The Cosmological Principle

The definition of cosmology is the study of the structure and evolution of the universe. In modern physics, cosmology begins with the application of Einstein's theory of gravity, or General Relativity (recall this post), to the universe. This is a difficult task and would probably not be possible without a basic assumption about the universe - that it is spatially homogeneous and isotropic on large scales. Isotropy is a statement that the universe is the same in all directions (the universe looks the same whether you are looking directly outward from the North Pole or the South Pole). Homogeneity contends that the universe is the same at all points. These two hypotheses are together known as the "cosmological principle," without which much of our presumed understanding of the workings of the universe would be invalid.

Over short scales, this is obviously not true. Looking at the Milky Way is clearly different from looking at other parts of the sky. This makes it hard to test the hypotheses, as we need to go to larger and larger length scales to really see this principle in action, by averaging large volumes (using painting again as an example, imagine a canvas entirely of one color. Up close, you can see individual brush strokes with a great variation from place to place. From far away, though, one section of the canvas looks much like any other section, as they are all one color. Our universe is like that, if you believe the cosmological principle) .

Viewed in that context (I originally wrote "viewed in that light" but didn't want anyone to think I was making a pun), this rather boring picture of the CMB (taken from the COBE satellite in the early 1990s) becomes much more exciting - as already discussed, the CMB photons are coming from all corners of the universe. And they all look exactly alike (to 1 part in 100,000)! The first measurement of the very smooth spectrum of the CMB provided strong supporting evidence to the foundational hypothesis of cosmology, as the universe truly does look the same in all directions (it's slightly harder to convince yourself of homogeneity, that the universe looks the same at every point, but Copernicus can help here - if we proceed under the conservative assumption [although perhaps contentious from a religious point of view] that we do not live in a particularly special place in the universe [the "Copernican principle"], we can conclude that since the universe is isotropic around us, it should be isotropic everywhere. This implies homogeneity).

The Horizon Problem
Of course, that is not the entire story. I will briefly discuss the "horizon problem" here, before talking about the "anisotropies" in the CMB in later posts (these are the 1 part in 100,000 fluctuations that you can't see in the above picture because they are too small). We've decided the universe looks the same in all directions (the left side of the picture is the same color pink as the right side of the picture). But is the entire universe in causal contact?

My mom might ask, "what does causal contact mean?" If two events in space and time can be caused by the same preceding event, they are in causal contact. Here on earth, this is generally understood in terms of time. If something happens after something else (say, for example, I get a book out of the library because my mother recommended it), there can be a causal relationship (I got the book because my mom recommended it). On the other hand, if things are happening at the same time, they can't be causal (if my mom's recommendation comes at the exact moment I'm getting the book [or after I do so], she clearly can't be the cause of my literary enjoyment).

On universal scales, things are slightly complicated by the finite speed of light which adds a dimension of distance to the picture. We all know that the speed of light is constant, but for most of us, this doesn't really mean anything. We turn on a light switch, and the light turns on immediately. That is because the speed of light is so fast that we don't notice the time it took for the information to travel down the wire to the light bulb and back to our eyes. In space, however, this is not the case. For example, it takes about 8 minutes for light from the Sun to reach us. That means that an event in the Sun can only cause a response on Earth 8 minutes later. Suppose there were explosion in the Sun followed by an explosion on Earth 4 minutes later. The Sun's explosion cannot be the cause of the one on Earth, because any information from the Sun cannot reach us in less than 8 minutes (of course, both explosions could have been caused by some event happening in between, but hopefully the idea is clear).

This gives rise to the horizon problem. We know roughly how old the universe is and we know the speed of light. That means we know how far light can have traveled since the "epoch of last scattering." The problem is that the far right side of the pink ellipse is too far away from the far left side of the pink ellipse to have been in causal contact. Imagine running time backwards and following a photon emitted from both edges directed towards the center. At the time of last scattering, those photons would not have reached the center yet. In other words, what is happening on the left side and what is happening on the right side could not possibly have been caused by the same thing. Yet, they clearly look the same. How is this possible, when they could not have been influenced by the same initial conditions? This is the horizon problem, because the two extremes are outside of each other's causality horizon.

There are some theories on how to solve the horizon problem (with the leading candidate being "inflation") but they are probably beyond the scope of this blog (an argument can be made that the CMB is beyond the scope of this blog, but I hope my loyal reader(s) ignores that argument).

