The Universe we see around us has some unusual properties. In every direction we see roughly the same number of galaxies on large scales. The cosmic microwave background has roughly the same temperature in all directions, and the Universe as a whole is topologically flat. In physics terms this means the Universe is homogeneous and isotropic. But according to the big bang model, we wouldn’t expect that to be the case. One way to solve this issue is through a process known as inflation, but this raises some interesting problems of its own.

The observational evidence for the big bang is quite strong, so we know the early Universe was extremely hot and dense. We also know the Universe is expanding at an ever increasing rate due to dark energy. But if cosmic expansion is only driven by dark energy, then it would seem the Universe is too homogeneous and isotropic. There simply wasn’t enough time for the Universe to reach a homogeneous state before things started collapsing under gravity. However, if the Universe had a period of very rapid expansion (known as the inflationary period), any major fluctuations in density and temperature would be smoothed out, and the Universe we observe would be a small fraction of the cosmos. The inflation model was first proposed by Alan Guth in the 1980s, but to understand the model we need a bit of quantum theory.

A false vacuum is a local energy minimum, but not the true minimum.

Physical systems tend to move toward a state of lowest energy. For example, a hot object will tend to cool down by emitting heat and light. The Universe is no exception, and so it’s tendency should be to expand and cool. A system will move toward the lowest energy if it can, but sometimes a system might reach a low energy state that isn’t the lowest possible energy. For example, a ball will tend to roll down a hill, but it might find itself in a shallow dip in the side of a hill. The dip is a local minimum, but the bottom of the hill is the true minimum. For an object like a ball, once it reaches a local minimum it is stuck there. The ball can’t climb out of the dip to keep rolling downhill. But quantum systems can shift out of a local minimum. Through a process known as quantum tunneling, they have a small probability of jumping the gap to reach lower energy.

Since the Universe is fundamentally a quantum system, the early Universe could have found itself in a local minimum, or what’s known as a false vacuum (since a vacuum would be the lowest state for the cosmos). It would stay in this false vacuum for a time before quantum tunneling to the true vacuum. What Guth found was that since the false vacuum state has energy, it could cause the Universe to undergo rapid expansion. Under the inflationary model, the early Universe was in such a false vacuum for a brief period, and thus had a brief period of inflation. The inflation model is actually pretty elegant, and since the  model solves these kinds of problems so well, it is generally thought to be the correct solution. Most astrophysicists figure it is just a matter of gathering enough data to detect its effects.

There are, however, some issues with inflation. One of the big ones is that there are lots of ways inflation could occur, and most of them wouldn’t lead to the type of Universe we observe. They might inflate so much that stars and galaxies never have a chance to form, or not enough to give us a homogeneous universe. There a very narrow range of inflation that would produce a universe like ours, and it seems odd that inflation would just so happen to occur that way. This problem is part of the larger issue of the anthropic principle, where some argue the Universe seems to be configured in just the right way for life to exist.

Eternal inflation would create countless pocket universes.

But a variation of the inflation model may solve the issue. Known as eternal inflation, it argues that the Universe might not collapse from a false vacuum as a single whole. Instead, different parts of the Universe might reach different false vacuums, and they might drop out of that false vacuum at different times. While our region of the Universe seemed to drop out rather quickly, other parts would have dropped out later, and still other parts might still be inflating. This model leads to a kind of multiverse, where there are pockets on non-inflationary universes surrounded by regions that are still inflating. As a result, all the different varieties of inflation would occur. Under eternal inflation, a universe such as ours is bound to occur.

Of course all of this is pretty speculative. Since we don’t have any way to observe the multiverse, we’d need to understand just how eternal inflation could arise. Right now we don’t even have any direct evidence for inflation, and until we have evidence we can’t narrow down the nature of inflation (assuming it occurred). So for now we’ll just have to keep gathering evidence.

Ever onward, ever upward.

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The Universe is big. Really big. The observable universe extends from the Earth to the horizon of the cosmic microwave background. When the light of the cosmic background was emitted about 13.8 billion years ago it was only 42 million light years away, but because of the expansion of the Universe that horizon is now more than 46 billion light years away. Using that definition, the known universe is about 93 billion light years in diameter. As large as that is, it’s only the portion of the Universe we can observe. The total Universe extends beyond our horizon. Just how far it goes is an interesting question. 

A flat universe implies that distant observers also see a homogeneous universe.

