# Dark Matter or Dark Mass?

Chalnoth, thanks again for your very helpful reply. The number of questions I have are growing exponentially with each answer!

However, there is one question I want to be clear about before the others and that is, why do some pictures show the Galactic plane and some do not? At the moment I am assuming that the galactic plane is removed later mathematically from some of the plots? This is an example here on page 32, one with the plane and one without:

http://lambda.gsfc.nasa.gov/product/map/dr4/pub_papers/sevenyear/anomalies/wmap_7yr_anomalies.pdf

PS. I really liked the S.H. initials. So unlikely and yet shows that unlikely things can do happen, but hopefully do not get built into theories! I also saw that the quadrupole effect looks like it could pose a problem of sorts.

Chalnoth
Science Advisor
However, there is one question I want to be clear about before the others and that is, why do some pictures show the Galactic plane and some do not? At the moment I am assuming that the galactic plane is removed later mathematically from some of the plots?
Right, so the image that doesn't show the galactic plane used a component separation technique known as Internal Linear Combination (ILC). ILC makes use of the fact that we know how the CMB scales with frequency. The WMAP maps were calibrated off of the CMB dipole due to our own motion, which is an order of magnitude larger than the other anisotropies in the CMB, but has the same dependence on frequency (this dipole is removed from all maps you see, by the way). With this assumption, the ILC technique can be described as follows:

1. Let's assume that the signal for each map at every pixel can be represented as:

$$d_i = a_i s + n_i$$

Here $$i$$ indexes the frequency band, $$a_i$$ is the frequency scaling of the particular signal, $$s$$ is the signal you're interested in (in this case CMB), $$n_i$$ is everything else, and $$d_i$$ are the individual frequency maps.

The goal is to find a linear combination of the maps $$d_i$$ that retains the signal you want while minimizing everything else:

$$\tilde{s} = \sum_i w_i d_i$$

If we exploit the fact that $a_i = 1$ for the CMB, then we know that if $\sum_i w_i = 1$, $\tilde{s} = s + \sum_i w_i n_i$. So if we use this constraint that the sum of the weights of the channels must equal to one, then we just minimize the variance of the output and we are left with a signal that is mostly CMB. This can be done analytically with just a tiny bit of linear algebra.

There are many other techniques for distinguishing between the CMB and the foregrounds in multi-channel maps, but this is the simplest and fastest.

PS. I really liked the S.H. initials. So unlikely and yet shows that unlikely things can do happen, but hopefully do not get built into theories! I also saw that the quadrupole effect looks like it could pose a problem of sorts.
Yeah, the SH initials were cute. But the quadrupole really isn't a problem, because statistically speaking, it's not a terribly unlikely value in the standard cosmology. There has been some work that may indicate it's just the result of correlated noise in the WMAP instrument, though, so with Planck we should be able to confirm or discount whether or not this quadrupole is real.

Chalnoth, thanks again for your reply.

Regrettably my maths isnt what it needs to be. e.g. di = ais + ni
Often I am not sure if I am looking at a simple algebraic equation where I can substitute di=1, ai=2 etc.

However, I am a pretty good RF engineer including radar receiver design so I can speak to the practical limitations of trying to extract a wanted signal from an interferer. Firstly there are frequency selectivity techniques using narrow band filters which can attenuate sources at other frequencies. Then there are FM techniques and FM chirp techniques which can extract a correlated signal right out of the noise. Similarly there are also digital spread spectrum techniques which can extract energy out of the noise by correlation, not possible here. I cant think of any other way of removing unwanted energy. Perhaps the mathematics you mention describes one of these methods?

Chalnoth
Science Advisor
Well, perhaps I can explain it a bit.

The equation I wrote before is:

$$d_i(p) = a_i s(p) + n_i(p)$$

I've added in the fact that the data, CMB signal, and noise all vary from pixel to pixel, so they are represented here as functions of a pixel. Yes, you can understand these as being simple numbers. $d(p)_i$ are the actual sky maps that WMAP observes at each frequency (WMAP observes the sky at 5 frequencies), and we are trying to extract a single map of the CMB, $s(p)$, out of these five maps.

Now, as I explained, we calibrate the instrument off of the CMB itself, so that the CMB signal is the same in all channels, so we can simplify it as:

$$d_i(p) = s(p) + n_i(p)$$

This is just a statement that in each data channel, the data in each pixel is a combination of CMB and other crap. The other crap will vary from channel to channel, but the CMB contribution is the same.

The idea with ILC is that we can extract the CMB by considering a linear combination of the channels:

$$\tilde{s}(p) = \sum_i w_i d_i(p)$$

Here $\tilde{s}(p)$ is our estimate of the CMB, the result of the ILC. And we select the weights $w_i$ such that the variance of the other crap that isn't CMB is minimized. In other words, each $w_i$ is just a number we multiply each map that WMAP observes. We then add these weighted maps together to get our estimate of the CMB.

Does that help?

