Could Dark Mass Be a Possible Explanation for Missing Particles in the Universe?

[Tanelorn]

Thanks Chalnoth. The 8% is related to the percentage of solid objects per unit area between us and the cosmic horizon?

 

[Chalnoth]

Thanks Chalnoth. The 8% is related to the percentage of solid objects per unit area between us and the cosmic horizon?

Nope. The universe as a whole is far, far too low in density for that. Almost none of the photons impact anything like a star or a planet.

Instead the majority of the optical thickness of the universe stems from diffuse ionized gas. Basically, when the stars started to turn on, the high-energy light they emitted ionized the intergalactic gas. Since light interacts strongly with charged particles, this turned the universe from very transparent to semi-transparent. However, by the time the first stars formed, the universe had already grown by a factor of 50-100 or so from the emission of the CMB, and so the gas was just too low in density to block much of the radiation.

 

[Tanelorn]

Chalnoth, presumably radiation was emitted from everywhere and in every direction within the sphere when the universe became transparent. However the background radiation coming to us now can only come from approximately 13.4? Billion lights away in every direction?

 

[Chalnoth]

Chalnoth, presumably radiation was emitted from everywhere and in every direction within the sphere when the universe became transparent. However the background radiation coming to us now can only come from approximately 13.4? Billion lights away in every direction?

Sort of, yes. Said more exactly, the light we see now is the light that has been traveling for around 13.7 billion years. Because of the expansion, though, it didn't come from that far away. Curved space-time tends to muck things up here.

Basically, when this light was emitted, it was a mere 43 million light years away, but at the time our universe was expanding so rapidly that the light that was heading in our direction actually lost ground with respect to the expansion. As the expansion slowed, the light was able to gain ground against the expansion, eventually reaching us 13.7 billion years later. Today, the stuff that emitted that light is an impressive 47 billion light years away.

 

[Tanelorn]

Thanks Chalnoth. Very interesting that the rate of expansion was faster earlier on. I have often wondered if this expansion and inflation of the inflaton are related and possibly even a continuation of the same effect.

If we plot the expansion of the observable universe radius and volume over time do we get any clues as to the nature of this expansion. eg. is it the increase in volume equivalent to a balloon being inflated by a constant amount of gas?

Perhaps the same amount of dark energy per unit volume has been applied somehow ever since the singularity and this results in much faster expansion at t=0 and less now?

Back to the WMAP and frequency variation of the CBR:

Why was 141deg chosen?

You said, "We want to know the small deviations in temperature across the sky" In WMAP we are measuring difference in intensity between two directions. How is this converted to frequency peak and temperature?

You said, "and in order to distinguish between the CMB and other sources, we need to look at the sky at multiple different frequencies." How are we doing this on WMAP and what is the level of uncertainty in the contribution of these other sources?

You said, "Well, things are, on average, moving away from us at a rate proportional to distance that is the same, again on average, in all directions, once we have subtracted our own motion." Are there any unexplained issues with just subtracting our own motion? I thought I read there were but now can't find the link. There was also the quadrupole issue but it wasn't about this.

 

[Chalnoth]

Thanks Chalnoth. Very interesting that the rate of expansion was faster earlier on. I have often wondered if this expansion and inflation of the inflaton are related and possibly even a continuation of the same effect.

Yes, well, consider the first Friedmann equation in flat space (with constants omitted for clarity):

$$H^2(a) = \rho(a)$$

Basically this says that the square of the Hubble parameter, which is the rate of expansion, is proportional to the energy density of the universe. Since the energy density in the very early universe was much, much higher, so was the expansion.

If we plot the expansion of the observable universe radius and volume over time do we get any clues as to the nature of this expansion. eg. is it the increase in volume equivalent to a balloon being inflated by a constant amount of gas?

Well, we definitely get clues, because different sorts of energy density tend to cause very different rates of expansion with time. This is, fundamentally, why we are now reasonably confident that some sort of dark energy exists.

Perhaps the same amount of dark energy per unit volume has been applied somehow ever since the singularity and this results in much faster expansion at t=0 and less now?

Well, not really. The dark energy tends to have most of its effect at late times. Basically, the dark energy density remains nearly constant as the universe expands. So at early times, the normal matter and radiation densities were vastly, vastly higher than the dark energy density. But as time went on, the radiation and the normal matter diluted away, but the dark energy density remained the same, or nearly so. So this means that the early expansion was just what we would expect from a universe without any dark energy, but the late-time expansion is much faster than we would expect.

