets with much more insight, based on your new found skills.

Btw, in the meantime, there's an excellent astrophysics course available at the Open University Yale site:

http://oyc.yale.edu/astronomy/frontiers-and-controversies-in-astrophysics/conten


Pay special attention to the sections, lectures 16 -21, especially 20 and 21!