Exploring the Cosmic Background Radiation

[marlon]

Guys,

I really have been wondering how cosmic background radiation has been generated. I mean, as far as i understand it this is just red shifted photons that we receive from very distant places.It cannot come from distant stars because this radiation is a black body spectrum. But the red shift comes from the fact that the universe is expanding right? How do i implement the cooling of the universe ? I mean, can someone give me a detailed explanation of how this radiation was generated and what kind of info it gives...and how ?

Thanks

regards
marlon

 

[SpaceTiger]

Excellent question. In fact, I'm not even sure of the whole process that goes into deriving the cosmological parameters from the CMB, but I can certainly give a rough idea. I think I'll have to split this treatise into parts (partially for my own convenience), so bear with me.

Let's start with the big picture and ask the simple question that heads this thread, "What is the CMB?". Let's imagine we have a radio/microwave telescope that operates at frequencies near 100 GHz and allows us to tune to a range of frequencies. How do we observe the CMB? Simple, point to any location on the sky! Unless you happen to be looking in the galactic plane or at a synchrotron source, then the majority of light hitting your telescope will be coming from the CMB¹. Once we've found the CMB, let's try changing the frequency a bit. If we compare the strength of the light in the range from, say, 50 to 500 GHz, we'll find that its intensity follows:

$$I(\nu)=\frac{2h}{c^2}\frac{\nu^3}{e^{\frac{h\nu}{kT}}-1}$$

This is a blackbody curve. We can find the temperature that the blackbody curve represents by simply measuring the location of the peak of the spectrum:

$$T\sim 2\frac{\nu_p}{c}~K$$

Measuring the peak, you ought to find that the temperature is around ~2.7 K. Alright, so that's the radiation field that we see, but what of it? Where did it come from? Well, we know that light is redshifted as the universe expands, following the basic law:

$$\nu=\nu_0(1+z)$$

where $$\nu_0$$ is the frequency we measure now and $$\nu$$ is the frequency of the same light at the time corresponding to redshift z. Thus, the light we see today would have redshifted by the above amount. Wouldn't this redshifting distort the spectrum so that it wasn't a blackbody anymore? No, it turns out if you redshift all of the light in blackbody radiation, you just get another blackbody with a lower temperature:

$$T=T_0(1+z)$$

This means that the effective temperature of the CMBR decreases with time (or increases with redshift).

So, we now have the following two facts:

1) In all directions, we see a blackbody spectrum of temperature 2.7 K.
2) At earlier times, this radiation would have followed a blackbody spectrum represented by a higher temperature.

This implies something rather striking, that the universe itself was once a blackbody emitter! If you believe the Big Bang theory, then this was indeed the case. In fact, current theories suggest that the radiation "decoupled" at z ~ 1100. What does that mean? Well, at some point, the matter in the universe was so dense that light would not be able to travel very far without being absorbed by an atom or electron. "Decoupling" is basically the era in cosmic time in which this is no longer true.

It's not immediately obvious that such an era would be well-defined (that is, it could take a while for the photons to decouple), but it turns out that the transition is very sharp. This allows us to define what's commonly referred to as a "surface of last scattering". Don't be confused by the terminology -- the transition does not occur at a surface in space, but rather a surface in spacetime. In other words, the entire spatial volume of the universe was decoupling in a thin slice of time.

Although the term "decoupling" is common, you'll also frequently hear people talking about "recombination". Turns out this is referring to the same era in cosmic time and if you can understand the reason that the two terms refer to the same thing, you can go a long way to understanding where the CMB came from.

I'll stop here for now. More to come...


¹Technically, you'd have to launch your telescope into space to avoid atmospheric absorption, but we'll disregard that for now.

 

[SpaceTiger]

So, I mentioned in the previous post that the CMB was "decoupled" from matter at z~1100 and that this era is also referred to as "recombination". I'll explain why that is in this post.

