Cosmic Static: The Stochastic Gravitational Wave Background

What would you hear if you could listen back to the very moment the universe burst into existence? Using the Cosmic Microwave Background (explained in Beatrice’s blog post), we have a picture of what the Universe looked like at ~380,000 years old, but we can’t use light to look any farther back in time because before the moment captured by the CMB, the universe consisted of an opaque plasma. Instead of using light, however, we can use gravity to probe our Universe’s earliest days. As explained in Sydney’s blog post, violent acceleration of extremely massive objects emits gravitational waves, and turbulent early universe processes like inflation (see Anne-Sylvie’s post) created the perfect environment for gravitational waves. The stochastic gravitational wave background is analogous to the CMB; it comes from the superposition of many gravitational wave signals that are individually indistinguishable, so it appears as a persistent background signal. The stochastic background can be dominated by cosmological sources like inflation, phase transitions, and cosmic strings, in which case it would provide a soundbite of the early days of our cosmic history. It can also be dominated by astrophysical sources- many overlapping individual signals coming from compact objects like black holes and neutron stars smashing into each other that are too weak or too distant to be detected individually- in which case it would provide a soundbite of our present astrophysical environment.

 

Why do we see the CMB but listen to gravitational waves? As a gravitational wave passes over Earth, it stretches space in one direction and contracts it in the perpendicular direction, so using extremely sensitive detectors, we can measure the frequency of these expansions and contractions, or measure their pitch. In order to explain some of the properties of the stochastic background, we will use the analogy of a crowded rock concert. Before the show, all the spectators are packed into the venue, each having a separate conversation. You can’t hear individual conversations, but you can hear the buzz of chatter. Each conversation represents an individual gravitational wave signal, too weak to be detected on its own, but combined with all the other conversations which are conducted at around the same volume, the room is filled with background noise. This background noise is the stochastic gravitational wave background.

 

If the concert is sold out, there is an equal conversation density in all directions. No matter which way you turn to listen, the background sounds the same in all directions, which means it’s “isotropic” in physics lingo. Cosmological backgrounds, a relic of an earlier time in the universe when matter was distributed nearly evenly across space, are expected to be isotropic. Now imagine several really loud groups of people come and sit down a few rows in front of you. You still can’t really hear their individual conversations, but you can definitely tell that the background is louder in their direction. If there was a dense population of coalescing stars or black holes in one specific region of the universe, the stochastic background would be louder in that direction, so it would be “anisotropic”.
 

If you’ve been waiting for the concert to start for a while already, the background chatter sounds the same now as it did 5, 10, or 15 minutes ago; it’s a stationary background that doesn’t depend on the time when you started listening. Similarly, if the background consists of independent conversations that last longer than the time between them, it is called a Gaussian background due to the Central Limit Theorem. However, if you’re one of the first people to arrive, you may be able to pick out bits and pieces of individual conversations starting up around you. The time between conversations is longer than the conversations themselves; this is a popcorn background. The same would be said of a stochastic background caused by overlapping gravitational wave signals whose duration is shorter than the period of time between individual events. This results in a background that sounds like popcorn in a microwave.

 

When Einstein predicted the existence of gravitational waves 100 years ago, his Theory of General Relativity (GR) predicted that gravitational waves could only move or stretch space in two ways, the plus and the cross tensor polarizations modes. Since we are interested in using gravitational waves to test GR, we can compare the polarization of the stochastic background predicted by GR to that predicted by alternative gravity theories, which allow gravitational waves to move in up to six directions, adding two vector and two scalar polarization modes to the two tensor modes already predicted by GR. The image below shows how a gravitational wave of each polarization would stretch and squeeze a test mass ring. Just like the ring responds differently to each polarization, so does the gravitational wave detector, so we can measure the polarization content of the stochastic background by analyzing the detector’s response and allowing for the possibility of all six modes. If we were to detect any polarization mode besides the two tensor modes predicted by GR, this would prove that GR is incorrect and force us to reconsider everything we thought we knew about gravity. For this reason, the stochastic background is a powerful tool not only for learning about our cosmic history and our astrophysical environment, it can also be used to learn about gravity itself.