Thanks Chalnoth, Is this perhaps the equivalent of automatic gain control, so that the average signal level in the galactic plane is the same as the average signal elsewhere in the sky, or perhaps you subtract a value to bring the average value in the galactic plane down to the same as the average value in the rest of the sky. The aim being to focus on the detail or difference between pixels which should then be the same background radiation as elsewhere?

You mentioned earlier about the background radiation is being measured at several frequencies. However doesn't this then equate to a range of background temperatures? I had understood that CMB temperature needed to be an exact figure for the standard model?

I just watched a BBC Horizon documentary "Before the big bang". Fascinating stuff, it seems that the standard model is not acceptable as a complete explanation to many of the original believers. "Plenty of effect and not enough cause". Well this is my outrageous contribution to such a speculative program :) https://www.physicsforums.com/showthread.php?t=440065

Chalnoth
Science Advisor
Thanks Chalnoth, Is this perhaps the equivalent of automatic gain control, so that the average signal level in the galactic plane is the same as the average signal elsewhere in the sky, or perhaps you subtract a value to bring the average value in the galactic plane down to the same as the average value in the rest of the sky. The aim being to focus on the detail or difference between pixels which should then be the same background radiation as elsewhere?
I don't exactly know what automatic gain control is. But the idea here might be described as thus:

Imagine you have a bunch of microphones in a crowded room. There are lots of people talking, but one thing you know is that they are all the same distance from George, so there's noise all over the place, and the microphones all measure different signals, but they each carry the exact same contribution from George.

The idea here would be that you can obtain the sound from George, to some degree of accuracy, by taking a weighted sum of the signals from each microphone. If you make sure that the weights sum to one, then you ensure that George's contribution to the noise is retained. Then you just need to minimize the amount of sound in the output. Since George's contribution is enforced by keeping the weights summed to one, minimizing the output minimizes everything but George's contribution, so that he comes in as clearly as possible.

You mentioned earlier about the background radiation is being measured at several frequencies. However doesn't this then equate to a range of background temperatures? I had understood that CMB temperature needed to be an exact figure for the standard model?
The CMB has a thermal black body spectrum, the most precise black body spectrum known to man. This spectrum corresponds to a temperature of 2.725K, with a peak at 160GHz, though it emits significant amounts of radiation at both lower and higher frequencies. Broadly, the CMB is most visible between about ~15GHz and ~500GHz. WMAP measures the sky between 23GHz and 94GHz (it stays in the lower frequency range because radiometers have difficulty measuring higher-frequency signals).

Thanks for your reply Chalnoth.

I just found this WMAP system block diagram, which I hope may also help me understand how the contribution for the galactic plane can be neglected.

http://wmap.gsfc.nasa.gov/mission/observatory_rec.html

In your description, why would the microphones all measure different signals?
Any antenna looking in the direction of the galactic plane is still going to see the noise from the galactic plane. Perhaps polarization comes into this?
Anyway, I think I will have to move on from this question until I can get a more detailed picture of the actual RF signals entering each of the difference receivers. There is plenty of other sky to consider.

It appears that with the center of the frequency peak at 160GHz so we would prefer to measure the signal there, but this is not easy or as accurate with today's technology. eg. The highest frequency I have worked on is 18GHz. What method was used to determine this frequency peak?

The WMAP is looking for tiny differences in RF amplitude, but shouldn't we be measuring the frequency of the frequency peak to determine the actual CBR temperature?

Has there been any resolution of the following: Since CBR is received from the edge of the observable universe, and we are at the center of our observable universe, why is there a large red shift on the CBR? How does the red shift affect the WMAP measurements?

Also what would be the average attenuation of the CMB after traveling 13.8 Billion light years? And what is the spread on this attenuation and how might this affect the WMAP measurements?

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Chalnoth
Science Advisor
In your description, why would the microphones all measure different signals?
In WMAP, the reason is that they get different amounts of the signal from the galactic plane. The reason they get different amounts of the galactic signal is that the galactic signal is not a black-body spectrum at a temperature of 2.725K.

In the microphone analogy, this is similar to there being another person in the room, Fred, who is also talking, sometimes much louder than George, but Fred is not situated at the same location, so some microphones pick up Fred's voice louder than other microphones. Thus we can use a linear combination of the microphones to cancel out Fred's voice while keeping George's. As long as Fred isn't moving around, this is a relatively simple operation.

Anyway, I think I will have to move on from this question until I can get a more detailed picture of the actual RF signals entering each of the difference receivers. There is plenty of other sky to consider.
Well, understanding the RF signals themselves isn't all that likely to give you an understanding of how the WMAP team went back and subtracted the galaxy from the maps to get the CMB.

But the basic idea is that each detector is a radiometer which detects the amount of radiation impacting the telescope from a particular direction within a small range of frequencies. The central frequencies of the detectors are 23GHz, 33GHz, 41GHz, 61GHz, and 94GHz. The instrument subtracts the signal from a detector looking at one part of the sky from the value of a corresponding detector (which measures the sky at the same frequency) looking at another part of the sky. As WMAP orbits the Sun, WMAP spins around, scanning the sky so that it is always pointed away from the Sun. Every six months, WMAP scans the whole sky once (well, almost...some holes are left, but these are covered in the next six months).

