The Big Bang time paradox

[Ogie Oglethorpe]

I don't see why evryone fawns over KH and thinks him this great "brane". How hard is it to become a beautician after all?

[Ned]

Originally posted by KrazyHorse

KH, could to "universe" at one time been composed only of dark matter?

Dark matter is assumed to have the same "equation of state" as regular matter. What the equation of state tells you is how much "pressure" is exerted by the component in question. Matter exerts 0 pressure. This is basically equivalent to saying that the "total amount "of matter is independent of the scale factor (except insofar as matter is annihilated or pair-created). More properly, it tells you that the density of matter goes down as the cube of the scale factor. Think of the Universe as a box. If you double the scale factor you increase its volume by 2*2*2 = 8. If you had 1kg of matter per meter cubed before doubling then after doubling you will have 1/8 kg per meter cubed. Both dark matter and regular matter are hit by the same scale factor cubed dependence, so to a first approximation the amount of dark and regular matter in the universe remain in the same proportion.

Radiation (light) and hot matter (stuff that's moving ultrarelativistically) are hit by an extra scale factor (from redshift), so they drop off quicker than matter. They also exert negative pressure on the Universe's expansion.

Finally, if dark energy is a true cosmological constant, its density remains a constant independent of the scale factor. It thus exerts positive pressure on the Universe's expansion (tending to force it to accelerate)

The thermal history of the Universe goes as follows, therefore: at early time, the Universe was hot and radiation dominated. Dark matter and neutrinos were so pressed together that they were in thermal equilibrium with the visible Universe. They behaved just like regular matter. Then the Universe expanded and cooled off. The dark matter stuff "froze out" (i.e. dropped out of contact with regular matter). It became real dark matter. The Universe expanded more and more. The radiation density dropped faster than the matter density. The Universe thus became matter dominated for a time. It kept expanding. The matter density kept dropping. The radiation density kept dropping faster, to the point where nowadays radiation density is negligible. The dark energy density, however, remained constant (if it's a true cosmo constant). Just a little while ago it caught up to the matter density and passed it. We now live in a dark energy dominated Universe. The pressure from this dark energy forces the Universe to accelerate.

Dark matter, if I understand it correctly,

1) has mass;

2) does not give off radiation; and

3) has very low or no interaction with "light" matter today, even though at the beginning, it was interactive with light matter.

Also, do not 2) or 3), either alone or together, suggest that dark matter has no charge?

Further question: assuming light matter was created at the beginning, was dark matter was well?

[Bill3000]

Hey, KH, do you act like the way you are when you are asking for grants?

[KrazyHorse]

Originally posted by Kuciwalker
KH: doesn't increasing the amount of dark matter/energy increase the amount of energy in the universe, so if the density is constant it would make the universe try to contract?

No. Think about it as work done on the Universe. If there's negative pressure P then if you expand a tiny bit dV the work done on the Universe is -PdV, so the Universe has less "total" energy than before. So vice versa, if your component drops faster than 1/(a^3) (a the scale factor) then it exerts a negative pressure, i.e. a deceleration (like radiation)

If there's positive pressure then the work done on the universe is PdV, i.e. the Universe gains energy.

Your problem is that you're thinking of the Universe "creating" this energy and applying some sort of conservation of energy equation, where the expansion rate (derivative of a wrt time) plays the role of the kinetic term. This is not applicable to GR. Throw total energy conservation out the window. Locally energy is conserved, but there's no real consistent way to define total energy in curved space-time.

[KrazyHorse]

Originally posted by Kuciwalker
No we're talking about dark matter/energy. We apparently (according to KH) don't know the rate at which they decrease wrt the volume of the universe. Radiation goes faster than 1/x^3, mass at 1/x^3, and if the density of dark matter is constant, then it doesn't decrease as the universe expands.

KH, please correct me if I misunderstood your post

You understood my post, but you don't understand the stress-energy tensor or Einstein's equation.

That's okay, though...

[Ned]

Just an hypothesis, could dark matter be singularities that formed at the beginning when matter was very dense?

[Bill3000]

Is it just me, or is Ned acting sane? What happened to you, Ned?

[Ned]

Second, could the close proximity of two singularities break down one or both event horizons thus allowing the release of the mass within? Could this explain the big bang if possible?

[KrazyHorse]

Also, do not 2) or 3), either alone or together, suggest that dark matter has no charge?