 

For more information about stochastic backgrounds and testing general relativity, check out this arXiv preprint!

Whispers in the cosmos: gravitational waves

Chances are good that you’ve thought about the concept of gravity once or twice. If you’ve ever taken a high school physics class, you might have heard that gravity is an invisible force that is responsible for keeping you planted on the earth. At the beginning of the 20th century, the young Albert Einstein was also interested in gravity. The accepted theory of gravity at that time had first been put forth by Isaac Newton in the 17th century, and it had seen great success in physics for centuries.

But Einstein was bothered by one of the key foundations of Newton’s gravity: that space and time are both independent, absolute entities. In his Principia Mathematica, Newton stated that

“Absolute, true, and mathematical time, of it self and from its own nature, flows equably without relation to anything external… absolute space, in its own nature, without relation to anything external, remains always similar and immovable”.

In the early 20th century, physicists were just beginning to understand electricity and magnetism, and while carefully scrutinizing these developments Einstein came up with a new idea: that space and time are not distinct, absolute quantities as Newton said, but rather that they are intertwined in a very special way.

Putting the dimensions of space and time together, into what we now call spacetime, turned out to be necessary to avoid paradoxical outcomes in electricity and magnetism. But the concept of spacetime also leads to some very strange outcomes. A new theory of gravity, called General Relativity, is one of these outcomes.

In General Relativity — Einstein’s theory of gravity — gravity is the curvature of spacetime itself. Physicists often say that spacetime is the “fabric of the cosmos”, but it’s not exactly made up of “stuff”, so how can it be curved?

This is difficult to conceptualize, but one can use an analogy to understand a little better. If you were to place a baseball on a spandex sheet of fabric, the ball would distort the sheet by bending it. A bowling ball would also bend the sheet, even more than the baseball. If you took a marble and added it to the sheet, the marble would follow the spandex surface, curving around the bowling ball (an orbit).

In this image, two masses both bend spacetime. [You can ignore the yellow lines, which are part of a bigger image not included.] This is the essence of Einstein’s gravity: massive objects bend spacetime, and in turn, spacetime tells matter how to move. Now we’re ready to talk about gravitational waves.
In this image, objects with different mass bend spacetime. The heaviest object, in yellow, bends spacetime more than the other two. Image credit: ESA – C. Carreau
This is the essence of Einstein’s gravity: massive objects bend spacetime, and in turn, spacetime tells matter how to move. Now we’re ready to talk about gravitational waves.

Imagine for a moment that you rotate the bowling ball about its vertical axis on the spandex sheet. The bowling ball has a smooth surface and is round, so there isn’t any effect on the sheet. However, if we took a pair of bowling balls and rotated them around each other, ripples would begin to spread outward on our spandex sheet. Similarly, if we took a bowling ball that wasn’t quite round (maybe with a lump of cement stuck to a side) and tried to rotate the ball, the lump would “catch” on the spandex and create ripples.

These ripples, produced either by two objects orbiting each other (we call this a binary system), or a lumpy object rotating about its axis, are gravitational waves. They propagate radially outward from the objects that produce them and travel at the speed of light. As you can imagine, this means that gravitational waves are being produced all the time, all over the universe, from all kinds of systems: the moon and Earth in their orbit; a pair of ice-skaters spinning while holding hands; a football wobbling from a poor throw; a distant rotating planet with mountains.

When the gravitational waves produced by any of these examples hit matter like you and I, the effect they have is to stretch and squeeze it. All the stretching and squeezing happens in the direction that’s perpendicular to the gravitational wave’s travel path (using more technical physics lingo, we would say that gravitational waves are transverse).