First, what does "recombination" mean? In general, it's a term used to describe a process in which a free electron "recombines" with an ion to form either an atom or another ion of different charge. In a hot gas in local thermodynamic equilibrium, there will be a balance between a process that removes electrons from their host atoms or ions (ionization) and the process that puts them back (recombination). If the gas is really hot, then most of the electrons will be free. Why? It's mainly because a faster-moving electron is less likely to be captured by an ion and recombine.

We said before that the universe was getting colder with time, so if we assume that the universe was once really hot, then there must have been a time in which nearly all of the electrons were free. This was basically the case prior to z~1100. As the universe expanded and cooled, however, it eventually reached a point at which a given ion would recombine with an electron much more quickly than it would be ionized. It is at this time that "recombination" occurred and the universe switched from a plasma with mainly free electrons and protons to a gas composed mainly of neutral atoms.

Let's get to the main issue at hand; that is, why recombination implies a decoupling of photons from the gas. The answer to this question can be understood classically by looking at the natural frequency of an atom. Since the universe is 90% hydrogen, we can get a rough idea of what's going on just by looking at this simple atom. We know that it has many resonant frequencies, ranging from the UV (the Lyman series) to the optical (the Balmer series) and even on into the infrared (the Paschen series). Thus, one might expect that any frequency of radiation has a decent chance of being absorbed by neutral hydrogen. However, a given atom will only absorb in a specific series and the series in which it absorbs will depend on its energy state. It turns out that most hydrogen atoms in space are in their ground state (n=1), meaning that it will have resonant frequencies in the UV (Lyman series). This will apply to the newly-recombined atoms at z~1100 as well.

Now, let's look at the frequency of the CMB light and determine whether or not we expect it to be absorbed. If we plug z=1100 into the temperature equation I gave in my previous post, we find that the CMB was at ~3000 K at decoupling. From the Wein displacement law that followed, we can determine the peak frequency at this temperature and we find that it lies in the infrared range. There we have it! Since hydrogen in its ground state absorbs mainly in the UV, we won't expect the CMB photons to interact with it very much. Prior to recombination, the electrons were free and could resonate at any frequency they desired, so light was much more readily absorbed. Afterwards, resonances were restricted mainly to the UV and CMB light could readily pass through the see of neutral atoms.

Thus, the light we see in the CMBR today is a very sensitive probe of the distribution of matter at the time of decoupling. This, it turns out, is why the CMB is such a good cosmological probe. In what I hope will be my last installment, I'll try to describe this in a bit more detail.

 

[marlon]

Spacetiger, that is probably the best explanation ever... I really thank you for that. As a matter of fact, would you be OK with the fact that i make an entry on this in my journal? Just a reference to this thread so that i remember it ?

Thanks again

marlon

ps : i am waiting for more texts of yours.. you have a very fascinating way of writing...

 

[SpaceTiger]

Spacetiger, that is probably the best explanation ever... I really thank you for that. As a matter of fact, would you be OK with the fact that i make an entry on this in my journal? Just a reference to this thread so that i remember it ?

Not at all, I'm flattered.

ps : i am waiting for more texts of yours.. you have a very fascinating way of writing...

Yeah, I've been thinking about where to go next. One of the concepts I struggled with at first was the power spectrum, so I'll probably discuss that.

 

[Nereid]

A couple of 'add-ons' for you marlon:

The WMAP website has not only the detailed results from the 'latest & greatest' CMBR satellite/observatory, but also some 'general public' summaries, lots and lots of technical papers, and links to other (non-crackpot) CMBR sites.

As you might expect, given how strongly the CMBR constrains cosmological models, interpretation of the data is a favourite among (astrophysics, cosmology) crackpots - including PF's recently banned Thomas, Thomas2, Thomas3, tss, ... The bad news for them is that alternative 'explanations' fall way short of accounting for ALL the good observational results.

