Answerer

So what kind of scalar field is the 'dark energy'? Higgs particles?

lpetrich

It would be difficult for the dark-energy field to be the Standard-Model Higgs particle. However, Grand Unified Theories typically produce a whole zoo of new particles -- the Dark Energy particle could be one of them.

AdamWho

So gather from the replies so far that people are ok with a theory where 96% of the universe is made of stuff we have never seen and don't have the ability to test for (yet), based on circumstantial astronomical data?

It just seems that we (physicists) should be more cautious.

Popper wrote that the measure of a good theory was if

1. it has the ability to make lots of predictions
2. it is falsifiable

So far the theory seems to more descriptive (ad hoc) than predictive and still is not falsifiable.

Maybe the falsifiable criterion gets tossed sooner in cosmological theories, since it is difficult to do testing.

Shadowy Man

Uh no... I'm not okay with it. I think that dark matter/energy is the greatest glaring problem in modern astrophysics.

Now, if we gave up looking for dark matter, that would be an indication that we are "ok with it". People are coming up with all types of experiments to attempt to measure the presence of dark matter and deduce what it might be; everyone from high energy physicists to cosmological theorists.

lpetrich

It looks like there is a big gap between me and some others here on what we find the most ad hoc.

I tend to view the question from the point of view of a theoretical physicist, complete with the ability to solve partial differential equations.

Newtonian gravity has the nice property that its gravitational potential solves Poisson's equation:

D^2 V = 4*pi*G*rho

The acceleration of gravity is:

g = - D V

I've seen a MOND version of Poisson's equation, and it looks impossibly kludgy. Something like:

D (mu(D V) * (D V)) = 4*pi*G*rho

where mu() is some function that produces the MONDishness. And try constructing a relativistic version of it, one that reduces to Special Relativity in the small-scale limit as General Relativity does.

By contrast, extra elementary particles looks like a much more reasonable possibility. The Standard Model already looks like some higgledy-piggledy zoo, and theorizing like supersymmetry and Grand Unified Theories tends to predict lots of extra particles. Most of these are expected to be relatively massive and unstable compared to known particles, but some are expected to be relatively stable and potentially observable in our present-day Universe.

AdamWho

lpetrich

D (mu(D V) * (D V)) = 4*pi*G*rho

So is the mu() term is just a tensor to allow for anisotropy, but shouldn't the D on the far LHS be a divergence operator? I know that a similar setup for the heat equation is used quite a bit to model nonlinear heat flow, mathematicians seem to favor the form for its generality--> div(L(Du)*(Du))=Dtu, it reduces easily to the normal for L(Du) = I

Shadowy Man

Hey.. no point sporting an attitude. I think it is silly to argue which is more ad hoc than the other. I have just been to many talks in which people talk about "the dark matter distribution this or that" and seen talks that show large scale structure formation with dark matter distributions, blah blah, and at every one I just want to raise my hand and ask "what is dark matter?" It just seems to be so casually accepted.

Ok.. so the theory isn't as simple as Newtonian gravity. Well relativity isn't as simple as classical mechanics either. That in and of itself is no reason to discard it. As for a relativistic version: so, it's not a complete theory yet, but then again neither is general relativity - there's no quantum version of it.

Look, even if MOND isn't correct, which by no means am I saying that it is, the fact that it actually appears to fit data very well with only one parameter (which it didn't really have to if you think about it) at the least is telling you something very interesting about the dark matter distribution in galaxies. So, I think it is definitely valuable to pursue the theory.

Well, the particles would have to be nearly ubiquitous, accounting for a significant fraction of the universe's mass, but also virtually impossible to detect, interacting with each other and 'normal' matter by gravity only. The particle physicists have their work cut out for them.


p.s. lpetrich: are you a physicist working at LLNL?

Answerer

Shadow, are you there as well?

Shadowy Man

Nope. Check my location.

lpetrich

Yes, I'm at LLNL, after a fashion. However, I haven't been very successful there, so I may move elsewhere before long.

I will now give an introduction to MOND, at least a simple version of it.

According to it, Newtonian gravity gets modified at large distances:

Normally, the acceleration of gravity is given by

g = GM/r^2

But MOND defines a length scale, r0, and if r > r0, then

g = GM/(r*r0)

This gives the "correct" galaxy-velocity curves, since

orbital velocity = sqrt(g*r) = sqrt(GM/r0)

a constant

The gravitational potential, however, is

V = (GM/r0)*log(r/r1)

with this resulting velocity and radius-time relationship (total energy absorbed into r1):

v = sqrt(2GM/r0)*sqrt(log(r1/r))

t = sqrt(r0/(2GM))*Integral(dr/sqrt(log(r1/r))

One cannot get Hubble's Law out of this; if M = 4*pi*rho*r^3/3, with density rho being constant, then

v = sqrt(8pi*G*rho/(3r0))*r^(3/2)*sqrt(log(r1/r))

By comparison, Newtonian gravity can easily yield Hubble's Law:

v = sqrt(2GM/r + 2E)

if E = (1/2)*w*r^2, for all of space at some time t, for some w then

v = r*sqrt(8pi*G*rho/3 + w)

Which is Hubble's law if rho is only a function of t.

Being more careful, we set r = a(t)*x

Then v = (da/dt)*x

and the velocity equation becomes

v = sqrt(8pi*G*rho*a^2*x^2/3 + 2E)

and if E = (1/2)*w*x^2, where w is a constant, then

v = x*sqrt(8*pi*G*rho*a^2/3 + w)

-- Hubble's Law!

and

da/dt = sqrt(8*pi*G*rho*a^2/3 + w)

rho, however, depends on a in this fashion:

3*da/a + d(rho)/(rho + P/c^2) = 0

and

rho ~ 1/a^3 for dust (zero-temperature gas)

rho ~ 1/a^4 for speed-of-light radiation, like the Cosmic Microwave Background

rho ~ constant for Dark Energy (pressure = - rho*c^2; note the negative sign)