The amount of stretching and squeezing is extraordinarily small because gravity is actually fairly weak [just think: you can defy the entire gravitational pull of the earth just by jumping or using a refrigerator magnet to pick up a paper clip!]. To produce “big” gravitational
waves, we have to look for waves that are produced by something called compact objects.To explai
n what a compact object is, imagine that you have a large round bread roll. The roll is made up of ordinary atoms and has mass; we could weigh it on a kitchen scale, and measure its diameter. Now imagine squashing the roll with your hands until it forms a dense lump of bread. If we place the squashed bread roll on our scale, it would have the same weight as it did before. It contains the same number and type of atoms it had before we squashed it. But now, the roll occupies a much smaller region of space, and the bread is more dense than it was before. It is now a compact object.

This figure shows how spacetime is curved for for objects with the same mass, but increasing compactness from left to right. You can see that the most compact object, on the far right, distorts spacetime in a much more violent way than the others. Image credit: National Geographic

Compact objects bend spacetime in a much more extreme way than other objects, and as a result, the gravitational waves they produce stretch and squeeze matter enough that we can actually detect it. Don’t get too excited about the amount of stretching, though. The most compact astrophysical objects in the universe (that we know of) are black holes and neutron stars, which are dead remnants of very massive stars. If a “big” gravitational wave produced by a pair of orbiting black holes or neutron stars were to hit you head-on, your height would only change by one thousandth the diameter of a proton!

Detecting gravitational waves is thus a very tricky business; the detectors we use must be capable of measuring changes in length that are smaller than the atoms the detectors are made of! We will discuss the methods that we use to construct such detectors and conduct searches for gravitational waves in a future blog post.

But before you go, it’s important to understand why any of this matters. One reason we’re interested in detecting gravitational waves is to test Einstein’s gravity. Although we have significant experimental evidence that supports General Relativity, there are feasible contending theories that are similar and vary only from Einstein’s in the way that gravitational waves behave. So far, our detections of gravitational waves have continued to support Einstein’s theory, but it is important to continue to test this.

The second reason to search for gravitational waves is to learn from them. Every telescope ever built has relied on light of some form (x-ray, gamma ray, infrared, visible, radio, etc.) to observe the universe. Gravitational wave detectors are completely different; they use gravity instead of light observe the universe. This allows us to study systems, such as black hole binaries, that can’t be directly studied using light. We now have the potential to unlock mysteries about black holes, neutron stars, stellar evolution, the Big Bang and much more.

And that’s not all. Any time our species has found a new way to observe the universe around us, we find unexpected things, things we didn’t even know that we didn’t know. There is no reason to suspect that this will be any different. We’re standing on the cutting edge of a new observational experience for mankind, and there are all kinds of beautiful, bizarre and unexpected things to be discovered!

Stay tuned to hear more about gravitational waves from the IGC. In the meantime, if you’ve got questions, I love to talk science! Feel free to email me.

The shape of our Universe

—A blogpost about a recent paper by Beatrice Bonga (author of this post), Brajesh Gupt and Nelson Yokomizo—

Have you ever wondered what the shape of our universe is? It turns out that you only need three categories to classify all the possibilities for the shape of our universe: closed, flat or open. The closed category contains all shapes that look like a 3-dimensional sphere or any deformation of it. To visualize this better, let me give you some examples in two dimensions:  the surface of a potato and the earth are both deformations of a 2-dimensional sphere. The flat category is like a 3-dimensional plane, with a sheet of paper (whether it is crumbled or not) being an easy to visualize example in two dimensions. The open category contains all shapes that look saddle shaped (or any deformation of it of course).

beatrice-figure

Is there a way to tell which category our universe belongs to? Observations from cosmology are so far all consistent with a flat universe, which also happens to be the easiest to visualize and do calculations with. This is typically the reason why most data is analyzed using the assumption that that our universe is flat. However, data is becoming increasingly more precise. So is there a chance that our universe is curved after all? We would be like the people of ancient Greece who were able to determine that the surface of the Earth is curved even though it looked flat from their perspective.