 

[Tanelorn]

Re: Well, we definitely get clues, because different sorts of energy density tend to cause very different rates of expansion with time. This is, fundamentally, why we are now reasonably confident that some sort of dark energy exists.

Also wondered if there are there any similarities to a fixed amount of gas being released into an infinite vacuum which then expands rapidly at first but slows down?

Wouldn't the rate of expansion early on be slowed by gravitation between matter/dark matter? So expansion is speeding up again? (I think you just touched on this in your last paragraph)

 

[Chalnoth]

Also wondered if there are there any similarities to a fixed amount of gas being released into an infinite vacuum which then expands rapidly at first but slows down?

I don't think that can work. If you consider a situation where you have a homogeneous, isotropic bunch of matter that is finite in extent, but at least large enough to enclose an observable universe, and said observable universe is also either closed, spatially flat, or nearly flat, then one of the things you find is that the Schwarzschild radius for that much mass is larger than the radius of the universe itself. So you can't actually have a universe expanding into a vacuum, as from the perspective of the outside, it must look like a black hole!

This indicates that if a new region of space-time is born within a pre-existing vacuum, it looks, to the outside, like a microscopic black hole that pops into existence and then immediately evaporates back to nothing. We can visualize this as a sort of bubble of space-time pinching itself off from its parent universe, becoming physically disconnected from the parent for all time.

Wouldn't the rate of expansion early on be slowed by gravitation between matter/dark matter? So expansion is speeding up again? (I think you just touched on this in your last paragraph)

Yes, the expansion was absolutely slowed down by the gravitation between matter/dark matter. Before that, the expansion was slowed even more dramatically by radiation (but radiation dilutes more rapidly than normal matter, because it also redshifts as the universe expands, losing energy as a result).

As for whether expansion is speeding up again, that depends a bit upon what you mean. Let's go back to the first Friedmann equation for a moment:

$$H^2(a) = \rho(a)$$

As time goes forward, the energy density $\rho(a)$ is slowly approaching a constant. This happens as the normal matter and radiation both dilute away with time, each becoming smaller and smaller. But the dark energy stays nearly constant, so the energy density of the universe approaches this constant value.

This means that the Hubble expansion rate, $H(a)$ will approach a constant as the universe expands. But what does this mean? Well, the definition of the Hubble expansion rate is:

$$H(a) = {1 \over a} {da \over dt}$$

If this is equal to a constant, then we have:

$$H(a) = H_0$$
$${1 \over a} {da \over dt} = H_0$$
$${da \over dt} = H_0 a$$

If you know a little bit about differential equations, you should recognize this one. It's a statement that the rate of change of the scale factor $a$ is proportional to the value of the scale factor.

This is a differential equation we see all over the place in science: it's an equation representing exponential growth. A sort of everyday example of this is interest. Imagine you have a bank account that earns 5% interest. The amount of new money in the bank account each year will be proportional to the amount of money in the bank account. That is, the rate of change of money in the bank account is proportional to the amount of money in the bank account. This is exponential growth!

So as the energy density of the universe approaches a constant, the scale factor will, as a function of time, get closer and closer to exponential growth. This is what we mean by "accelerated expansion".

 

[Tanelorn]

Thanks Chalnoth. Wouldn't the extremely fast inflation of the inflaton also be aided by its almost infinitely high pressure?

If the above is correct then we would have three contributions to the expansion of the observable universe, whose contributions vary with it's size. Plasma Pressure, gravity and dark energy.

Regretably with mathematics I became lazy and started to rely on concepts, pictures and intuition. So I haven't used any real mathematics for probably 33 years. I will have to become much more fluent in mathematics again to see the detail. For complete understanding I think the best is a full description in words of what an issue is about and followed by an exact mathematical treatment.

 

[Chalnoth]

Thanks Chalnoth. Wouldn't the extremely fast inflation of the inflaton also be aided by its almost infinitely high pressure?

Nope. When you take gravity into account, having high pressure actually seeks to increase the gravitational attraction. Radiation has positive pressure, for instance, and a radiation-dominated universe slows its expansion more rapidly than a matter-dominated one.

Instead, during inflation, there was lots of negative pressure. Negative pressure is what is required to get an energy density that remains nearly constant. During this era, there was a nearly constant energy density in a field we call the inflaton. It wasn't exactly constant, but nearly so. The magnitude of this energy density was vastly higher than the dark energy we have today.

