What are the Consequences of Non-Uniform Expansion?

[Hydr0matic]

If the accelerated expansion of the universe is due to dark energy, wouldn't this cause temperature fluctuations in the CMBR - as seen by COBE & WMAP ?

Is it reasonable to assume that the dark energy is evenly distributed in the universe ? I think not ...

... but if it's not, the expansion should also be non-uniform, right ?

In fact, the WMAP images might not be imprints from the early universe at all, it might be dark energy ?


I'm sure there are other more significant consequences of non-uniform expansion than this though ... so it can be ruled out ... but what are they ?

 

[Hydr0matic]

.. just saw the other thread ... How do I delete this one ?

 

[marcus]

Is it reasonable to assume that the dark energy is evenly distributed in the universe ? I think not ...

Hydro0matic I believe the special thing about dark energy is the negative pressure

it is the negative pressure that enters in the Friedmann equation and causes acceleration, so without that quality dark energy would not meet the requirements of the model-builders

in the simplest conception of dark energy it has negative pressure *because*
it has a uniform spatial density.
it is so-and-so joules per cubic kilometer

Actually the estimate is 0.6 joules per cubic kilometer.

But any constant uniform energy density would result in a negative pressure
because if you expand a volume of space you thereby create energy and this takes work, so the volume has negative pressure (it takes work to make it expand).

So the idea of acceleration requires negative pressure
and negative pressure implies (or at least the simplest mechanism for it implies) uniform distribution-----a constant X joules per cubic km.

-----------------

this does not prove it is uniform
but I disagree with you that it is unreasonable to assume uniformity
Indeed I think it is the simplest (and thus by Occam razor) the most reasonable explanation
for the surprising fact of acceleration.

---------
your idea that we can see dark energy fluctuation in the random temperature
anisotropy of the CMB is attractive. it may be (probably is) wrong
but it is an intriguing idea

 

[marcus]

.. just saw the other thread ... How do I delete this one ?

Why should you delete this. This is a good thread.
I like the idea you offer.
there is no harm in having two threads about possible non-uiniform dark energy

 

[marcus]

Hydr0matic do you know these two equations?

in units where c = 1:

$$\frac{a''}{a} = - \frac{4\pi G}{3}(rho + 3p)$$

$$(\frac{a'}{a})^2 = \frac{8\pi G}{3}rho - \frac{k}{a^2}$$

I think you very likely do know them.
These are the Friedmann equations basic to cosmology.

what governs acceleration is the eqn with a''
and you see a minus sign
so there can only be positive acceleration
when (rho + 3p) is negative!

but rho, energy density, is always positive, so there must be
something with strongly negative pressure p, so the 3p will overcome
the rho
and make the combined thing negative
so there must be negative pressure!

there is more about the Friedmann equations at lots of cosmology
websites but also at this PF post
https://www.physicsforums.com/showthread.php?p=210120#post210120

 

[Hydr0matic]

Like the guy in the other thread I'm also a programmer, so I can't say I'm too familiar with the friedmann eqns no... But as far as the maths go, I completely get what you're saying. I have no idea why friedmanns apply though . I always figured dark energy as a positive pressure ... more intuitive ... but what do I know ...

but I disagree with you that it is unreasonable to assume uniformity
Indeed I think it is the simplest (and thus by Occam razor) the most reasonable explanation
for the surprising fact of acceleration.

Yes, it's simpler in the sense that it's easier to express and work with mathematically (as you explained in the other thread)... But purely based on observation of the universe, a non-uniform distribution of dark energy seems more likely .. - that is, if there's any relation between dark energy and ordinary matter.
But perhaps there isn't ? .. Just assuming things ...

your idea that we can see dark energy fluctuation in the random temperature
anisotropy of the CMB is attractive. it may be (probably is) wrong
but it is an intriguing idea

Yes, but I think I've read somethin' about seeing imprints of superclusters like "the great wall" in the CMBR, confirming current ideas... but I'm not sure.

 

[marcus]

there are many things we could talk about here
I will go light because I hope other people will join the discussion
Friedmann derived those two equations from the 1915 Gen Rel eqn of Einstein by making a simplifying assumption that the universe was homogeneous so instead of detailed distribution of matter there was just the average density of matter---called rho.
In cosmology the Friedmann equations take the place of the 1915 Einstein equation because they are much simpler.


Do you have an idea of a quantum mechanical or quantum field theoretical
"vacuum energy"? After taking all possible energy out of a cubic meter of empty space, the idea is that because of virtual particles or uncertainty or some such weird thing there is still a tiny fraction of a joule left.
And this would be the same anywhere in the universe at any time---if quantum field theory stays the same throughout.