This question has been studied by numerous physicists. One of the most amazing data available in cosmology is the Cosmic Microwave Background (CMB). The CMB is radiation emitted when our universe was ~380,000 years old and we are able to observe this radiation now with incredible precision. You could think of it as the baby picture of our universe because our universe is now close to 14 billion years old. To be precise, if you compare the age of our universe with a 100 year old person, the CMB is a picture of a one-day old baby. By analyzing this baby picture carefully, we don’t just learn things about the universe when it was 380,000 years old but also about the years before. During one of those earlier years, the universe underwent a phase of inflation (for more information about inflation, see Anne-Sylvie’s blog post). This phase is important to understand our approach to the question: is it possible that our universe is not flat, but closed?

post_closed_universe_fig_timeline

So how does one usually study the shape of our universe? Typically, when studying the CMB one calculates how the data should look at the end of inflation in their favorite inflationary model and then apply Einstein’s and Boltzmann equations to evolve this data to today. This data is then compared to the baby picture we observe today and the better the match between the evolved data and the actual observations of the CMB, the better the calculated form of our data at the end of inflation was. Scientists so far have looked at the effect of a closed universe on the evolution from the end of inflation to today, but they have not calculated how a closed model changes the data at the end of inflation. This is what we did. We then evolved it with the known evolution equations and compared it to what we observe today.

What did we find? The calculated data at the end of inflation looks different, however, the differences are small and the data remains consistent with a flat model. The differences between the flat and the closed model appear at large scales, for which the closed model does moderately better than the flat model, but at these scales the observational error margins are also largest. Thus, the difference is statistically not very significant.

If you want to know more, you can find the pre-print of our article here. You can also always shoot me an email if you have more questions.

Inflationary Cosmology: the Story of the Early Universe

My research interests revolves around inflationary cosmology.

Owing to several observations that started with Edwin Hubble, we know that our universe is in expansion. On very large scales, the distance separating two objects grows, as the fabric of spacetime expands more and more. This means that, if we look back in the past, the universe was much smaller, hotter and denser than it is today.

The model that describes most accurately the history and evolution of the Universe today is called the Λ-CDM (or concordance) model. According to the theory, about thirteen billion years ago, all the matter and energy of the universe was forming an insanely dense, hot and homogeneous soup. Well, actually, the soup was not completely homogeneous; some inhomogeneities, however extremely minute, were present. And the existence of these inhomogeneities in our primordial soup had dramatic consequences. Indeed, as they were denser, they could attract more matter, which would make these regions even denser. Therefore, as billions of years passed, the overdense regions saw their density increase, while the underdense regions became less and less filled with matter. This led to the growth of large scale structures that we observe today, such as clusters of galaxies.

A relic of those very homogeneous times is the faint radio signal, called Cosmic Microwave Background (CMB), that we receive from all the directions in the sky. Here is a picture taken by the Planck satellite:

CMB by Planck
Credits: ESA and the Planck Collaboration

On this picture, we see a snapshot of the universe when it was approximately 380 thousand years old. The red and blue spots show the tiny differences in temperature (or in density) of the universe. At this time, the fluctuations in temperature are one part in a hundred thousand!

Therefore, from very small inhomogeneities present in the early universe, were born today’s galaxies and stars and nebula and all the rest. But where were those inhomogeneities coming from? This question can be answered by the paradigm of inflation, which describes a phase of exponentially accelerated expansion of our spacetime at the beginning of the Universe. While we don’t have strong observational evidence for inflation yet, it solves many of the problems of the Λ-CDM model of cosmology, and therefore many physicists are working on inflation.

Inflation didn’t last long, but was quite considerable; in about 10-32 seconds, the universe expanded by a factor of more than 1026! During that time, the small quantum fluctuations in density of the pre-inflationnary universe were brought to large, classical scales. And that’s how the primordial inhomogeneities were born!