There are indications that the Universe extends far beyond what we can observe. The universe we see has a fairly uniform distribution of matter. Sure, matter clumps into galaxies, and those galaxies clump into clusters of galaxies, but on a scale larger than about 300 million light years those clusters appear randomly distributed. In other words, it is homogeneous and isotropic. If what we observe were the extent of the universe, then we would be basically in the center. Since we see about the same amount of mass in all directions, the gravitational pull from all that matter would basically cancel out. But for a galaxy on the edge, it would see a great deal of matter in one direction and basically nothing in other directions. Gravitationally it would be pulled toward the center of the universe. Because of dark energy this universe wouldn’t collapse upon itself, but it would mean that galaxies would tend to clump toward the center. Since gravity is a curvature of spacetime, this would distort the overall shape of the universe. What we observe, however, is that the Universe is flat. At the very least this means an observer at the edge of our horizon must also see a homogeneous and isotropic universe. Given the flatness limit that would mean the total Universe is at least 400 times larger than the observable universe.

Two regions of space can’t be thermally connected.

But it could be much larger. Another point of evidence is the fact that the cosmic microwave background (CMB) has an almost perfectly uniform temperature. There are small fluctuations of temperature throughout the background, but the overall temperature is the same in all directions. The thing is, it shouldn’t be. The CMB was emitted when the universe was about 380,000 years old. At best, that means that only regions of space within a radius of 380,000 light years would have any way to reach thermal equilibrium. For anything more distant, there simply wasn’t enough time for the regions to communicate, even at the speed of light. When we look at the cosmic background in different directions, we can see different regions that couldn’t have reached the same temperature. They were simply too far away from each other. And yet, they have the same temperature. What gives? The dominant idea is known as early inflation. Basically, a fraction of a second after the big bang the Universe entered a short period of extremely rapid expansion. In a brief moment the Universe expanded by a factor of 10⁶⁰ before settling down to its current rate of expansion. While we don’t have direct evidence of early inflation, it does agree with several observational aspects.

According to the inflation model, the observable universe was roughly the size of a quark before early inflation, and about the size of a grain of sand afterwards. If the size of the total Universe before inflation was the distance light could travel since the big bang, then the current Universe is about 10²⁷ larger than the observable universe. In other words, comparing the observable universe to the entire Universe is like comparing a grain of sand to the observable universe. It could be much larger, perhaps even infinite.

The game Asteroids is a closed universe where you can travel in one direction forever.

Of course all of this assumes the cosmos doesn’t have some kind of strange topology. Since space and time can warp and weft, one could imagine a universe that loops around to itself, being finite in volume, but infinite in distance. Imagine a cosmic version of the surface of the Earth. It has a finite area, but due to the Earth’s curvature you could travel in a particular direction forever, simply looping around the Earth over and over. In cosmic terms that would mean a beam of light traveling through space would eventually find itself back where it started. If the Universe were closed and smaller than the observable universe, we would expect to see multiple versions of the same galaxies. There have been studies looking for periodic fluctuations in the cosmic microwave background that would indicate such a closed-universe effect, and they’ve found no evidence of such a thing. If the Universe is truly closed, then it must be at least 78 billion light years in diameter. Of course there is no reason to presume the Universe has such a closed topology, so that lower bound should be taken with a grain of salt.

So the short answer for the size of the Universe is that it’s huge. Likely very, very, very huge. Possibly infinite.

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With all the brouhaha over the latest Planck satellite data and the revelation that the BICEP2 claim about early cosmic inflation didn’t hold up to scrutiny, it’s easy to imagine that all this work simply brings us back to where we started, with no idea of whether inflation is real, or just an incorrect model that happens to work. But in fact, the Planck results do tell us some things about inflation. It hasn’t validated the model, but it has pruned some limbs from the theoretical tree.

Inflation is a popular idea because it would solve several of the nagging mysteries of the universe. For example, when we look at the cosmic microwave background, we see it has a nearly uniform temperature. There are small scale fluctuations, but overall the temperature is too uniform. When the cosmic microwave background first appeared the observable universe was about 10 million light years across, but it was only about 380,000 years old, which isn’t nearly enough time for temperatures to even out. Inflation solves this problem by allowing the observable universe to be teeny tiny before expanding rapidly, which allows temperatures to even out before inflation.

Another issue is known as the flatness problem. If you average out all the curvature of space and time, both due to gravitational mass and cosmic expansion, we find that it adds up to zero to the limits of observation. In other words, the universe is flat. It seems odd that the universe would happen to be flat just by chance, but if early inflation occurred it would have flattened out the observable universe.

As an added bonus, inflation provides a mechanism for galaxies to cluster on the scale that we observe. Basically inflation would accentuate the gravitational clumping of matter in the early universe, allowing galaxies and clusters to form easily. It also resolves some issues in theoretical physics, such as the magnetic monopole mystery.

