Gravity 9: The Evolving Universe

by Shane L. Larson

Of all the fundamental forces in Nature, gravity is the weakest. What do we mean by that? Let’s forego our usual thought experiments, and do something real to demonstrate this idea.

First, go eat a piece of pizza (or any other food you enjoy). This is the process by which you accumulate the eenrgy needed to make your body go. Without pizza, you wouldn’t be able to do anything.  Second, go stand in the middle of the room (where you won’t hurt yourself) and jump straight up in the air, as high as you can.

Energy from pizza, gives me the power to defy the gravitational pull of the entire planet.

What happened? Since I’m pretty sure most of you reading this aren’t superheroes and can’t fly, you probably ascended up in the air a bit, and then came back down to the floor. It’s an everyday sort of thing, completely ordinary. But this is science, and there are remarkable and deep truths hiding in the simplest of circumstances. So consider this:

Using some simple chemical energy, which your body gleaned by breaking down some food you ate, you were able to (momentarily) overcome the gravitational pull of the ENTIRE EARTH.

This is what we mean when we say gravity is weak. But despite this fact, it is fundamentally the most important force of Nature if we want to think about the Cosmos as a whole. It has no competitor on the largest scales imaginable, meaning that even with its weak ability, gravity is able to change the Cosmos over the long, inexorable flow of time. It made sense that general relativity could and should be used to consider the past, present and future of the Universe itself.

The night sky over the Pando Forest in central Utah. Pando is an 80,000 year old aspen grove — it has seen almost 30 million nights like this one, but very little has changed. The constellations change over thousands of years, but the sky is still full of stars, and the Milky Way still arches over the sky, giving the impression that the Universe is unchanging. [Image: Shane L. Larson]

In 1915, when Einstein first presented general relativity to the Prussian Academy of Sciences, there was precious little we knew about the Universe, though perhaps we didn’t realize it at the time. The only objects outside the solar system that we knew a lot about were stars, and many scientists (including Einstein) supposed the Universe was comprised entirely of stars. Einstein himself made one of the first attempts to use general relativity to describe the Universe. He considered the case where the Universe was uniformly filled by stars, and found a result that disturbed him — no matter what he tried, general relativity predicted the Universe would collapse. To counteract this, Einstein modified general relativity through the introduction of a “Cosmological Constant” that made the Universe slightly repulsive. The result was precisely what Einstein hoped to find, what he and most scientists thought the Universe was: static, unchanging in time. But great changes were afoot, being driven by our ability to see the Universe better than ever before.

Henrietta Swan Leavitt, in her office at the Harvard College Observatory. She made one of the most important discoveries in the history of astronomy: how to measure distances to a common type of star, known as a Cepheid variable.

In 1915, the largest telescope of the day was the 60-inch reflector on Mount Wilson, though it would be eclipsed two years later by the 100-inch Hooker Telescope, also on Mount Wilson. Enormous telescopes such as these were enabling us to probe the size of the Cosmos for the first time. The key to making those measurements was discovered by a pioneering astronomer at the Harvard College Observatory, Henrietta Swan Leavitt.

Delta Cephei is a naked eye star, in the lower corner of the constellation of Cepheus.

Leavitt was studying a class of stars known as Cepheid variables. Named for the archetype, delta Cephei, these stars are “radial pulsators” — they grow and shrink over time in a regular pattern over the course of many days. The observational consequence, if you are watching, is the brightness and the temperature the star changes. What Leavitt discovered was a regular pattern between the time it took a Cepheid star to change its appearance (its “period”), and its true brightness (its “luminosity”).

The brightness of Cepheid variables goes up and down over the course of many days. The curve here is for Delta Cephei, which changes brightness every 5.4 days. (TOP) The observed change in brightness is a direct result of the stars size pulsating in time.

How does that help you measure distances? Let’s imagine a simple example here on Earth. Suppose you have a 100 Watt lightbulb and a 10 Watt lightbulb side by side.  The 100 Watt bulb looks brighter — way brighter. This is the intrinsic brightness of the bulb — it is clearly putting out more energy than its smaller, 10 Watt companion, which you can easily discern because they are right next to each other.  This intrinsic brightness at a known fixed distance is what astronomers call absolute luminosity or absolute magnitude.

Is there any way to make the 100 Watt bulb look dimmer? Yes! You can move it farther away — the farther you move it, the dimmer it appears. In fact, you could move it so far away that the 10 Watt bulb you leave behind looks brighter! By a similar token, you can make it look even brighter by moving it closer! How bright something looks when you look at it is what astronomers call apparent luminosity or apparent magnitude.

Disentangling distance and brightness is one of the most difficult problems in astronomy. Observing how bright an object is depends on two things: its intrinsic brightness, and its distance. (TOP) A bright light and a dim light are side by side at a fixed distance; one is obviously brighter than the other. (BOTTOM) If the brighter light is farther away, it can look dimmer than the closer light!

By comparing apparent brightness (how bright something looks in a telescope) to absolute brightness (how bright something would look from a fixed distance away) you can measure distance. The biggest problem in astronomy is we don’t know what the absolute brightness of objects are.