One example of the latter is http://www.eso.org/outreach/press-rel/pr-2000/pr-27-00.html - a difficult observation which puts mild constraints on the temperature of the CMBR ... several billion years ago! (oh, and it's consistent with the standard interpretation of the CMBR, as well as being consistent with the concordance model of cosmology).

 

[marlon]

thanks Nereid

marlon

 

[SpaceTiger]

Before describing how we use the CMB to measure cosmological parameters, let me step back and talk about one of our powerful cosmological tools: the power spectrum.

Normally, when we're describing objects, we describe them as some set of three-dimensional spatial coordinates. For example, if I wanted to describe a ball, I would specify the position of its center in space and then say that it constituted the sum of all points (or "delta functions") within a radius "R" of the center. Since the ball is really simply described in this coordinate system, it turns out this is a nice way of representing it. What about something else; say, a sound wave? Would I want to represent that as a sum of points? Probably not. Instead, we would usually think of it as a sum of sine waves, each with different phase and amplitude. Obviously, it's much simpler to say that a sound is composed of, for example, a combination of 400 Hz and 200 Hz sine waves than it is to describe the position of all of the particles in the wave as a function of time.

So what about the ball? Can I also represent this as a set of sine waves? Yes, it turns out that, as a consequence of Fourier's theorem, I can describe any function as a combination of sines and cosines. The theorem is generally applied to things that vary as a function of time (like sound waves), but it works just as well on things that only "wave" in space. This is not a good description of the ball, however (try thinking about how you might combine sines and cosines to describe it's shape -- it's not simple), so we were better off with the set of points.

But what if we were to make small modification to the ball that would make it more realistic. That is, let's say that the ball does not have a smooth surface, but is instead "rough", either by the intrinsic structure of the solid or by wearing with use. Many of these imperfections are very small and there are quite a large number of them, so it would take a lot of points to describe them well. What about our combination of sine waves? Can that do any better? Since the imperfections are not evenly periodic (there's clearly a lot of randomness involved), it's not obvious that this description would be any simpler. However, Fourier space provides us with a nice function, known as the power spectrum, that describes how prominent the imperfections are on a given scale.

To make this more concrete, let's try to see if we can reason out where we might find "peaks" in the power spectrum of, say, a beach. For simplicity, let's only stick with variations that we can see. What's the smallest variation? That's likely to be about the size of a grain of sand. Thus, we expect a peak in the power spectrum at around a millimeter. On what other scales is the beach "wavey"? Well, there will likely be pebbles and rocks interspersed with the sand (washed up by the waves), so we might also expect the power spectrum to rise on ~10 cm scales. There's a lot less fluctuation on this scale, however, so we wouldn't expect it to rise as much as on sand grain scales. Finally, what about on scales comparable to the size of the beach itself? In my experience, one will often find that the sand is somewhat wavey on these scales, implying that some mechanism is adding extra power at the longest wavelengths. I don't know exactly what it is, but it may have something to do with the wavelengths in the water hitting the beach or the collective weight of beach goers.

Hopefully you get the basic idea. The reason I'm talking about all this is that it's very common in cosmology to talk about the universe in terms of its power spectrum. We want to know how it fluctuates on a given scale and why. You can calculate power spectra for galaxy distributions, gas distributions, and even the CMB. The CMB is a bit different, however, because it's only a power spectrum in two dimensions (angular position) and on a spherical surface (the entire sky). Thus, rather than talking about wavelengths or wave vectors, we represent the power spectrum in terms of spherical harmonics (low l -> long wavelength, high l -> short wavelength). Here's a sample of recent data on the CMB power spectrum:

http://kicp.uchicago.edu/~davemilr/ISW/wmap_p_spec.JPG

Unfortunately, I think I might need yet another post if I'm going to explain the significance of this, so bear with me...

 

[Nucleonics]

Far out!

Thanks for all the time you put into the explanations, SpaceTiger! I'm looking forward to whatever insight we will gain on this topic from the Gravity Probe-B data.