I am not saying that dark energy is the same as "vacuum energy". Only that vacuum energy is another thing that is uniform (if it exists) and if it exists it would have a negative pressure simply because it is uniform.

A uniform energy density X joules per cubic meter---must have negative pressure because if you have a pump cylinder with one cubic meter of empty space in it and you pull out the piston some----it must take work because
when you have pulled it out so there are two cubic meters in the cylinder then there is 2X joules of energy. It must take X joules to pull the piston out.

You have to do this experiment outside the universe and outside the physical vacuum so that there is nothing around the cylinder---really nothing.

The field theorists did not yet calculate a satisfactory figure for the vacuum energy but AFAIK they think it is there and someday maybe will be able to calculate it.

It is interesting that some bumps or dents in the CMB could be associated with known superclusters. Can you find more about this? Does anyone know
of a link to some paper about it? (there are some very knowledgeable people that post here sometime who might know about this)

I think Friedmann was in the 1920s in St Petersburg---or it was Petrograd or Leningrad then.

 

[Hydr0matic]

Do you have an idea of a quantum mechanical or quantum field theoretical "vacuum energy"?

Yes, on a conceptual level.

I am not saying that dark energy is the same as "vacuum energy". Only that vacuum energy is another thing that is uniform (if it exists) and if it exists it would have a negative pressure simply because it is uniform.

I understand. Up until now I've been under the impression that dark energy was some "mysterious anti-gravity force" - a misconception often stated in articles on the subject. This, and my misconception about the big bang (which I just resolved in the other thread), has made me pretty uninterested in cosmology actually. At least until now.

How can dark energy contribute to the expansion rate if it has a negative influence ? (i.e. it makes it harder (takes work) to expand the volume)...

So does the "new" volume take this energy from somewhere ?

Why does it have to be done outside the universe ? Will a cylinder shaped volume between two points in space not experience the same effect when the two points recede from each other ?

If after a certain time this cylinder shaped volume has increased and gained energy respectively (with constant density), would this mean the universe had gained an infinite amount of energy ? (since space is infinite, any (non-infinitesimal) fraction of it is also infinite)

Can there be any conversion between dark and "normal" energy ?

It is interesting that some bumps or dents in the CMB could be associated with known superclusters. Can you find more about this?

Tried, but couldn't. I think I may have missinterpreted something.. I suspect what I read was rather a comparison in size between "the bumps" and the visible universe.

 

[marcus]

I'm reading these questions
and I can't see how to answer.
I looked in a good survey article by a top cosmologist Michael Turner
"Making Sense of the New Cosmology"
http://arxiv.org/astro-ph/0202008
and even though it has a lot (starting on page 7) about dark energy
it didn't help me reply to your questions.

We have no reason not to suppose the universe is infinite.
If it is flat then infinite is the simplest assumption (or else we must think
of torus shapes which is more trouble)
So if we think of infinite approximately flat U with constant energy density
then that is an infinite amount

and suppose there is a vacuum energy, a constant amount per cubic meter, then there is an infinite amount of vacuum energy
and now suppose the U doubles in size------then there twice as much vacuum energy
and yet it is still the same amount-----oo + oo = oo

also in Gen Rel there is no global energy conservation law
already the CMB photons have been stretched out by a factor of 1100
(the redshift since the CMB was emitted as 3000 kelvin black body)
and so all the CMB photons have lost all but 1/1100 of their energy
and no one has told us where this energy went
no one thinks to ask because in GR there is no energy conservation law

one can easily panic

there are unintuitive things in cosmology which I suppose the cosmologists
have learned not to think about
because it would be a waste of time just now to think about them

I like the general direction of the questions you are asking but can't help, sorry

 

[marcus]

Hydro, it has always been unintuitive to me that pressure is gravitationally attractive.

part of what makes a star attractive, so the planets go around it, is the PRESSURE down in the core

if you just would take the attractiveness associated with the mass-energy of each particle in the sun that would not add up right
and there is some mass associated with the heat energy
but just adding up energies does not give the right answer

some of the mass of the sun is actually attributed to the pressure

in the einstein equation curvature = "stress-energy tensor" and when the equation is simplified the stress boils down to pressure
so the original 1915 einstein equation was saying that it is not only energy density in something that makes it attractive, also the pressure does, the stress inside it

this is extremely mind-boggling

because for one thing, gravity makes things contract
but here the einstein equation says the (positive) pressure inside the core of the sun contributes to its gravity, which makes things contract,
but you and I always thought that pressure is expansive!

yes pressure is expansive of material, like air
but it is not expansive of the gravitational field!
positive pressure acts on the gravitational field like an attractor
like something analogous to mass or energy density.