So inflation has a lot going for it, but the catch is that you can come of with lots of different mechanisms for inflation, and people have. There have been dozens of models proposed, and most of them fit the limited data we’ve had. But with Planck we can now start distinguishing between models. Assuming inflation to be true, we now know certain things.

For one, we know that it must have been adiabatic. That is, it must have occurred such that the ratio of electrons to photons must have remained fairly constant. This eliminates some of the more exotic models. We also know something about the inflation potential Φ, which governs the rate of inflation. Based on the data, inflation depending on Φ² or higher powers are excluded.

There are still lots of variations that remain viable, but we aren’t searching in the dark any more. Even the models that are still in the game now have some limitations placed on them. This is where inflation begins to shift from a largely theoretical model towards an experimental one. Variations are now living or dying on the data.

Now we just have to keep pruning the tree.

Paper: Planck Collaboration. Planck 2015 results. XIII. Cosmological parameters. arXiv:1502.01589 [astro-ph.CO] (2015)

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The existence of early cosmic inflation is one of the big questions in cosmology. It seems to be necessary to explain the uniformity of the cosmic microwave background, but confirming it observationally has been a challenge. Last March, BICEP2 released announced that they had detected evidence of primordial gravitational waves in the polarization of the CMB, which is one prediction of early inflation. This started a firestorm of debate over whether it was an actual detection of inflation, or whether it was simply an effect of light scattering off interstellar dust. Yesterday a new paper was released combining results of BICEP2, Planck, and Keck studies, and it’s being presented in the press as the killer of cosmic inflation. But in reality things aren’t so cut and dry.

BICEP2 and Keck observation surveys (outlines) are where dust effects should be low.
Credit: Caltech Observatory

It should be noted that this new paper hasn’t been peer reviewed, and is even designated as a draft on the paper itself, so it shouldn’t be taken as authoritative just yet. What the paper does is combine the data from these three independent studies to see what the combined results say about cosmic inflation and the question of dust. This is useful because BICEP2 and the Keck Array (both located in Antarctica) look at specific patches of sky where dust contamination is expected to be low. Planck, in contrast, made an all-sky survey including both dusty and non-dusty regions. Combining these very different approaches is a good way to test the validity of the results.

This new paper makes several conclusions. First, it compares the B-mode polarization results of BICEP2 and Keck with those of Planck, and finds that they strongly match. The agreement is at a 7-sigma level, which means the chance of the data not being an actual result is about 1 in 390 trillion. In short, we are absolutely detecting B-mode polarization in the cosmic microwave background. This is great, because it means there’s no debate about whether the data is valid.

There’s a hint of cosmic inflation in the data. Credit: BICEP/Keck

The next question is whether this B-mode polarization is due to primordial gravitational waves from early inflation, light scattering off interstellar dust, or some combination of the two. (There’s actually a third effect due to gravitational lensing, but we understand that effect pretty well.) The primordial gravitational waves are measured in terms of what is known as an r factor, where a larger r means stronger gravitational waves and therefore stronger inflation. The original results from BICEP2 found that r is between 0.15 and 0.27, with the best result being r = 0.2 at a 5-sigma level. Taken by itself, this would seem to be a home-run discovery of cosmic inflation. But BICEP2 didn’t have great data on the distribution of interstellar dust, which Planck has.

In this new combined-data result, the teams find that r is 0.12. So the new results do show evidence of cosmic inflation. However, the confidence of this result is only 2-sigma, or about 95%. This means there’s about a 5% chance of it being a false positive. Given the significance of such a discovery, this isn’t remotely strong enough to declare it valid. What this means is that the BICEP2 results didn’t “discover” cosmic inflation. As it stands, there is evidence of cosmic inflation, but not strong evidence. The data hints at early inflation, but we don’t yet have a smoking gun.

In short, this new paper confirms the validity of the BICEP2 data, but disproves the conclusion drawn from that data. Early inflation has not been disproven, but it hasn’t been proven either. So we’ll have to dust ourselves off and keep looking for an answer one way or the other.

Paper: A Joint Analysis of BICEP2/Keck Array and Planck Data. new.bicepkeck.org/BKP_paper_20150130.pdf

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Polarization in the cosmic microwave background (CMB) is in the news again. This time with new results from a project known as POLARBEAR. The results were published this week in the Astrophysical Journal, and it swings the observational needle back towards the existence of cosmic inflation.