Yes, on the whole. There may be some sort of neutral bound state whose components each have charge, but that hypothesis gets a little complicated. Dark matter must interact negligibly (outside of gravitation) at normal energy scales and densities (or even abnormal ones; only at ultrahigh energy/density should its presence become apparent)

And at high enough temperature, both dark and regular matter would be constantly created and destroyed. In the high-T limit all the different kinds of particles are given an equal share of the available energy (as a statistical statement). This is because all particles look fundamentally massless at high enough energy. As time goes on the mass terms become important because the available energy goes down. It costs more to create an electron than a photon because you have to climb the mass hill to make the electron. Whatever dark matter is was created in the same type of process out of the vacuum. When it basically became fixed happened at a different point than for regular matter (as it was different for each component of regular matter)

[KrazyHorse]

Originally posted by Ned
Just an hypothesis, could dark matter be singularities that formed at the beginning when matter was very dense?

Under the current understanding of how singularities work, no. The distribution of DM is smooth enough that these singularities would have to be very tiny and would thus "evaporate" quickly. However, this penomenon is not well understood for low-mass black holes. So it is possible. And there are papers exploring this and related possibilities. This type of explanation gets really complicated really rapidly. I don't understand the current state of this subfield.

EDIT: in addition to the evaporation problem there are a bunch of other problems with this, not least of which that you would expect DM to vacuum up light crossing through it. To play with this you need to make some fundamental modifications to a lot of things. I'm not putting my money on this option. It seems as though a couple of new particle species would be an easier solution.

[Ned]

Originally posted by Bill3000
Is it just me, or is Ned acting sane? What happened to you, Ned?

[Kuciwalker]

Originally posted by KrazyHorse
Your problem is that you're thinking of the Universe "creating" this energy and applying some sort of conservation of energy equation, where the expansion rate (derivative of a wrt time) plays the role of the kinetic term. This is not applicable to GR. Throw total energy conservation out the window. Locally energy is conserved, but there's no real consistent way to define total energy in curved space-time.

[Geronimo]

Originally posted by KrazyHorse

KH, could to "universe" at one time been composed only of dark matter?

Dark matter is assumed to have the same "equation of state" as regular matter. What the equation of state tells you is how much "pressure" is exerted by the component in question. Matter exerts 0 pressure. This is basically equivalent to saying that the "total amount "of matter is independent of the scale factor (except insofar as matter is annihilated or pair-created). More properly, it tells you that the density of matter goes down as the cube of the scale factor. Think of the Universe as a box. If you double the scale factor you increase its volume by 2*2*2 = 8. If you had 1kg of matter per meter cubed before doubling then after doubling you will have 1/8 kg per meter cubed. Both dark matter and regular matter are hit by the same scale factor cubed dependence, so to a first approximation the amount of dark and regular matter in the universe remain in the same proportion.

Radiation (light) and hot matter (stuff that's moving ultrarelativistically) are hit by an extra scale factor (from redshift), so they drop off quicker than matter. They also exert negative pressure on the Universe's expansion.

Finally, if dark energy is a true cosmological constant, its density remains a constant independent of the scale factor. It thus exerts positive pressure on the Universe's expansion (tending to force it to accelerate)

The thermal history of the Universe goes as follows, therefore: at early time, the Universe was hot and radiation dominated. Dark matter and neutrinos were so pressed together that they were in thermal equilibrium with the visible Universe. They behaved just like regular matter. Then the Universe expanded and cooled off. The dark matter stuff "froze out" (i.e. dropped out of contact with regular matter). It became real dark matter. The Universe expanded more and more. The radiation density dropped faster than the matter density. The Universe thus became matter dominated for a time. It kept expanding. The matter density kept dropping. The radiation density kept dropping faster, to the point where nowadays radiation density is negligible. The dark energy density, however, remained constant (if it's a true cosmo constant). Just a little while ago it caught up to the matter density and passed it. We now live in a dark energy dominated Universe. The pressure from this dark energy forces the Universe to accelerate.

Ok, stupid questions as I know I've heard an explanation before. How does this relate to the 1st law of thermodynamics? When the expansion of the universe alters the proportion of say, Radiation and hot matter to the rest of the "stuff" in the universe, won't the total energy of the universe change as well in at least the case of a finite universe?

Do all changes in the ratio of one form of matter/energy to another that result from the expansion necessarily involve increasing the total energy of the form whose proportion increases to exactly match the total energy "lost" by the form whose proportion decreases?

I'm especiall puzzled when considering something like dark energy whose density remains constant even as the volume it occupies increases. The total energy of the universe doesn't change even in that case?

[KrazyHorse]

Ok, stupid questions as I know I've heard an explanation before. How does this relate to the 1st law of thermodynamics? When the expansion of the universe alters the proportion of say, Radiation and hot matter to the rest of the "stuff" in the universe, won't the total energy of the universe change as well in at least the case of a finite universe?

Global energy conservation is gone. Please see my post to kuci.

[Ned]

Have we any information on the spacial density of dark energy? If it has mass, wouldn't int interact with light matter and dark matter in the same gravitational way as light matter?