What Leavitt discovered was if you measure how long it takes a Cepheid to change its brightness, then you know its absolute brightness. Comparing that to what you see in the telescope then let’s you calculate the distance to the star! This discovery was a watershed, arguably the most important discovery in modern astronomy: Leavitt showed us how to use telescopes and clocks to lay a ruler down on the Universe. Leavitt died of cancer at the age of 53, in 1921.

Harlow Shapley.

Despite her untimely death, astronomers rapidly understood the power of her discovery, and began to use it to probe the size of the Cosmos. Already by 1920 Harlow Shapley had used the Mount Wilson 60-inch telescope to measure Cepheids in the globular clusters in the Milky Way. What he discovered was that the globular clusters were not centered on the Earth, as had long been assumed, but rather at some point more than 20,000 lightyears away. Shapley argued quite reasonably that the globular clusters are probably orbiting the center of the galaxy. This was the first indication that the Copernican principle extended far beyond the Solar System.

In 1924, Edwin Hubble, who Shapley had hired at Mount Wilson Observatory, made a stunning announcement — he had measured Cepheid variables in the Andromeda Nebula, and it was far away. At 2.5 million lightyears away, the Andromeda Nebula was the farthest object astronomers had ever measured the distance to. In fact, it wasn’t a nebula at all — it was a galaxy. Here, for the first time, some of the long held, cherished beliefs about Cosmology that were prevalent when Einstein introduced general relativity began to unravel. (Historical Note: Hubble’s original distance to the Andromeda Galaxy was only 1.5 million lightyears. Why? Because there are two different kinds of Cepheids, both of which can be used to measure distances, but calibrated differently! Astronomers didn’t know that at the time, so Hubble was mixing and matching unknowingly. Eventually we learned more about the Cosmos and arrived at the current known distance — science is always on the move.)

The Hubble Ultra Deep Field (UDF), showing what can be found if you stare at an “empty” part of the sky for long enough. Virtually every object in this image is a distant galaxy.

The Universe was not full of stars…. it was full of galaxies, and those galaxies were further away than we had ever imagined. This was a dramatic discovery that shook astronomers deeply. But it was only the beginning. A scant five years later, Milton Humason and Hubble, using the 100-inch telescope at Mount Wilson, made another astonishing discovery: every galaxy they looked at was receeding away from the Milky Way, in every direction. Furthermore, the farther away the galaxy was, the faster it was receding from us.  This result is now known as “Hubble’s Law.” Humason and Hubble had stumbled on one of the great secrets Nature — the Universe was not static, as a casual comparison of the night sky from one year to the next may suggest.  But what was going on? Why were all the galaxies flying away from us, in every direction we looked? This would seem to contradict the Copernican principle that we weren’t the center of everything!

(L) Alexander Friedmann. (R) Georges Lemaître.

As it turns out, the answer was already in hand. It had been discovered several years before Humason and Hubble by two scientists who had sought to use general relativity to describe the Cosmos: Alexander Friedmann, a Russian physicist, and Georges Lemaître, a Belgian priest. Friedmann had used general relativity to describe a Universe that was homogeneous (the same everywhere) and isotropic (looks the same in every direction). The “Friedmann Equations,” as they are now known, describe the evolution of such a Universe as a function of time. Lemaître derived the same result in 1927, two years after Friedmann’s death. In the mid 1930’s, American physicist H. P. Robertson and UK physicist A. G. Walker showed that the only solution in general relativity describing a homogeneous and isotropic Universe as that of Friedmann and Lemaître. This is now called the FLRW (“Friedmann-Lemaître-Robertson-Walker”) Cosmology.

What the FLRW cosmology tells us is that the galaxies aren’t really flying apart from one another — if the Universe is homogeneous and isotropic, then spacetime itself is changing, stretching and deforming. The reason the galaxies are receding from one another is the spacetime between them is expanding — the Universe is getting larger, expanding all the time.

Imagine the galaxies floating in spacetime, unmoving with respect to one anther (they are stapled down to their location in spacetime). General relativity predicts that the galaxies don’t move, but that spacetime itself expands, it stretches, so the distance you measure between galaxies increases.

Lemaître was the first person to think differently about this problem. He had the presence of mind to ask, “We see the Universe is expanding, but what if I run time backward? What did the Universe look like in the past?” In 1931, he argued that the expansion seen in every direction suggested that the Universe had expanded from some initial point, which he called the “primeval atom.” If today we see everything expanding away, and you look backward in time, it must have all been much more compressed and compact, a state which would have made it hot, and dense. Lemaître didn’t know what might have initially caused the expansion of this primeval atom into the Cosmos we see today, but he did not see that as a reason to suppose the idea was invalid.

Lemaître with Einstein in California, 1933.