Some history

In the 1940s and 50s, a few scientists (George Gamow, Ralph Alpher and Robert Herman among others) predicted the continued existence of the photons that last scattered in the very early universe. Theoretically, those photons had continued to travel through the universe, cooling as the universe expanded. The early theorists tried to predict what the temperature of these photons would now be (with varying degrees of success). These photons should be all over the place and hence providing a constant "background" to any antenna on earth. In addition, they should have cooled enough that now their wavelength would be in the microwave range. Thus, these photons came to be called the cosmic microwave background.

In the mid 1960s, a group at Princeton led by Robert Dicke began building a radiometer to detect the CMB. At the same time, Arno Penzias and Robert Wilson at Bell Labs observed some noise in a sensitive antenna they were planning to use for radio observation. After careful work, they decided that this noise had to be external and coming from all directions in the sky. Eventually they made contact with the Princeton group, and this background noise was interpreted as being the CMB (after first talking to Penzias and Wilson, Dicke supposedly got off the phone and told his collaborators, "Boys, we've been scooped"). The two groups published companion papers on the observation and the interpretation, and in 1978 Penzias and Wilson received the Nobel Prize.

Although important, that first observation is not on its face all that exciting. The CMB is remarkably smooth or isotropic (meaning it looks the same in all directions). The picture below shows what Penzias and Wilson might have seen if they'd been able to observe the CMB in all directions (courtesy http://map.gsfc.nasa.gov/), and it's hard to see what all the fuss is about. But I'll leave that for the next post.

Thermal equilibrium recap

The last post is rather long and involved, so I will try and recap in briefer terms. The early universe was very hot, so that everything was in thermal equilibrium. In particular, because reactions were constantly taking place, the universe was strongly "ionized" or charged. Therefore, photons were constantly scattering off the charged particles.

Eventually the universe began expanding and cooling.* As it did so, the ions and free electrons "recombined" (during the time romantically referred to as the era or epoch of recombination) to form neutral atoms, after which photons no longer scattered (romantically referred to as the "surface of last scattering," a phrase that always puts me in mind [for whatever reason] of the "Last Homely House" in the Lord of the Rings [yes, I am a physicist and I love Tolkein and I write a blog for my mom]). Those photons remain unmolested since that time.

*Aside: my mom asks in a comment "why did the universe cool?" The short answer to that is because it expanded. Temperature is in some sense a measure of how many collisions occur in a space [recall my analogy about money in the last post] - at high temperature, there are lots of collisions. Suppose we expanded the space, but kept the number of particles the same. All of a sudden, the number of collisions would go down, because the particles wouldn't be able to find each other to collide. Therefore the temperature drops. Many [if not all] refrigerators operate this way, by allowing a compressed gas to expand rapidly and thereby drop in temperature. A follow-up question is then "why did the universe expand?" and I have a less satisfactory answer to that. My best explanation is that there was a lot of energy released in the big bang, and it was that energy that drove the expansion. We may have more to say on this subject at later times).

Thermal equilibrium

Last week was graduation at Yale, and a few of my closest friends here were getting their degrees. As such, some celebrating ensued. One of my friends is now doing post-doctoral work at UCLA, while another is working for a financial firm outside of New York. One night we spent some time in the early morning hours discussing the economy and the stock market. In that discussion, I came up with a somewhat stilted metaphor that I'm now going to invert to describe the concept of thermal equilibrium, which is where I want to begin the series on the CMB. In physics, temperature plays a similar role to that of money (or liquidity) in the markets.

First, I'm going to define "ionization" by referring briefly to the Bohr model I described here. Ionization is the process by which an atom loses (or gains) an electron and becomes charged. In the old post, I compared an atom to a building with an elevator which could transfer people (or electrons) between discrete levels. Using that image, ionization would occur if the elevator dropped you off on the roof, at which point you could leave the building entirely. As long as you were within the building, you remained trapped, just as an electron remains trapped by the electric field of the protons at the center of the atom (or as the Earth is trapped by the gravitational field of the Sun). On the roof, however, you have gained enough energy that you can leave the building; if an electron gains enough energy, it can escape from the electric field and be free, leaving the atom positively charged. This positively (or negatively, if it picks up an electron) charged nucleus is referred to as an ion.

One more thing that we should keep in mind about charged particles is that they interact rather strongly with light (or photons, as faithful readers will remember that light is a particle called a photon). A photon traveling through a cloud of charged particles will scatter many times, so that the photon that appears on the other side of the cloud will have very little to do with the one that entered it.