Given the similarities, many theorists have tried to develop models which connect inflation with dark energy, but so far none of these models are compelling.

Regretably with mathematics I became lazy and started to rely on concepts, pictures and intuition. So I haven't used any real mathematics for probably 33 years. I will have to become much more fluent in mathematics again to see the detail. For complete understanding I think the best is a full description in words of what an issue is about and followed by an exact mathematical treatment.

Fair enough. Just bear in mind that there is no such thing as a full description in words. The only full description of what we know is a mathematical description. And the mathematical description, sadly, never exactly maps onto natural language (though some are better than others at conveying the underlying meaning).

 

[Tanelorn]

Thanks Chalnoth.

Am I right when I say ordinary matter eg. hydrogen gas will always have what is called positive pressure? Also radiation will always have positive pressure?
What about plasmas that we can create in a lab, do they also have positive pressure?

What can cause negative pressure in an inflaton? Is it the sheer speed of inflation like someone drawing in a deep breath really fast? Or some property of the plasma itself?

 

[Chalnoth]

Thanks Chalnoth.

Am I right when I say ordinary matter eg. hydrogen gas will always have what is called positive pressure? Also radiation will always have positive pressure?
What about plasmas that we can create in a lab, do they also have positive pressure?

Yes, normal matter always has positive pressure. However, on cosmological scales, normal matter and dark matter have pressure that is so small it is effectively zero. For quite a while, some physicists thought it was actually impossible for anything to have negative pressure. To get matter with negative pressure, you have to go for some rather exotic quantum fields.

What can cause negative pressure in an inflaton? Is it the sheer speed of inflation like someone drawing in a deep breath really fast? Or some property of the plasma itself?

It's just the nearly constant energy density that does it.

If we take the simplest sort of model for inflation, for instance, we have the following scenario. First, we imagine a particle, called an inflaton. The inflaton is a scalar particle. This means that this particle can be described as a field that takes a particular value at every point in space. This is to be contrasted with vector fields like the electric and magnetic fields which take on both a direction and magnitude at every point in space. A scalar field has no direction, just a value.

Now, this inflaton has a potential energy associated with this value. For some reason, the microscopic physics (which are unknown) are such that certain configurations of this inflaton field have more energy than others. So what tends to happen with this field is that if it starts at a particular configuration, the value of the inflaton will decrease towards the minimum energy configuration.

Now, what makes it cause inflation is this: as the universe expands, this induces a sort of friction on the inflaton, so that it has a hard time changing its value. The faster the expansion, the more the value of the inflaton field stays the same. So if the energy in the inflaton field is high enough, the energy density in the inflaton field just doesn't change much at all as the universe expands, which causes a rapidly-accelerated expansion.

When you look at the stress-energy tensor of this sort of field, you find that the reluctance of the field to change its energy density comes in as a negative pressure.

 

[Tanelorn]

Thanks Chalnoth, You really got me with that negative pressure reply, I can't even come up with a question. So I am going to need to brain booster to get around it. Its a shame they blew up that Krel Machine in the Forbidden Planet! I may be some time :)

PS I hope that Occam's razor is still being satisfied there!

 

[Tanelorn]

Chalnoth, I am not sure where to ask this but I have two questions:

Firstly, Regarding Black Holes, as they are created from collapsed stars, and/or, as they swallow all forms of matter and energy, is there any possible way that this removal of matter and energy from our universe is in some way connected to the same expansion of space that dark energy is believed responsible for? I am just playing a hunch here, they seem to be the 800 pound gorillas in the room, and there is a quasi infinite number of them of various sizes scattered all around the universe.

Secondly, back to the background temperature, do you know of a graph plotting temperature of the universe back in time to the time of last scattering?

 

[Chalnoth]

Chalnoth, I am not sure where to ask this but I have two questions:

Firstly, Regarding Black Holes, as they are created from collapsed stars, and/or, as they swallow all forms of matter and energy, is there any possible way that this removal of matter and energy from our universe is in some way connected to the same expansion of space that dark energy is believed responsible for? I am just playing a hunch here, they seem to be the 800 pound gorillas in the room, and there is a quasi infinite number of them of various sizes scattered all around the universe.