Change in science is hard, especially when data is new and our ideas are undergoing a dramatic evolution from past modicums of thought. Einstein is widely known to have critically panned both Friedmann’s and Lemaître’s work before the discovery of the expansion, still believing in the notion of a static Universe. Once the scientific community had come to understand and accept the expansion data, it required another great leap of faith to contemplate Lemaître’s notion of a hot dense initial state. Einstein again was skeptical, as was Arthur Stanley Eddington. For more than a decade, the arguments about the idea raged, and in 1949 during a BBC radio broadcast, astronomer Fred Hoyle coined the term by which Lemaître’s “primeval atom” idea would forever be known as: the Big Bang.

All ideas in science stand on equal ground — they are valid for consideration until they are proven wrong by observations. If the Universe did indeed begin in a Big Bang, then the obvious question to ask is what signatures of that dramatic event would be observable today? As it turns out, there are many observational consequences of the Big Bang, and they all have been observed and measured by astronomers, lending confidence to Lemaître’s initial insight.  This will be the topic of our next chat.

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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.

Behind the Curtains of the Cosmos 3: Keys to the Cosmos

by Shane L. Larson

The fact that the curtain of the Cosmic Microwave Background exists is a huge boon to astronomers, giving us confidence in our understanding of Big Bang cosmology. But is that all? We have all this microwave light coming at us from every direction in the Cosmos — what can we do with it?  Is there anything else we can learn?

As it turns out, there is more to the light than meets the eye. Astronomers excel at taking information from the Cosmos and digging deeper, to tease out secrets and information that at first glance are not easy to see.  If you look closely at the Cosmic Microwave Background you discover some Very Important Things. One thing is that it is not absolutely, perfectly smooth. Imagine picking up a ball off a pool table — it looks and feels very smooth; that is analogous to the uniform temperature of the Cosmic Microwave Background looking the same no matter where we look on the sky.  But if you take that same pool ball and look at the surface closely with a magnifying glass, you find that it has some scratches and roughness to it — they are so small as to not be detectable by your fingertips, nor to your naked eye.

(L) A billiard ball looks and feels smooth to your eye and your finger tips. (R) But if you can look at it very carefully under a microscope, you find there are minuscule imperfections that are only detectable with excellent technology.

The Cosmic Microwave Background is very similar. If we use a highly accurate microwave telescope to look, we find that there is a small scale  “roughness” to the sky; astronomers think this roughness is an indicator of clumpiness at the time atoms formed, ultimately leading to what you and I see today — galaxies and clusters of galaxies in the Universe. This roughness was first detected by the COBE satellite in 1992. It was later mapped at even finer precision by the WMAP mission, and by the Planck mission.The spots on this map can be thought of as hot and cold spots on the sky. The red spots are the hottest, at only about 2.7 Kelvin (1 Kelvin is 1 degree Celsius) above absolute zero. The blue spots are the coolest, about 0.00001 Kelvin cooler than 2.7 Kelvin — a difference almost so small as to be undetectable except with the most exquisite astronomical instruments! Before the microwave background broke free from matter, the small variations in the density of matter were spread across the Cosmos. When the matter condensed to form neutral atoms, these variations imprinted themselves in the Cosmic Microwave Background. The spotted map of the Cosmos seen by COBE, WMAP and Planck is a message from the other side of the curtain!

The Planck All-Sky Map of the Cosmic Microwave Background variations. [Planck Collaboration]

Is there any other property of the Cosmic Microwave Background that might be measured? Is there any other physical imprint that might tell us something about the early days of the Cosmos?  Of course there is!  It is called polarization. Light is known to scientists by its proper name, “electromagnetic radiation.” As the name suggests, it has an electric part and a magnetic part, called “fields.” The way we visualize light is as a wave of electric fields and magnetic fields travelling together, at right angles to each other. For any light you receive, the direction the electric field is waving defines the polarization of the wave.

Light is a propagating “electromagnetic field,” a waving electric field travelling together with a waving magnetic field. The direction the electric field waves defines the polarization of the light.

Polarization encodes many kinds of information, related to how light and matter interact with one another. The most common way you encounter this every day is with sunglasses. Reflected light is polarized, so we build sunglasses that block polarized light, cutting down glare off of reflected surfaces. You might have noticed that the display of your smartphone is polarized too — you can’t see it in certain orientations through your polarized sunglasses.

Light reflected off of surfaces is polarized, like these mud flats. (L) The waves and the sand look bright when polarized light is seen. (R) When polarized light is blocked, as with polarized sunglasses, the appearance changes dramatically. [Image from Wikimedia Commons]

Light from the Cosmic Microwave Background is expected to be polarized, imprinted with patterns because during decoupling (the time when electrons were binding to nuclei to form atoms) the light bounced off of the free electrons (in physics-speak: it “scattered”) giving it a definite polarization. Astronomers call these polarization patterns “E-modes” and they are recognizable because they make symmetric patterns in the sky — the polarization pattern looks exactly like itself if you look at a reflection of the pattern in a mirror. This kind of pattern was discovered by the DASI experiment in 2002.

Polarization of the Cosmic Microwave Background detected in 2002 by the DASI Collaboration. These are “E-mode” polarizations, caused by scattering.