if you squeeze something in a vise you actually make it more massive
because of the positive pressure you create in it


OK so the negative pressure of vacuum energy can counteract that somehow
and make space less massive and more expansive (?whoah, too weird!)
the energy itself is just like any other energy and would favor contraction but the negative pressure has this expansive effect.

what can I say. its fundamentally wacky. I really wish I could help make better sense of it for both of us

maybe someone else here will help

 

[Hydr0matic]

LOL ... first of all, I agree - ".. whoah ... !"

some of the mass of the sun is actually attributed to the pressure

Ok, is there anything supporting this claim at all ? Cause it sounds very silly to me. I mean, we're not even close to fully understanding the sun and all it's strangeness.
.. and wouldn't this gravity / pressure relationship be an unstopable process? It would have the same effect as if a particles mass increased in a gravity field. The particles would increase in mass which would increase their gravity which increases there mass even more... and so on. The same would happen with pressure, right ? and our universe would only consist of black holes.

what can I say. its fundamentally wacky. I really wish I could help make better sense of it for both of us

Hey, I'm learning a lot here .. I appreciate it.

 

[kurious]

some of the mass of the sun is actually attributed to the pressure


The pressure may be causing the sun to interact with more Higgs particles which
would increase the mass - but no-one even knows if Higgs particles exist yet so this idea is speculative.

 

[marcus]

...and wouldn't this gravity / pressure relationship be an unstopable process? It would have the same effect as if a particles mass increased in a gravity field. The particles would increase in mass which would increase their gravity which increases there mass even more... and so on. The same would happen with pressure, right ? and our universe would only consist of black holes.
...

thoughtful question!
the answer is in the small size of the effect, at ordinary densities

algebraically the unit of pressure (pascal) has the same dimensions as the unit of energy density (joule per cubic meter)

so one can do an immediate comparison

the mass density of water is 1000 kg per cubic meter corresponding (by em-cee-squared) to an energy density of 9 x 10¹⁹ joule per cubic meter.

so a typical condensed ordinary matter just sitting there has a massenergy density of 9E19 in metric units.

to create pressure equivalent of that energy density would take a pressure of 9E19 Newton per square meter------9E19 pascal


[Newton per square meter is dimensionally the same as Newtonmeter per cubic meter----which is joule per cubic meter]

this comes out of the 1915 Einstein eqn (stress-energy tensor includes energy density and pressure) which actually yields also a factor of three (!)
in the comparison of the effects----I am ignoring the factor of 3 because I only want a crude comparison.

my handbook says the pressure at center of sun is only around
E16 pascal

this corresponds to an energy density that is roughly a ten-thousandth
of the normal density of water

that is, it is around 1/10000 of 9E19

so indeed the pressure makes it seem as if there was a little bit more matter present, than there really is
but the effect is so small that it could not cause a runaway contraction
at least in ordinary star-core conditions

maybe the effect does come into play when a neutron star collapes to a black hole----I can imagine that it might help the black hole to form, but I didnt check this by even rough calculation

 

[marcus]

some of the mass of the sun is actually attributed to the pressure


The pressure may be causing the sun to interact with more Higgs particles which
would increase the mass - but no-one even knows if Higgs particles exist yet so this idea is speculative.

it is good to speculate about how energy density and pressure can
interact with geometry
(the gravitational field is the geometry of spacetime----what determines curvature, lengths, areas, volumes)
personally I can only agree that one should try to speculate how it can happen that matter effects geometry and bends light and all that

but I cannot discuss it, personally, because I am clueless

one must have a model that represents the geometry of spacetime, perhaps a simplicial lattice, and then one must imagine it occupied by particles or fields of matter---and perhaps having some stresses and strains along its legs and at its nodes---and perhaps then changing its geometry(?) beginning down at the quantum level, but this project (quantum description of how gravity works) has stumped professional theorists for many decades

there could be a Country and Western song about how hopeless it is

 

[kurious]

The pressure may be causing the sun to interact with more Higgs particles which
would increase the mass - but no-one even knows if Higgs particles exist yet so this idea is speculative.


I've looked at the Fermilab website with regard to the above sentence.
Increasing the number of Higgs particles does not increase the mass - the mass results solely from the "drag" of the Higgs Field. Apparently Higgs particles can interact with anything but the Higgs field does not interact with photons or with gluons which is why they are massless.
I would guess that pressure concentrates the Higgs field -the mass of the sun must depend on the density of the Higgs field around it.
Mass increases in special relativity with speed - maybe relativistic length contraction puts more of the Higgs field in a smaller area and concentrates it.