Although I have to say, I'm a little disappointed this thread has become dead. It's one of the best PF threads, if you ask me.

 

[Garth]

I agree Nucleonics - and a belated well done ST for such an informative thread, (which I appear to have missed last April).

To introduce some discussion into ST's expert description of the CMB; if you look at ST's link above in post #8 http://kicp.uchicago.edu/~davemilr/ISW/wmap_p_spec.JPG , you will see that the peaks at the high-l end fit almost perfectly, representing the grains of sand, pebbles, rocks etc. in ST's analogy. However at the largest scales, the low-l end, representing the beach on the largest scales, you will see the data points drop below the brown line predicted by the standard LCDM model.

One question is, "Is this low-l discrepancy a real feature or just a statistical fluke (they are not many of them)?", and was discussed on PF on this thread: absorption in 'CMBR' wavelengths - observations? processes?.

This largest scale is measuring the large scale geometry of the universe, ST's 'whole beach', as he said

The CMB is a bit different, however, because it's only a power spectrum in two dimensions (angular position) and on a spherical surface (the entire sky).

The peaks in the power spectrum match a flat geometry very well, except at this low-l end. So is this low-l discrepancy a real feature or not? And if it is real how can it be explained?

Now, you can conformally transform the geometry of space-time:

[tex]g_{\mu \nu }\rightarrow \widetilde{g}_{\mu \nu }=\Omega ^2g_{\mu \nu }\text{,} \label{eq9}[/itex]

which changes the localised scale of the metric (where $\Omega = \Omega(x)$) but preserves angular relationships between objects described by it. (See for example Conformal relativity versus Brans-Dicke and superstring theories) Therefore, as the power spectrum data is describing the angular position of fluctuations in the CMB, those peaks are also concordant with a conformally flat geometry. Such a geometry that might describe a finite, but unbounded, geometry, which would not have enough room at the surface of last scattering for these largest fluctuations to exist.

Garth

 

[Chronos]

. . . One example of the latter is http://www.eso.org/outreach/press-rel/pr-2000/pr-27-00.html - a difficult observation which puts mild constraints on the temperature of the CMBR ... several billion years ago! (oh, and it's consistent with the standard interpretation of the CMBR, as well as being consistent with the concordance model of cosmology).

Glad you mentioned that one, Nereid. BB bashers run like scalded squirrels every time that study is mentioned. Just another stake in the heart of SST - I sometimes wonder how many it takes to kill the beast.

 

[RobtO]

I just came across these forums recently. I hope it's OK to resurrect this thread, as it seems like a good place to post my question about the CMB power spectrum.

What I've never understood about all this is how any expansion model can make any kind of prediction about the power spectrum. Naively, all that the expansion will do is take whatever power spectrum is already there and blow it up. So you have to assume some initial power spectrum in order to calculate the current power spectrum. In which case you might as well just assume the observed power spectrum.



What am I missing? How does inflation or its lack predict anything about the power spectrum?

 

[marcus]

What I've never understood about all this is how any expansion model can make any kind of prediction about the power spectrum.

you will get several explanations from several people so if mine doesn't work for you, or only does part of the job, don't worry

the prediction is helped by what we know about hydrogen gas

cool dilute neutral hydrogen is transparent, it does not scatter light

if you raise the temp up to like 3000 kelvin then a small but signif fraction of the gas ionizes and it becomes OPAQUE and scatters photons

that is why the surface of the sun appears opaque and doesn't let you see down into the guts of the sun, the boundary is a temperature and an extent of ionization

OK, so in cosmology there is something analogous to the surface of the sun, called the "SURFACE OF LAST SCATTERING". It is WHERE THE CMB CAME FROM and it was 3000 kelvin at a certain time about 300 ky from start of universe.