So what does this all have to do with inflation? Inflation happened shortly after the Big Bang, before anything that you and I might recognize as a particle had formed. The forces of Nature spontaneously appear as the Universe cools, enabling different kinds of physical interactions to appear. Gravity had appeared sometime before inflation, during a time cosmologists call the “Planck epoch.” Inflation was the sudden, rapid expansion of everything — the energy soup, and spacetime itself — from the incredibly tiny point that expanded to become the Observable Universe. Think of spacetime like a balled up bundle of wrapping paper being unfolded, flattened and smoothed out by inflation.  On the smallest scales, spacetime is changing — expanding, stretching, flexing of the folds in our bundle of paper. Physicists call these happenings “quantum fluctuations.” The stretching and unfolding of spacetime means the gravitational field is changing. But that’s exactly what we said causes gravitational waves! As the Universe inflates, the quantum fluctuations in spacetime itself generate gravitational waves. This has physicists really excited, because detecting these gravitational waves would be the first hint of the quantum nature of gravity itself.

As we noted last time, gravitational waves interact with matter very weakly, so they propagate through the slowly evolving soup of the Cosmos, pushing matter here and their until the formation of the Cosmic Microwave Background.  What is the net result? The net result is that gravitational waves leave a polarization imprint in the microwave light. Just as with the expected polarization from electron scattering, there is a pattern to the polarization made by the gravitational waves. Astronomers call this pattern “B-modes” — they have a twist to them.  You can recognize a B-mode pattern, a twist, because in a mirror the pattern appears reversed.

(L) E-mode polarization patterns look identical if viewed in a mirror. (R) B-mode polarization has a “twist.” If the twist is clockwise, then when viewed in a mirror the twist is counter-clockwise, and vice versa.

Which brings us back to the story of BICEP2. Astronomers have been looking for the tell-tale twist of polarization in the Cosmic Microwave Background for some time. Major experiments have been slowly gearing up to look for and characterize the unique, gravitational-wave signature of inflation. The science team at BICEP2 won the race. What has all of us so excited is the measured value is larger than we anticipated, indicating the relative importance of the gravitational waves is large.  This has provided sudden and unexpected guidance for theoretical physicists trying to model inflation, and for future experimenters attempting to build new experiments to probe the early Universe.

The BICEP2 polarization map, showing B-mode (“twist”) patterns.

So what now?  Astronomy is a spectator sport — we keep looking!  Now that our colleagues at BICEP2 have made the initial detection, we are gearing up to look more closely at the result, and to dissect it for clues that confirm we are on the right track to understanding the Cosmos.  New papers are appearing rapidly (I counted about 100 at the time of this writing). The result doesn’t precisely agree with other results we already have (there is “tension” between the results, in physics-speak), and some of us still have reserved skepticsm.  The field has been thrown into a big mess, and now we have to figure out what happened. It’s a bit like coming home to find your living room in a disastrous state, and trying to figure out if it was the kids, the cat, the dog, or some combination thereof that made the mess! But astronomers don’t mind — it’s the figuring out of the mess that is so rewarding. But make no mistake — it was an outstanding achievement, a triumph of the human intellect and human ingenuity. And onward we go.

The BICEP2 Telescope at the South Pole. [Image: National Science Foundation]

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This is the last installment in a 3-part series about the March 2014 BICEP2 announcement about the detection of a putative signal from inflation in the Cosmic Microwave Background.  Part 1 can be found here.

Behind the Curtains of the Cosmos 1: Inflation and the Microwave Background

by Shane L. Larson

The world was all atwitter last week (on twitter and otherwise) with the announcement from our friends at the BICEP2 collaboration that they had detected the echo of the Universe from the earliest moments after the Big Bang. (links to press releases and videos discussing the result can be found here).

The BICEP2 Telescope at the South Pole. [Image: National Science Foundation]

Have no doubt — this achievement is remarkable, a testament to our ability to probe and understand the secrets of the Cosmos that Nature has left for us to find. Nobel Laureate Stephen Weinberg once waxed poetic in his book The First Three Minutes, claiming, “The effort to understand the universe is one of the very few things which lifts human life a little above the level of farce and gives it some of the grace of tragedy.”  This is one of those moments; an instant in time when every member of our species should raise up their head, stand a little taller with pride and know that despite all the trials and tribulations that face our race and our planet, we are capable of great things.

But what does it all mean? What is the hub-bub all about?  There are two elements of this that you will hear people talking about.  One is about inflation and one is about gravitational waves.  Today, let’s talk about inflation.

What is inflation all about?  In order to understand inflation, let’s first talk about The Big Bang.  Most of us have heard about The Big Bang, a model for the Cosmos that arises naturally from the notion of taking what we can see today (the expansion of the Universe) and running the movie backward in time.  The development of Big Bang cosmology evolved as many ideas in science do — a few fundamental observations inspire someone to imagine what the underlying Laws of Nature might be. Those ideas are written down, and everyone begins to think of all the possible consequences — what kinds of things must be true, and how could we observe them? Big Bang cosmology is a result of imagining “running the movie backward” from the current, expanding state we see when we look out from the Earth.  If you shrink the current Observable Universe into the distant past, then it should have been smaller, and as a consequence much denser and hotter.