So, we have a mechanism explaining the existence of the small inhomogeneities of the early universe. But there exists a large variety of ways to implement that mechanism. How do we set apart all the models that cosmologists came up with? By studying the statistics of the inhomogeneities.

In particular, we can look at correlation functions. These functions describe the correlation between two – or more – points in the sky that are separated by a specific angle. And what we see is that the statistics of the fluctuations is very well described by a Gaussian distribution. But small deviations from this Gaussian statistics, that we call non-Gaussianities, could tell us a lot about the history of the universe, and it would help tremendously in discriminating the different inflationary models. Therefore, cosmologists are really excited to observe non-Gaussianities in the near future!

Loop quantum cosmology and the early universe

Over the history of mankind, the understanding of our Universe has evolved and matured, thanks to remarkable advancements both on theoretical and experimental fronts in the fields of quantum mechanics and general relativity (GR).

Quantum mechanics describes the physics at small scales such as the scale of sub-atomic particles, while gravity is weak and remains practically inert. On the other hand, the large scale structure of the universe is dictated by gravity, which is governed by GR, while quantum mechanics plays no role. Both theories have proved to be robust in their own territory under various theoretical and experimental tests. Unfortunately, it turns out that, as they are, GR and quantum mechanics do not play well with each other when brought under the same umbrella. This leaves us clueless about the situations when the size of the system is small enough for quantum physics to be important and at the same time gravity is so strong that it cannot be neglected anymore.

The very early stage of our own Universe is an example of such a situation, where neither GR nor quantum mechanics can alone be trusted. Although the large scale structure of the universe is very well explained by Einstein’s theory of general relativity (GR), it fails to provide a consistent picture of the early stages of the universe, due to the presence of cosmological singularities such as the big bang. Evolving Einstein’s equations backwards in time from the conditions observed in a large macroscopic universe today, we see that the universe keeps contracting and the space-time curvature keeps increasing, until the universe reaches an extremely high curvature regime where the classical GR description is not reliable. In fact, if one naively continues evolving Einstein’s equations in this regime, one encounters the big bang singularity.

To gain a reliable understanding of the physics in such cases one needs an amalgamation of ideas from both GR and quantum mechanics: a quantum theory of gravity.

lqg_foam
Visualization of quantum structure of space-time in LQG. (Credits: Albert Einstein Institute)

Loop quantum gravity (LQG) is one of the leading approaches to quantum gravity, which gives a consistent picture of the discrete quantum structure of space-time geometry (as opposed to the continuum description given by GR). The quantum space-time geometry provided by LQG opens up new avenues to explore the physics of the early universe and cosmological singularities under the paradigm of loop quantum cosmology (LQC). One of the key features of the discrete quantum geometry of LQG is that when the space-time curvature is sub-Planckian, equations of LQC are extremely well approximated by those of classical GR. The difference becomes important when the space-time curvature becomes significant for quantum discreteness to kick in. This leads to the resolution of the big-bang singularity via a quantum bounce, which serves as a smooth quantum geometric bridge between the current expanding branch of our universe and a contracting phase that should have existed in the far past (Fig.2).

inflation
Schematic impression of early universe in LQC. (Credit: APS/Alan Stonebraker)

In the paradigm of LQC, the history of the Universe is different from that in the standard GR. As shown in Fig.2, there exists a quantum geometric pre-inflationary phase. The origin of quantum perturbations which result in the formation of cosmic microwave background (CMB), and that of the large scale structure observed today, can now be traced all the way back to the quantum gravity regime. Due to a modified pre-inflationary dynamics of LQC, these quantum fluctuations experience a different background evolution than in the standard paradigm, which can in principle have observational imprints on the temperature and the polarization power spectrum observed in the CMB. Understanding the evolution of the quantum fluctuations and extracting out loop quantum geometric imprints in the recent observational data are among the main directions of research pursued by the scientists at IGC.

In forthcoming articles, I will describe different aspects of LQC and its connection with observations, in particular, with the CMB anomalies observed by the recent Planck and WMAP missions.