The reason the theory can PREDICT is because hot partiallyionized hydrogen at 3000 K radiates light with a Planck blackbody THERMAL SPECTRUM that is characteristic of blackbody at 3000 K.

the Planck spectrum has a nice property that if you STRETCH OUT all the wavelengths by some factor (like 1100) then you just get a new thermal spectral distribution for blackbody at temperature of, guess what, 3000/1100 kelvin.
You just have to divide the initial temp by the stretchout factor and you get the new temp. And the distribution of energy over wavelength is still the same beautiful breast-like curve of a perfect blackbody radiator. Just at a different temp.

So yes, the theory does make a prediction. But it helps that you have an idea of what was there back at the time of last scattering.

what happened was at that time the U cooled JUST ENOUGH that the hydrogen became neutral (not ionized) just enough that it became effectively transparent and the light at that moment GOT LOOSE
and it has been flying freely ever since--------and getting its waves graduallys stretched out by the expansion of space.

So physics, stuff about ionization and optical density and scattering, goes into making the prediction. the expansion theory does not do it all by itself

hope that helps!
=================
PS, the surface of last scattering, where the CMB comes from, is at a distance which corresponds to redshift z = 1100. Maybe I didnt make that explicit enough.

 

[hellfire]

Inflation predicts a specific initial or primordial power spectrum and the anisotropies in the CMB give information about the form of it.

Naively, all that the expansion will do is take whatever power spectrum is already there and blow it up.

I don't think this is true. The primordial power spectrum $P_{pr}$ is modified, especially by dark matter. Usually the measured power spectrum can be written as:

$$P(k) = T^2(k) P_{pr}(k)$$

where $T(k)$ is the "transfer function" that depends strongly on the properties of dark matter ($P(k)$ is the power spectrum in Fourier space).

 

[marcus]

...
What I've never understood about all this is how any expansion model can make any kind of prediction about the power spectrum.

I see that I may have misunderstood your question. I thought you were talking NOT about the CMB anisotropy spectrum (variation in temperature with direction)

but about the overall 2.75 K blackbody spectrum-----the distribution of CMB power in various wavelength bands.

Did hellfire interpret your question correctly? Were you asking about the anisotropy power spectrum?

 

[RobtO]

Yes, it's the anisotropy I'm confused about.

Inflation predicts a specific initial or primordial power spectrum and the anisotropies in the CMB give information about the form of it.

This is what I don't get. HOW does inflation predict the INITIAL power spectrum? Inflation simply says that expansion of the universe is accelerating. It doesn't say anything about the conditions of the universe before the acceleration starts, right?

I don't think this is true. The primordial power spectrum $P_{pr}$ is modified, especially by dark matter. Usually the measured power spectrum can be written as:

$$P(k) = T^2(k) P_{pr}(k)$$

where $T(k)$ is the "transfer function" that depends strongly on the properties of dark matter ($P(k)$ is the power spectrum in Fourier space).

OK, I see in a general way that there could be a transfer function. But how does this arise? Is it from propagation during the inflationary phase, after it, or both?

 

[hellfire]

HOW does inflation predict the INITIAL power spectrum? Inflation simply says that expansion of the universe is accelerating. It doesn't say anything about the conditions of the universe before the acceleration starts, right?

The theory of inflation describes an exponentially expanding space with a scalar field (the energy density of all other matter fields is negligible). Quantum field theory of a scalar field in an expanding space-time background predicts the conversion or the "freeze" of quantum fluctuations of the field into real perturbations of the spacetime metric. These perturbations can be clasified into scalar, vector and tensor perturbations. The power spectum follows from the distribution of scalar perturbations. In short, the quantum properties of the field during inflation lead to the power spectrum. I hope this helps, for details you could try sections 4.5 and 4.6 of: http://arxiv.org/astro-ph/0301448

OK, I see in a general way that there could be a transfer function. But how does this arise? Is it from propagation during the inflationary phase, after it, or both?

The transfer function describes how the primordial power spectrum created during inflation is modified to lead to the observed power spectrum. There are several ways how the power spectum can be modified. For example, neutrinos or hot dark matter lead to a suppression of small scale power.