From the time-ordered data, the WMAP team produces maps of the whole sky at each frequency. These are not maps of absolute amount of radiation hitting the telescope at each frequency, but of the deviation from the average amount of radiation hitting the telescope.

It appears that with the center of the frequency peak at 160GHz so we would prefer to measure the signal there, but this is not easy or as accurate with today's technology. eg. The highest frequency I have worked on is 18GHz. What method was used to determine this frequency peak?
This was done earlier with the COBE satellite's FIRAS instrument, which measured the spectrum of the CMB to tremendous accuracy:
http://lambda.gsfc.nasa.gov/product/cobe/cobe_images/firas_spectrum.jpg

On this plot, the error bars are smaller than the trend line at every point. Not just slightly smaller, but mind-bogglingly, absurdly smaller. The measurement error at the peak is around 0.0035%. All but the last three data points have an error less than 1%.

The WMAP is looking for tiny differences in RF amplitude, but shouldn't we be measuring the frequency of the frequency peak to determine the actual CBR temperature?
Well, this was done by FIRAS to tremendous accuracy, and so isn't really that interesting to scientists any longer. We want to know the small deviations in temperature across the sky, and in order to distinguish between the CMB and other sources, we need to look at the sky at multiple different frequencies.

Planck, by the way, should measure the CMB near the peak. It has detectors that look at the sky in nine different frequency bands from 30GHz to 857GHz. The 30GHz-70GHz detectors are radiometers, like WMAP (but actively cooled instead of using the differencing strategy). The 100GHz-857GHz detectors are bolometers, which instead of being antennas are designed so that energy deposited in the bolometer increases the temperature of the bolometer slightly, leading to a change in electrical resistance that can be measured. I believe the frequency of the radiation that strikes each detector is singled out by constructing a horn which only permits the passage of radiation within a specific wave band.

Has there been any resolution of the following: Since CBR is received from the edge of the observable universe, and we are at the center of our observable universe, why is there a large red shift on the CBR? How does the red shift affect the WMAP measurements?
The redshift comes from the expansion of the universe. The universe has expanded by a factor of about 1090 since the emission of the CMB, which has multiplied the wavelength of each photon emitted at that time by a factor of 1090.

Also what is the average attenuation of the CMB from after traveling 13.8 Billion light years? What is the spread on this attenuation and how does this affect the WMAP measurements?
About 8% of the radiation is lost in transit. This can be measured due to the correlation between the polarized signal and the unpolarized signal, as the ionized gas in between us and the CMB is sensitive to the polarization of the light.

Thanks Chalnoth. I still have one question regarding "We want to know the small deviations in temperature across the sky". By this you mean variation in the center frequency?

The WMB is measuring intensity how does this translate to frequency variation?

I am astonished that only 8% of the energy is lost in transit. Even a 10ft coax would lose more than this!

On WMAP what is the relationship in angle or direction for the two inputs used to generate the relative or difference temperature?

Regarding redshift I understood that all directions are moving away from us equally fast. Yet measurements show our galaxy is moving at a considerable speed causing a CBR red shift in one direction and a CBR blue shift in the other. I read that something about this could not be explained since we are at the center of our observable universe.

http://www.astro.ucla.edu/~wright/CMB-DT.html

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Chalnoth
Science Advisor
Thanks Chalnoth. I still have one question regarding "We want to know the small deviations in temperature across the sky". By this you mean variation in the center frequency?
Well, that's not so easy to measure. But small differences in temperature do lead to different amounts of radiation at every frequency, and the amount of radiation of a particular frequency striking the telescope we can measure. The way the maps are calibrated is that if the CMB deviates from its central temperature of 2.725K by 100uK in one direction, then the corresponding pixel takes on the value of 100uK at every frequency, up to instrument noise and contamination from other sources.

I am astonished that only 8% of the energy is lost in transit. Even a 10ft coax would lose more than this!
Yes, the universe has been extremely transparent since the CMB was emitted!

On WMAP what is the relationship in angle or direction for the two inputs used to generate the relative or difference temperature?
They observe the sky at an angle of 141 degrees from one another. The satellite rotates and precesses so that each detector points at each direction in the sky over the course of a little over six months.

Regarding redshift I understood that all directions are moving away from us equally fast. Yet measurements show our galaxy is moving at a considerable speed causing a CBR red shift in one direction and a CBR blue shift in the other
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.

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

Chalnoth
Science Advisor
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.

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
Science Advisor
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.

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 cant find the link. There was also the quadrupole issue but it wasn't about this.

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Chalnoth
Science Advisor
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.

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
Science Advisor
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".

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 havent 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
Science Advisor
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 havent 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).

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
Science Advisor
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.

Thanks Chalnoth, You really got me with that negative pressure reply, I cant 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!

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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?

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Chalnoth
Science Advisor
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.