So what was it like, the tiniest fraction of a second after the Big Bang?  It was hot. Our understanding of the densities and temperatures then suggest it was 10³² ºC = 100,000,000,000,000,000,000,000,000,000,000 ºC. What does that even mean? A temperature like that is so far outside our common, everyday experiences with coffeepots and campfires as to seem quite ridiculous.  But to an astrophysicist, high temperatures are synonymous with great speeds.  If the Universe was this hot, then that means everything in the Universe was flying around at tremendous speeds. Since the Universe was much denser, everything was tightly packed together, increasing the number of collisions.  What happens when you have collisions at high speeds? You break things apart!

At this time, things are crashing together so hard that atoms can’t exist. In fact, things are crashing together so hard that the nuclei of atoms can’t exist.  The entire Universe is filled by a Primordial Soup of protons, neutrons, electrons, and photons (light) — energy, and the building blocks of atoms.

As the Universe expands, it cools. By 100 seconds after the Big Bang, the Universe has cooled to a mere 10 billion ºC.  At that temperature, protons and neutrons can stick together to form the cores of the first atoms. At these temperatures, when they crash together, the strong nuclear force is strong enough to keep them together. This moment of creation of the nuclei is called nucleosynthesis.

Nucleosynthesis was the formation of the cores (the nuclei) of atoms. Most were hydrogen nuclei (single protons) with a little bit of helium, and an even smaller amount of lithium. Observations of these proportions is one of the strongest pieces of data supporting Big Bang cosmology.

Now, 10 billion ºC is still too hot for electrons to bind to these newly formed nuclei; each time they try, a collision knocks them loose, so no proper atoms can form at this time.  The result is that the early Universe is a swirling maelstrom of charged particles. The consequence of that fact is that light is effectively trapped. Photons (light) are easily deflected (astronomers use the term “scattered”) by charged particles. If a photon is flying along minding its own business and happens upon a charged particle, it gets bumped off its path in a new direction. Since the early Universe is very dense, it soon encounters another charged particle and it gets scattered again! The result is that a photon’s path through the early Universe is a bit like a drunken sailor’s walk, and has little chance of ever looking like anything else.

The Universe continues in this state for about 400,000 years, continuing to expand and continuing to cool. Around 400,000 years the temperature has fallen to a balmy 3000 ºC. At that temperature, electrons can stick strongly enough to nuclei that collisions don’t knock them free.  Suddenly, neutral atoms form!  This event is called “recombination,” which always struck me as a funny term because this is the first time particles combined to form atoms! Almost all of the atoms that form are hydrogen, mixed with a good amount of helium, and a little bit of lithium. These amounts have been measured by astronomers and agree exquisitely with the amounts predicted by Big Bang Cosmology; this is one of the strongest pillars of evidence convincing us that the Big Bang is the correct model for the Universe.

(L) Before atoms form, the Universe is filled with a vast soup of charged nuclei and electrons, and photons cannot travel very far without scattering off of them. (R) When the electrons bind to nuclei (“recombination”) to form neutral atoms, the photons no longer scatter so easily, and they fly free — the Universe has become transparent.

The most important consequence of recombination is that all the charged particles are bound together into neutral atoms. As far as the photons are concerned, the Universe is suddenly devoid of any charged particles to scatter off of, and they burst free and start travelling on long, unscattered paths. This is called “decoupling” — the photons no longer strongly interact with the “stuff” that became atoms. Free to stream through a suddenly transparent Universe, the photons begin their long 14 billion year journey to us.  We see them here on Earth as microwaves, coming from every direction on the sky.  We call these microwaves the Cosmic Microwave Background, and it is the relic light from the moment that atoms formed.

Arno Penzias (L) and Robert Wilson (R) in front of the Bell Labs microwave antenna that first detected the Cosmic Microwave Background. They were awarded the 1978 Nobel Prize in Physics for their discovery.

The Cosmic Microwave Background was discovered in 1965 by Penzias and Wilson at Bell Labs. As expected, it was coming from every direction on the sky, and exceedingly uniform — it looks exactly the same, to our ability to measure it, no matter which direction we looked. The Cosmic Microwave Background is relic radiation that is a precise probe of the temperature at the time atoms form. The fact that we see the same microwaves in every direction means atoms formed at the same time in the same amounts at the same temperature in every direction.

A recreation of the 1965 Cosmic Microwave Background map, covering the entire sky (Penzias and Wilson could not see the entire sky from Bell Labs). The band of stronger microwave light is the signature of the Milky Way Galaxy.

Despite the fact that this is exactly what was predicted, it poses a certain problem for us to understand. The uniformity is confusing because the way things get to be the same temperature is through thermal contact — they talk to each other, and trade bits of energy (heat) until they are at the same temperature. This is why Popsicles melt if you leave them on your counter — heat from the counter flows into the Popsicle, melting it until the puddle of goo is the same temperature as the counter. This is why your cup of coffee cools down — heat from the coffee flows into the air, warming the air in the room until the coffee and the air are at the same temperature.  So why should that bother us with the Cosmic Microwave Background? Because there is an ultimate speed limit in the Universe — the speed of light.