The evidence for cosmic inflation has been very publicly playing out in the media. It began with BICEP2 announcing that they had discovered evidence of primordial gravitational waves, which is a signature of early cosmic inflation. After their public announcement there was a flurry of criticism, particularly on whether BICEP2 had eliminated the effects of dust from their data. The BICEP2 paper did make it through peer review, but then the Planck team showed pretty clearly that dust was still a problem. It began to look like perhaps the entire “signal” of BICEP2 was due to dust.

Now POLARBEAR has tossed their hat into the ring. Their paper is more cautious, and they waited until surviving peer review before announcing it. As with BICEP2, it all comes down to dust, and whether its effects can be eliminated from the data.

Different modes of CMB polarization.
Credit: Sky and Telescope

Like the other projects, POLARBEAR has been observing polarized light within the cosmic microwave background, specifically a type of polarization known as B-mode polarization. The CMB is polarized due to the small fluctuations in temperature and density that existed at the time. This primordial polarization is known as E-mode polarization. If there was cosmic inflation in the early universe, then the primordial gravitational waves of inflation would distort some of the E-mode into B-mode polarization.

It would seem then that any detection of B-mode polarization is evidence of primordial gravitational waves, and thus of inflation. But the problem is that lots of other things can also create B-mode polarization. One of the big alternative sources is dust. The cosmic microwave background is the most distant light we can observe, so all the galaxies, dust, interstellar plasma and our own galaxy is between us and the CMB.  if you don’t account for them properly, then you could get a “false positive.”

The way POLARBEAR dealt with this challenge is two-fold. First, they took data from regions of the sky where dust contamination is at a minimum. Second, they gathered data at a higher resolution. This latter part is important, because at higher resolutions B-mode signals from gravitational lensing should be more dominant than those due to dust. They then did something rather interesting. Taking their data they tried to see if they could subtract out all the contaminating sources to get a null result.  In other words, started with the assumption that everything was a contaminant, and then tested whether that model worked.  What they found was that it didn’t. Specifically, they excluded the null result model with 97% certainty.

So their data showed that it’s not nothing. Within the B-mode data there is a portion of it that is due to gravitational lensing. It isn’t all due to dust and contaminants, as some have feared. So does that mean they found evidence of early inflation? Not quite. They’ve shown that they can see a gravitational signal, but they haven’t proven that the signal is due to primordial gravitational waves. The authors are being cautious here, which is probably a good thing.

So there’s hope that we will be able to observe the fingerprint of inflation (assuming it occurred). It just keeps getting more interesting.

Paper: P. A. R. Ade et al. A Measurement of the Cosmic Microwave Background B-Mode Polarization Power Spectrum at Sub-Degree Scales with POLARBEAR. ApJ 794 171 (2014)

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Yesterday a research project known as BICEP2 announced important results regarding cosmic inflation.  The result centers on what is known as B-mode polarization in the cosmic microwave background.  This is pretty big news, but it is also pretty complex, so let’s look at what’s really going on here and why this matters.

A polarized light wave. Credit: Hyperphysics

Let’s start with the idea of polarization.  Light waves are a type of wave known as transverse waves.  This means their oscillation is perpendicular to their direction of travel.  You can see this in water waves, where the up and down motion of the wave is perpendicular to its motion along the water’s surface.  With light waves (and electromagnetic waves in general), the vibration is that of the electric and magnetic fields.

Because of this, transverse waves can have an orientation to them known as polarization.  If you imagine a vibrating string, the waves could move up and down, or side to side, or at some angle.  There are other types of polarization that are more complex, but you get the idea.

Generally, the light emitted by a hot source is randomly oriented, or “unpolarized”.  However if light scatters off a material it can be polarized by the interaction.  The atmosphere does this to sunlight a bit, which I’ve written about before.  This is why a good pair of polarized sunglasses can eliminate glare.  They block light with horizontal polarization, which most reflections have.  Polarization happens in scattering when source of light is not uniform.  For example, polarized scattering occurs in the atmosphere because sunlight comes from the direction of the Sun, not evenly across the sky.  If daylight came equally in all directions, then you wouldn’t see the scattering polarization.

The CMB has small variations in temperature. Credit: WMAP

So what does this have to do with the cosmic microwave background (CMB)?  The CMB is the light from the earliest point where the universe became transparent.  That is, when the universe finally became cool enough for atoms to form.  Before that point, the electrons and nuclei were too hot to come together, meaning that they were a thick plasma of charged particles.  The light would keep scattering off the charged particles and couldn’t travel freely. In the last moments of this plasma stage, when the electrons finally started to bond with nuclei, the photons created in the big bang would have one last scatter off an electron before making its long journey across the universe.  Now if the early universe were perfectly uniform, then we wouldn’t see any polarization from that last scattering.  But there were small variations in the early universe, so we would expect to see some polarization in the CMB.  Since this last scattering occurred at a particular moment in the early universe, cosmic polarization gives is a precise window into the earliest moments of the big bang.