Nope. The mass doesn't disappear when it enters a black hole, it adds to the black hole's mass. So if, for instance, we have a star with some mass collapse into a black hole, then the total mass of the star will be equal to the total mass of the black hole plus whatever mass was ejected during the ensuing explosion.

Furthermore, outside of both objects, a star with the same mass as a black hole has the exact same gravitational field.

Secondly, back to the background temperature, do you know of a graph plotting temperature of the universe back in time to the time of last scattering?

No, but it's easily calculated. The temperature is inversely proportional to the expansion. So that:

$$T(z=0) = (1+z)T(z)$$

Or:

$$T(a=1) = {T(a) \over a}$$

So, for instance, when the CMB was emitted at a redshift of $z=1089$, the temperature was 1090 times as high as it is today.

 

[Tanelorn]

Thanks Chalnoth,

I make that 2.725K x 1090 = 2970K
Also the radius of what is now the observable universe is just 300,000 light years, about 3 times the diameter of the milky way.
Also matter at that time had just taken the form of normal, non ionized Hydrogen and Helium atoms.
Is it in a gaseous form or is it much to dense? What is the density or pressure or number atoms per unit volume?

 

[inflector]

Any chance we can get back to the topic of the OP after the 30-post diversion on general cosmology?

 

[Tanelorn]

Sorry. Maybe we can start a general Ad Hoc questions thread and copy it there?

 

[Driftwood1]

We know particles have mass. Thusfar we don't know of anything that has mass which is not a particle so we assume the likeliest explanation for apparent missing mass must be missing particles.

particle-wave duality?

photons have no mass

what do you mean by a particle?

or a wave?

or mass for that matter

 

[Driftwood1]

So, for instance, when the CMB was emitted at a redshift of $z=1089$, the temperature was 1090 times as high as it is today.

Does the speed of light remain constant as one goes back in time towards the initial Big Bang event?

 

[Chalnoth]

particle-wave duality?

photons have no mass

what do you mean by a particle?

or a wave?

In quantum mechanics, all matter has wave-like behavior. A quantum-mechanical particle is a quantum of a field. An electromagnetic field, for instance, is made up of tremendous numbers of quanta called photons, which we understand as being particles in the quantum-mechanical sense (which includes having wave-like behavior).

or mass for that matter

Mass is the non-kinetic energy of an object.

 

[Driftwood1]

In quantum mechanics, all matter has wave-like behavior. A quantum-mechanical particle is a quantum of a field. An electromagnetic field, for instance, is made up of tremendous numbers of quanta called photons, which we understand as being particles in the quantum-mechanical sense (which includes having wave-like behavior).


Mass is the non-kinetic energy of an object.

E = mc^2

E = hf

so mc^2 = hf

which defines mass, m as

m = (h/c^2) f = Kf

Mass is merely a "vibration"

Notice how small the constant (h/c^2) is?

 

[Chalnoth]

E = mc^2

E = hf

so mc^2 = hf

Non-kinetic energy. Planck's constant times the frequency of a photon is the kinetic energy of the photon. Photons have no non-kinetic energy.

 

[Driftwood1]

Non-kinetic energy. Planck's constant times the frequency of a photon is the kinetic energy of the photon. Photons have no non-kinetic energy.

...and yet photons exert pressure (photoelectric effect, solar sails)

interesting

 

[Weeble]

I'm new to blogs so this is my first post. I'm also no physicist by any stretch of the imagination but I love science. My question is this, if light is slowed when it moves through a medium which has mass, and it seems the belief is that dark matter has mass and is everywhere, isn't light actually slowed by dark matter? It seems to me that if this is true then light should actually be faster than what we know it to be. If, for example, there was a true "vacuum" devoid of any dark matter would light travel faster or is the speed of light already based on a true vacuum with no dark matter in the equation?

 

[Chalnoth]

...and yet photons exert pressure (photoelectric effect, solar sails)

interesting

Yes, because photons also have momentum equal to their energy. In relativistic terms, the total energy of a particle is:

$$E^2 = p^2 c^2 + m^2 c^4$$

Notice that in the case of zero momentum ($p$ is the momentum of the particle), this equation reduces to the more familiar:

[tex]E = mc^2[/itex]

This is actually just a special case, as the energy is only equal to the mass in the non-moving case. With photons, which have zero mass, the energy reduces to:

$$E = p c$$

Since photons have momentum, they can impart that momentum on other objects when they are absorbed or bounce off of them. And so a bunch of photons hitting an object together exert pressure.