To understand this, look up in the sky to your left. The microwave background in that direction is so far away it has taken the entire age of the Universe for the light to reach Earth!  Now look up in the sky to your right — the microwave background is just as far away in the other direction! In the entire age of the Universe, these two patches of the sky have only had time to send light to the Earth, NOT to each other.  But that means we have a great mystery! The two patches are at EXACTLY the same temperature as each other. How did they know to be the same temperature if they aren’t in thermal contact, if they can’t talk to each other and trade heat in less than twice the age of the Universe?   This is called “The Horizon Problem” — pieces of the sky are too far away from each other to collude to have the same appearance and physical properties.

The page from Alan Guth’s research notebook where he had the first idea for inflation (box at the top). [[On display at the Adler Planetarium; the notebook is part of the collection curated by the Adler’s Webster Institute for the History of Astronomy.]]

The solution to the problem was initially discovered by Alan Guth in 1979.  Guth imagined a moment very early in the Universe. How early? About 10^–35 seconds after the Big Bang (about a hundred-billionth of a trillionth of a trillionth of a second!). At that time, the Universe was very small, and as a result very hot and very dense. The fact that it was very small means than the entire Universe was in thermal contact — it could all trade heat until it all had the same temperature.  So how to you grow a very tiny, uniform temperature Universe into a gigantic huge Universe that still looks like it is in thermal equilibrium?  Guth realized the way to do this was to grow the Universe very large, very fast.  This sudden, rapid expansion is called inflation, and it occurred very shortly after the Big Bang, from about 10^–36 seconds to 10^–34 seconds! During that time, the Universe inflated, like a balloon, by a factor of about 10²⁶ in size.  Now 10²⁶ is clearly a big number (100 trillion trillion), but what does it mean to expand by that factor?  Imagine an atom.  An atom is about 10^–10 meters across (1 angstrom).  By contrast, a lightyear is nearly 10¹⁶ meters, or a factor 10²⁶ bigger than an atom. If you grew an atom to be a lightyear across, it would have increased in size by a factor of 10²⁶.

Cosmologists put this all together in a chain of reasoning that can be hard to keep in your head. Here are the salient points:

1. Early on, everything was extremely close together and the Universe was in thermal equilibrium — all the parts of it were in contact and reached the same temperature.
2. Inflation suddenly occurs — the Universe is stretched and pushed apart, so that different parts of it are so far away they are no longer in thermal contact.
3. The now distant parts have the same thermal properties because they were in equilibrium before the expansion!
4. Now, after inflation, the different parts of the Universe continue to cool, but they all cool in exactly the same way, so they look as if they are at the same temperature.

Voila! Horizon problem explained!  🙂

At this point, you might think we’re done because the idea of inflation neatly explains some of the observational questions we have about Big Bang cosmology. But we’re scientists, so we’re always pushing hard on our ideas to make sure they are right, to understand all that they imply.  So what else does inflation do that we can measure?  Is there anything we can observe that continues to confirm the basic principle of inflation? Are there measurements that can be made that might explain more about how inflation started, how it stopped, or whether is is something more complicated than plain old simple inflation?

Observing the Universe at the time of inflation is hard.  Why? We know inflation happened right after the Big Bang, almost 400,000 years before the creation of the Cosmic Microwave Background.  The Cosmic Microwave Background is like a curtain — it is the oldest light we can see, because it was released at the first moment when light could travel freely.  Before that moment, light was inhibited from travelling very far at all — it scattered and bounced around and could never make a beeline for Earth and our telescopes.  As a consequence, we can’t see beyond the Cosmic Microwave Background. If we have any hope of probing our ideas about inflation, we’re going to have to find a way to see beyond the Curtain, or discover some unique signature that inflation left in its wake that imprinted itself in the Cosmic Microwave Background.  Fortunately for us, these are not idle wishes.  One thing inflation should have done is generate an echoing background of gravitational waves that should have left their imprint on the Cosmic Microwave Background.  This will be our focus next time.

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This is the first in a three-part series to explore physics and astronomy behind what the BICEP2 observation of the Cosmic Microwave Background is all about. The other two parts are:

2: Gravitational Waves (5 April 2014)

3: Keys to the Cosmos (11 April 2014)

Cosmos 10: The Edge of Forever

by Shane L. Larson

My parents are both natural scientists — my mother is a forester, and my father is a plant ecologist. As kids, we would spend long weeks in the summer camping doing “field research” in the wild backwoods of the Rockies.  Tents were optional, and at night I would often lie in my sleeping bag staring up into the blackest night you can imagine.  

The Milky Way, rising over a campsite near Crater Lake, Oregon. [Image by Shane Black, Website]

From the dark valleys and meadows of the Rockies, the sky is a seemingly endless tapestry of black velvet, studded with a sparkling horde of stars converging on the vast gossamer seam of the Milky Way.  It is impossible to scan that deep darkness, as you slowly drift into that fuzzy netherworld between wakefulness and sleep, and not feel like you are falling into an infinitely deep sea that goes on forever.