Different modes of CMB polarization.
Credit: Sky and Telescope

Because of these small variations, the polarization of the CMB varies at different points of the sky.  To get an understanding of the structure of the early universe, we need to look at the overall distribution of polarization across the sky.  This is where the different “modes” of polarization come in.  You can imagine the polarization measurement at each point can be represented by a line.  Where the lines appear to follow a path, or appear to radiate out from a particular region, then that is known as E-mode polarization.  Where the lines appear to twist relative to each other, that is known as B-mode polarization.  They are so named because their orientations are similar to those simple electric (E) or magnetic (B) fields.

These two modes are important because they have different causes.   The E-mode polarization is caused by the variations in density and temperature in the early universe, so it should follow the same pattern as the temperature variations seen in the cosmic background.  This was first observed in 2002 by the DASI interferometer, and the results agreed with the temperature fluctuations as expected.

Gravitational lensing can twist E-mode into B-mode.
Credit: NASA

The B-mode polarization has two causes.  The first is due to gravitational lensing of the E-mode.  The cosmic microwave background we see today has travelled for more than 13 billion years before reaching us.  Along its journey some of it has passed close enough to galaxies and the like to be gravitationally lensed.  This gravitational lensing twists the polarization a bit, giving some of it a B-mode polarization.  It is this polarization that was observed for the first time this past July.

But there is another mechanism for B-mode polarization that is more subtle, and requires more data to observe.  This mode is due to gravitational waves produced during the inflationary period of the big bang.  You see, the cosmic background only has small fluctuations, and we aren’t sure why.  Given the size and age of the universe at that time, its temperature shouldn’t have been able to even out.

We think the solution is that the universe was incredibly tiny in its earliest moments, but soon entered an inflationary period where the observable universe expanded at a furious pace.  This would explain not only the evenness of the cosmic background, but also why the universe is flat.  We’ve never seen direct evidence of this inflationary period, but we should be able to observe the effect of inflation in B-mode polarization. If the inflationary period occurred, then it would have produced gravitational waves on a cosmic scale.  Just as the gravitational lensing produces B-mode polarization, the gravitational waves would produce a B-mode effect.  Observe this subtle B-mode, and you have direct evidence of the inflationary period.

The B-mode results. The solid line is expected for lensing alone. The dotted line is gravity waves at r = 0.2. Credit: BICEP2.

Which brings us to this new work.  What the team has found is evidence of more B-mode polarization than expected by gravitational lensing alone.  Since there are two ways in which B-mode polarization can occur, they needed to show that this “extra” was not just due to lensing.  They found that the extra B-mode polarization was seen at a five-sigma level, which means (barring a 1 in 2 million fluke) the excess is due to primordial gravitational waves.  So we can say that primordial gravitational waves are real.

They then analyzed the polarization to determine the strength of these waves, and this is where things get interesting.  Gravitational waves are measured in terms of what is known as an r factor, where a larger r means stronger gravitational waves and therefore stronger inflation.  Results from the Planck space telescope determined that the upper limit of r should be r < 0.11.  What these new results find is r is between 0.15 and 0.27, with the best result being r = 0.2.  This is much higher than expected, and it conflicts with the Planck results.  Or at least it seems to.  Analyzing this kind of data is very tricky, so this may be an effect of how the data is analyzed, or it may be an effect of real physics.

So where do we stand with all this?  Although the research is now public, it has yet to be peer reviewed.  So it is worth being a bit cautious about these results.  The next thing we’ll look towards is new research from the Planck telescope team.  They are currently analyzing their own B-mode polarization data, and if this r=0.2 result is valid Planck will see it as well.  Then there is the question of how to resolve the apparent conflict between the initial Planck result and this new one.  It should also be kept in mind that while these results are consistent with the inflationary model, there are other less popular models that haven’t been ruled out.  Personally I find the evidence for inflation pretty convincing, but I could be wrong.

At the same time, I don’t want to downplay this result too much.  The result is very strong, and it points pretty clearly at inflation.  If it holds up, it means we are now able to study the earliest moments of the universe.  Much earlier than we have before.  After all, the inflationary period ended when the universe was about 10⁻³² of a second old.

And we can see echoes of it from 13.8 billion years away.

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