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# Category: Center for Fundamental Theory

## Cosmic Static: The Stochastic Gravitational Wave Background

## The shape of our Universe

## Loop quantum cosmology and the early universe

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!

*—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).

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?

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.

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*.

**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 **(

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.