I'll now switch gears completely to describe the relationship between temperature and money. Suppose my mother in her younger days was living in a rather small apartment in London. My mom is a rather accomplished amateur interior decorator, and we'll assume she had those skills in her flat in London. I'm going to go one step further and ascribe a fickle nature to my mother which I would like to emphasize for posterity that she does not in actuality possess; in my hypothetical situation, this invented nature of hers combined with her penchant for interior design led her to continually change her mind on how she wanted to decorate her small house.

Ok, now we'll add money. If my mom had a lot of money, she could indulge her ever-changing whims. One week she could go for ultra modern and the next for antiques. Basically, the furniture would be coming and going, styles would be in and out, her little flat would be in a constant state of flux. Suppose, however, that she suddenly lost all her money; my mother would be forced to pick the cheapest option with which to decorate her house and stick with it. While she may still desire a change, she would have to settle for the most practical option.

In the physics of chemical reactions, temperature is like money. If my mom has money, she can change her flat at will - she can bring in new stuff, get rid of the old stuff easily whenever she wants. If the temperature is very high, a chemical reaction can occur easily and can go in both directions. Specifically for the purposes of the CMB, at high temperatures atoms can easily lose electrons and become ionized, before quickly finding other electrons freed from other atoms to become neutral again. In the early universe, the temperature was very hot and this was happening all the time; the universe was a soup of charged particles and photons bouncing off each other constantly. In particular, the photons never went very far before hitting another charged particle.

However, when my mom no longer had any money, she was forced to pick the cheapest option and stick with it. Similarly, after the big bang the universe began expanding and cooling. As the temperature dropped, it was no longer so easy to ionize atoms. Eventually, the universe cooled enough that it dropped out of thermal equilibrium. That meant that all the atoms had to neutralize, because a neutral atom requires less energy than an ionized atom and free electron, and nature prefers to minimize the amount of energy in any system (just as my mom had to settle for the cheapest decor). Once the atoms were all neutral, any photons that were bouncing around no longer had to travel through a soup of charged particles. In effect, the photons that were produced just as the universe become neutral did not scatter again. These photons are still traveling through the universe and we can detect them now; they are the CMB. They still contain information from the last time they interacted with matter, which was 13 billion years ago, right when the universe became neutral.

Introduction to the Cosmic Microwave Background

The first series of posts contained one argument for the existence of dark matter. The response from my mother among others was tentatively positive, although most comments seemed to agree that I was perhaps going a bit too fast with the math and trying to pack too much in (my beloved sister has weighed in with a somewhat more negative opinion for which I thank her with all the fraternal feeling I can muster). I take the point that this blog may need more romance and less dry insistence, and I will attempt to respond accordingly.

Therefore, my next topic will be another argument for the existence of dark matter, and in my opinion one of the cooler phenomena in physics (I understand that my stating something is "cool" is not necessarily sufficient evidence, but I will try to explain) - the Cosmic Microwave Background or CMB for short (another good name, by the way).

In very broad strokes, the CMB is an echo or an image of the universe as it was 13 billion years ago (when it was only four hundred thousand years old - relative to the human lifespan, it's like we have a baby picture from when the universe was 1 day old). Much as archaeologists can learn about prehistoric epochs from fossils (or mosquitos trapped in amber) and geologists can infer the climate from ice cores that have been frozen for thousands of years, physicists can discover information about the contemporary contents and future evolution of the universe by studying the CMB.

So what is the CMB? It's a sea of light streaming across the universe in all directions that was produced 13 billion years ago and has not touched anything since that time. This light isn't visible to us, because its wavelength (remember these posts) is in the microwave band (i.e. too long to be visible by our eyes, but with enough intensity [thankfully not present in the actual CMB or else we'd all be in trouble], perfect for heating up instant hot chocolate [too quaint?]). It's always there though, and like a photograph, each individual photon contains an image of the universe shortly after the big bang.


The illustration (click for a bigger view) shows the history of the universe from the Big Bang to the present. The CMB is produced at the green and blue ellipse during the very early universe and detected in the present by the satellite labeled "WMAP."

I'll stop there for now, but hopefully the reader will want to know more. I'll probably refer to two web sites a great deal in the coming posts. The best existing CMB experiment is the Wilkinson Microwave Anisotropy Probe, or WMAP, and they have a great resource at http://map.gsfc.nasa.gov/ from which I've taken the illustration. The second web site is where I learned most of what I'll be talking about, the homepage of Professor Wayne Hu of the University of Chicago. He's done a great job explaining all the details and implications of the CMB in simple terms, and I hope to do half as good a job.

Baby blues

The aforementioned picture of me (narcissism being a commonly found flaw among physicists).