And for all we know, it does go on forever! The vastness of the Cosmos, especially compared to the typical scales of our everyday lives, is mind-bogglingly large. It is a fact that we have always been cognizant of — our stories, our legends, even our everyday experiences place the sky very far away, beyond the simple reach of human hands. The glitter of distant stars provide an ideal tapestry upon which we can paint our wonderings about the Universe and our place within it. Where did the stars come from? Where did the Earth come from? Where did we come from?  These are the oldest questions we know of, uttered around campfires and over late night dinners and in scholarly classrooms for countless generations.  The answers to these questions are part of an exquisitely interlinked puzzle that starts with the birth of the Universe, and leads ultimately to me and you.  The study of that puzzle is called cosmology.

Cosmology is a branch of science that is a bit like history — we are reconstructing the past history of the Cosmos as a way to understand what we see around us today, and to predict what the ultimate future and fate of Everything might be.  We reconstruct that past history by looking deep into the Cosmos, and with the Laws of Nature in hand, attempt to explain what we see.  As we have talked about before, looking out into the Cosmos is a kind of Wayback Machine — looking across space is looking back in time.  Today, we can see farther across the Universe than at any other time in human history; we have discovered and know more than all the 40,000 generations of humans who have come before us.  And we’ve discovered something remarkable; we’ve discovered that in the beginning, something happened.  Cosmologists call that something, “The Big Bang,” the origin of Everything that Is.

When studying cosmology, you will often read a sentence about the Big Bang and the Origin of the Universe.  The Origin Statement goes something like this: everything in the Universe began in an infinitely dense point smaller than the period at the end of this sentence.  What does that mean?  The answer is the basis for our current understanding of all of the Cosmos.  Let’s parse that question into several smaller questions.

The first obvious question is what do we mean by Universe?  Here, we will take the fundamental definition of Universe to be “everything that exists.”  But there is an unspoken subtlety in the Origin Statement as we wrote it here — in this case, the use of the word “Universe” actually means “Observable Universe.”  What’s the difference between “The Universe” and “The Observable Universe?”

My favorite lunch dive, in Logan, UT.

Consider an example from your everyday life — lunchtime.  Imagine one sunny day you decide to forego the sack lunch you brought with you and instead decide to go out to lunch with some of your friends.  You only have 1.5 hours before you have to be back, and you are walking on foot.  You can only walk so fast, so where are you going to go?  Perhaps Guy Fieri has pointed you toward an excellent BBQ joint on a late night episode of “Diners, Drive-Ins and Dives,” but that would require either a plane flight or a very long road trip, both of which will take far longer than the 1.5 hours you have. Instead, you confine your attention to restaurants within a certain distance — reachable if you walk as fast as you can for a limited amount of time.

The Universe is kind of the same way — there is a maximum speed that anything can attain, namely the speed of light. Thus, in the age of the Universe, there is a maximum distance over which any information can come to the shores of Earth — the distance that light can travel in the age of the Universe!  The “Observable Universe” is that part of the Universe from which we could have received some light that started travelling at the moment the Universe was born, and is just now reaching Earth today (analogous to how far you can walk during your lunch hour).  It is a small part of the “Entire Universe,” most of which we know nothing about because the light from there has not had the chance to reach us (analogous to the entire vast world full of restaurants, which you cannot reach during your lunch hour!).

The Observable Universe is just a small part of the Entire Universe. It is bounded by the farthest distance light could have travelled in the age of the Cosmos. If Earth is at the center of this boundary, then light from outside the blue boundary (such as from the yellow galaxy on the right) hasn’t had time to reach us yet. [Illustration by S. Larson]

In the beginning, the Entire Universe was just a vast (possibly infinite) collection of the ultra-dense points mentioned in the Origin Statement.  The Big Bang was not really an explosion, not in the sense of an exploding stick of dynamite; the Big Bang was the apparently spontaneous and rapid expansion of every single point in the Entire Universe.  What is expanding?  The fabric that makes up the Universe itself is expanding, carrying everything that would become stars, galaxies, trees, kangaroos and people along with it.  Cosmologists call that fabric spacetime.  The very stuff that the Universe is made of — spacetime — is stretching.

Now if that doesn’t immediately make sense, don’t worry! It is a disconcerting and unfamiliar idea. The contemplation of big ideas is always a bit uncomfortable, because we’re stretching our brains in ways that it is not used to; that’s the way science works.  One way to help settle your mind around unfamiliar concepts and to build intuition is to appeal to analogies.  Analogies and metaphors are not perfect, but they help connect the ideas that need to be connected.  One of the classic analogies to understand the Big Bang is to imagine other things that stretch and expand.

Consider a large piece of spandex, with a checkerboard on it, as in the figure shown here.  The checkerboard pattern is not necessary, but it provides a quick and easy way for us to see and talk about distances. This checkered fabric is an analogy, a metaphor that we use to think about the Universe, and in this picture imagine it stretches far beyond the boundaries of the page of your computer screen.  For the moment, I have made the checkers large enough to see, but you could easily imagine them being smaller than what is drawn here, even much smaller (perhaps as small as the proverbial period at the end of the Origin Statement).