 

[Chalnoth]

I'm new to blogs so this is my first post. I'm also no physicist by any stretch of the imagination but I love science. My question is this, if light is slowed when it moves through a medium which has mass, and it seems the belief is that dark matter has mass and is everywhere, isn't light actually slowed by dark matter? It seems to me that if this is true then light should actually be faster than what we know it to be. If, for example, there was a true "vacuum" devoid of any dark matter would light travel faster or is the speed of light already based on a true vacuum with no dark matter in the equation?

Light isn't slowed by mass. It's slowed by electromagnetic interactions. So light is basically unaffected by dark matter, which has no charge with which light can interact.

 

[Driftwood1]

$$E = p c$$

... p=$$\frac{h}{c}$$f

Momentum is dependent on the frequency (or wavelength) of the photon

(just trying out the cool symbols etc availiable on this chat site)

 

[dman124]

"Mass is the non-kinetic energy of an object." originally posted by chalonth

what do you mean by this i thought mass was the amount of matter inside an object

 

[dman124]

I'm interested to see Ich's response but in thinking about it, it's obvious that spacetime moves back to straight/flat if you take the matter away, so in that sense, it wants to be straight/flat.

i agree but then what would happen i too big of a mass made a rip in space time and then that mass dissapeared?(theoretically of course)

 

[Chalnoth]

"Mass is the non-kinetic energy of an object." originally posted by chalonth

what do you mean by this i thought mass was the amount of matter inside an object

Nope. If you have a block of wood, and raise its temperature, its mass increases. It just so happens that for reasonable temperatures, that mass increase is almost completely negligible. But for quantum systems the mass difference due to similar effects can be significant.

For example, if you compare the masses of a proton and a neutron separately, and then to a deuterium ion (which is a bound state of a proton and a neutron), you find that the deuterium ion has about 0.1% less mass. This is an indication that the deuterium ion is a lower-energy configuration than a separate neutron and proton.

Even more striking, however, is what happens inside the protons and neutrons. The masses of the individual quarks that make up the proton and neutron are only around 1-2% of the total mass. The rest of the mass comes from the binding energy of the quarks.

 

[Chalnoth]

i agree but then what would happen i too big of a mass made a rip in space time and then that mass dissapeared?(theoretically of course)

So far as we are aware, no amount of mass can cause anything like a rip in space-time.

 

[Driftwood1]

Even more striking, however, is what happens inside the protons and neutrons. The masses of the individual quarks that make up the proton and neutron are only around 1-2% of the total mass. The rest of the mass comes from the binding energy of the quarks.

Intreresting...

Are you saying that whilst the quarks are bounded together inside the protons and neutrons that about 98% of that mass is in the form of binding energy?

It would seem to me that what happens is that this energy is released as a direct result of separating the quarks.

Whilst mass and energy can be interchanged - they are not equivalent states

One must be careful when comparing quarks on their own with quarks bounded together in a neutron or proton

 

[Chalnoth]

Intreresting...

Are you saying that whilst the quarks are bounded together inside the protons and neutrons that about 98% of that mass is in the form of binding energy?

It would seem to me that what happens is that this energy is released as a direct result of separating the quarks.

Nope, actually. The strong force doesn't allow that. If it did, protons would decay rather rapidly! The effect that prevents protons from breaking apart into their constituent states is known as "confinement", and it means that you have to put so much energy into a system to pull its quarks apart that soon quark/anti-quark pairs will pop into existence between the quarks you're pulling apart.

So in the case of, say, a proton, made of two ups and a down, if I started to pull on one of the quarks, eventually the tension would "snap", producing a quark/anti-quark pair. The new quark will bind with the proton, leaving it either as a proton or a neutron (depending upon whether the quark I leave behind is the same or different), and I'll be left holding onto the quark I was pulling on and an anti-quark in a bound state, which is known as a meson.

It turns out that the way the strong force behaves, protons are the lowest-mass configuration of three quarks, and you just can't pull them apart to make more energy. Other three-quark configurations all have more mass. This includes the neutron, which, if it is unbound, will decay into a proton, electron, and anti-neutrino after a little while. It's just that neutrons, when bound to protons, can be stable in some configurations.

Whilst mass and energy can be interchanged - they are not equivalent states

Nope, mass and energy are equivalent. Mass is non-kinetic energy. That is all.