 

[RobtO]

Thanks for the link! I'll need to study that a while...

 

[Chronos]

Short answer: the Fourier transform.

 

[hurk4]

Primordial powerspectrum

Inflation predicts a specific initial or primordial power spectrum and the anisotropies in the CMB give information about the form of it.


I don't think this is true. The primordial power spectrum $P_{pr}$ is modified, especially by dark matter. Usually the measured power spectrum can be written as:

$$P(k) = T^2(k) P_{pr}(k)$$

where $T(k)$ is the "transfer function" that depends strongly on the properties of dark matter ($P(k)$ is the power spectrum in Fourier space).

Hi Helfire
Maybe I am a bit late, but certainly this primordial powerspectrum will be a key to better understand the evolution of our BB. Can you or anyone else explain it to me, or can you give me a link where it is explained? I am also interested in the "transfer function" caused by dark matter.

 

[hurk4]

You already gave the link. Thank you Helfire

Hi Helfire
Maybe I am a bit late, but certainly this primordial powerspectrum will be a key to better understand the evolution of our BB. Can you or anyone else explain it to me, or can you give me a link where it is explained? I am also interested in the "transfer function" caused by dark matter.

Dear Helfire,
Excuse me, I overlooked that you already gave the link http:/arxiv.org/astro-ph/0301448 I was looking for. So I will first try to study and hopefully understand it a bit.
Many thanks and kind regards
Hurk4

 

[hellfire]

Try also this. There you will find more detailed information about the transfer function and the differences between CDM and HDM.

 

[shaun11]

I have read the „Fabric of the Cosmos“ and realize that a lot of what is written are theories that are still being worked on. The following is talked about: just before inflation there was a field called the inflaton field. What caused the big stretch was that for the briefest of time the highest energy level possible in this field happened causing repulsive gravity. This started the very brief inflation period when the space streched at emormous speed and volumes. What the book says is that it was only after this period that the pent up energy of the field formed matter. If I understand this all correctly, then how did the particles (that were only formed after the dramatic expansion) get to be spread throughout the universe uniformly thereby creating the CMB ? I am obviously not an expert, but these topics fascinate me. Any comments would be appreciated.

 

[hellfire]

Due to this big stretch any previous inhomogeneity disappeared or became negligibly small, so that at the end of inflation the energy density of the inflaton was homogeneously distributed through space and therefore the process of energy transfer from the inflaton to the other matter fields (called "reheating") did take place homogeneously in space.

 

[Mike2]

Due to this big stretch any previous inhomogeneity disappeared or became negligibly small, so that at the end of inflation the energy density of the inflaton was homogeneously distributed through space and therefore the process of energy transfer from the inflaton to the other matter fields (called "reheating") did take place homogeneously in space.

OK... so was it after the acceleration of universal expansion (when the expansion rate began to achieved a steady rate) that particles received there mass from the inflaton? Or was it when the expansion rate began to actually decelerate that reheating occured?

I'm thinking that at first the much larger false vacuum energy is what forced the great acceleration in expansion, then I suspect that some momentum in the expansion drove the vacuum energy into an unstable state that fell by providing mass to the particles. Such a theory would be supported if reheating occurred after any acceleration in the expansion rate and happened when expansion was being driven by momentum (not actually accelerating but perhaps starting to decelerate). Does this sound right?

P.S. Check your personal messages. Thanks.

 

[hellfire]

As far as I know inflation takes place because the kinetic term in the Lagrangian of the scalar field coupled to gravity is negligible compared to the potential term. It can be shown that for a scalar field this implies an equation of state w = -1. This leads to an exponential expansion of space. Afterwards, the magnitude of the potential decreases and reheating starts when the kinetic term (and the terms coupling to other fields) become more or less equal to the potential term. For a scalar field a kinetic term equal to a potential term means an equation of state w = 0. An accelerated expansion, however, takes place as long as w < -1/3. I am not sure when inflation is considered to be finished.