Imagine I have two ants sitting on the spandex, one named Xeno (the black ant) and one named Scarlett (the red ant).  They have both staked out a square they like, and are staying put, watching closely that the other ant does not move off their chosen territory.  This is the case shown in the first figure.

(L) Consider two ants, Xeno and Scarlett, on a stretchy sheet representeding the spacetime fabric of the Cosmos. (R) When the Cosmos expands in every direction and at every point, the two ants get farther apart. [Illustration by S. Larson]

Now, unbeknownst to our ants, the very fabric of the Universe is expanding around them, as shown in the second figure. It expands uniformly, in every direction. The result of that, in the context of my spandex checkers, is that every square gets larger (though our ants remain the same size, comfortably bound together by the biological goop and intermolecular forces that give their bodies form).  What are the observational consequence for our ants, keeping their beady little ant eyes on each other?  Much to their surprise, they find themselves slowly getting farther apart!  Scarlett looks around, and clearly she is not moving — she has not moved at all since our little experiment began. Never-the-less, it is quite clear that Xeno is receding from her. Meanwhile, Xeno is thinking the same thing. He has not shifted nor moved at all, but Scarlett is inexorably getting farther away.  The explanation? The very space between them, the stuff that the Universe is made of, is expanding.

What is interesting is that every square in the fabric of our Universe is expanding — the squares are getting larger, and everything is getting farther apart.  No matter how tiny every square started, if we wait long enough, it gets bigger.  The consequence is that from the perspective of anyone anywhere in the Universe, every other point is flying away from them.  Consider a few more ants: Xeno, Scarlett, Kermit (the green ant) and Indigo (the blue ant). If each one of them measures the distance to every other ant, they find that if they wait a while, the distance to every other ant increases.  From  the perspective of any ant, firmly rooted to their little territory in the Cosmos, every other point in the Universe is slowly getting farther and farther away, no matter what direction they look.

Imagine an army of ants (clockwise from the top: Kermit, Scarlett, Indigo, and Xeno). If they all watch each other as the Universe expands, they think ALL other ants are moving away from them, no matter what direction they are. [Illustration by S. Larson]

This is how we think about the Big Bang.  Everything that you can see (the Observable Universe) was once contained in a dot smaller than the period at the end of this sentence; it was like a teeny, tiny square on our spandex.  Then the Big Bang happened, and every point in the Entire Universe — every point on the spandex — started to expand.  The part of the Universe you can see is only one small part of the vast fabric that is everything, but it all started long ago in a very tiny spot.  Everything you can see in the Universe began in an infinitely dense point smaller than the period at the end of this sentence!

On the surface, this story sounds fantastical, almost beyond belief. We can always make up fantastical ideas about the nature of the Cosmos, but for those ideas to move beyond mere speculation and into the realm of science, we must be able to test those ideas.  There must be something we can look for, something that we can observe. In the case of cosmology, there is.

One of the things that physicists know about the world is that if you compress things they get hot. This is the principle behind pressure cookers, this is why it is hot in the core of the Earth, and this is why the Sun burns hydrogen in its core. When the pressure goes up, things get hot!  If the Universe is expanding today, we can imagine running the movie backward in time, watching everything run backward toward the Big Bang.  Because we see everything flying apart now, when we run the movie backward what we see is the entire Observable Universe being compressed down into a small point. The pressure in that point would have been enormous, which means it would have been tremendously hot.  If that were true, there should be some thermal signature of that early, hot, dense state of the Cosmos.

There is such a signature. Arriving on Earth from every direction on the sky, is a faint fog of microwave radiation, known as the Cosmic Microwave Background. It is the light that was released from the birth of all the atoms in the Cosmos, 400,000 years after the Big Bang.  Before this time, the Universe was so hot and dense that atoms could not hold together; they would constantly crash together and break apart into the fluff from which they are made, melting back into the primordial soup of light and sub-atomic particles. But as the Universe expands, it cools slowly until atoms could hold together. The moment that happened, the soup immediately thinned and the light flew free, carrying the message of the birth of the atoms.

The Planck map of the Cosmic Microwave Background. [ESA/Planck Collaboration]

This picture of the Cosmic Microwave Background is the most accurate map every made of the microwave sky; it is the youngest picture of the Cosmos we have ever taken, and the strongest piece of evidence we have that the Big Bang unfolded in the way we have just discussed. This picture, an image of the Cosmos very shortly after its birth, is one of the greatest legacies of our race. It captures, in an exquisite map of subtle patterns and colors, the ability of our species to reduce our ignorance, to become more enlightened about the Cosmos and our place in it.

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This post is part of an ongoing series, celebrating the forthcoming science series, Cosmos: A Spacetime Odyssey by revisiting the themes of Carl Sagan’s classic series, Cosmos: A Personal Voyage.  The introductory post of the series, with links to all other posts may be found here:  http://wp.me/p19G0g-dE