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cosmic microwave background

The universe’s shape and its oldest light

The 3-torus is a strange and wonderful shape. We can’t readily visualise it because it has a complicated structure, but there’s a way. Imagine you’re standing inside a cube in which light is moving from the left face towards the right face. If the two faces are opaque, the right face will absorb the light, say, and that will be that. But say the two faces are not opaque. Instead, if the light passes through the right face and reemerges from the left face — as if it entered a portal and emerged on the other side — you’ll be standing inside a 3-torus.

If you look in front of you or behind you, you’ll see a series of cubes: they’re all the same cube (the one in which you’re standing) illuminated by the light, which is simply flowing in a closed loop through a single cube. In the early 1980s, physicists proposed that our universe could have the shape of a 3-torus at the largest scale. “There’s a hint in the data that if you traveled far and fast in the direction of the constellation Virgo, you’d return to Earth from the opposite direction,” a 2003 The New York Times article quoted cosmologist Max Tegmark as saying. The idea is funky but it’s possible. Scientists believe our universe’s geometry was determined by quantum processes that happened just after the Big Bang, but they’re not yet sure what that geometry really is. For now, the data are not inconsistent with a 3-torus, according to a paper a team of scientists calling themselves the COMPACT collaboration published in April 2024.

Scientists try to determine the shape of the universe just the way you would have standing inside the 3-torus: using light, and what it’s revealing ahead and behind you. Light passing through a 3-torus would be in a closed loop, which means the visual information it encodes should be repeated: that is, you would’ve seen the same cube repeated ad infinitum, sort of (but not exactly) like when you stand between two mirrors and see endless repetition of the space you’re in on either side. Scientists check for similar patterns that are repeated through the universe. They haven’t found such patterns so far — but there’s a catch. The distance light has travelled matters.

Say the cube you’re standing in is 1 km wide. The light will cross this distance in one-trillionth of a second. If it is 777 billion km wide, the light will take a month. And it will take a full year if the cube is 9.5 trillion km wide. We’re talking about whether the universe could be a 3-torus, and the universe was created 13.8 billion years ago. In this time, light can travel a distance of more than 100 sextillion km. If the width of the cube is less than this distance, we might have seen repeating patterns if the universe is shaped like a 3-torus. But if the cube is even wider, the light wouldn’t have finished crossing it even once since the universe was born, therefore no repeating patterns — yet the possibility of the universe being 3-torus-shaped remains. We just need to wait for the light to finish crossing it once.

Since we can learn so much about the universe’s geometry by studying light, and light that’s travelled the longest would be most useful, scientists are very interested in light ‘left over’ from the Big Bang. Yes, this light is still hanging around, and it’s measurably different from all the other light. Scientists call it the cosmic microwave background (CMB), a.k.a. ‘relic radiation’. It’s left over from a cosmic event that happened just 370,000 years after the Big Bang. We need to subtract the distance light could have travelled in this time from the 100 sextillion km figure (I’m tired of looking at zeroes; you can give it a shot if you like) to find the maximum distance the CMB could have travelled.

In its April paper, the COMPACT collaboration considered data about the universe that astrophysicists have collected using ground and space telescopes over the years — including about the CMB — and with that have checked whether the possibility still exists that our universe could be shaped like three types of a 3-torus. The first type is the one I’ve considered in this post, and they’ve concluded (as expected) that if the cube is less wide than the distance light could’ve travelled since the universe was born, our universe can’t be shaped like this particular 3-torus. The reason is that the data astrophysicists have put together doesn’t contain signs of repeating patterns.

(Update, 8.20 pm, June 23, 2024: Here’s a good primer of what these patterns will actually look like, courtesy Nirmal Raj.)

However, the COMPACT team adds, our universe could still be shaped like one of the other two types of 3-tori even if their respective cubes are smaller than the max. distance. This is because these two shapes include twists that will produce two subtly different images of the universe once the light has completed one loop. And according to the COMPACT folks, they can’t yet eliminate the presence of these images in the astrophysics data. The collaboration’s members have written in the April 2024 paper that they intend to find new/better ways to ascertain their hypotheses with CMB data.

Until then, look out for… déjà vu?

Jun 22, 2024
Where is the coolest lab in the universe?

The Large Hadron Collider (LHC) performs an impressive feat every time it accelerates billions of protons to nearly the speed of light – and not in terms of the energy alone. For example, you release more energy when you clap your palms together once than the energy imparted to a proton accelerated by the LHC. The impressiveness arises from the fact that the energy of your clap is distributed among billions of atoms while the latter all resides in a single particle. It’s impressive because of the energy density.

A proton like this should have a very high kinetic energy. When lots of protons with such amounts of energy come together to form a macroscopic object, the object will have a high temperature. This is the relationship between subatomic particles and the temperature of the object they make up. The outermost layer of a star is so hot because its constituent particles have a very high kinetic energy. Blue hypergiant stars, thought to be the hottest stars in the universe, like Eta Carinae have a surface temperature of 36,000 K and a surface 57,600-times larger than that of the Sun. This isn’t impressive on the temperature scale alone but also on the energy density scale: Eta Carinae ‘maintains’ a higher temperature over a larger area.

Now, the following headline and variations thereof have been doing the rounds of late, and they piqued me because I’m quite reluctant to believe they’re true:

This headline, as you may have guessed by the fonts, is from Nature News. To be sure, I’m not doubting the veracity of any of the claims. Instead, my dispute is with the “coolest lab” claim and on entirely qualitative grounds.

The feat mentioned in the headline involves physicists using lasers to cool a tightly controlled group of atoms to near-absolute-zero, causing quantum mechanical effects to become visible on the macroscopic scale – the feature that Bose-Einstein condensates are celebrated for. Most, if not all, atomic cooling techniques endeavour in different ways to extract as much of an atom’s kinetic energy as possible. The more energy they remove, the cooler the indicated temperature.

The reason the headline piqued me was that it trumpets a place in the universe called the “universe’s coolest lab”. Be that as it may (though it may not technically be so; the physicist Wolfgang Ketterle has achieved lower temperatures before), lowering the temperature of an object to a remarkable sliver of a kelvin above absolute zero is one thing but lowering the temperature over a very large area or volume must be quite another. For example, an extremely cold object inside a tight container the size of a shoebox (I presume) must be lacking much less energy than a not-so-extremely cold volume across, say, the size of a star.

This is the source of my reluctance to acknowledge that the International Space Station could be the “coolest lab in the universe”.

While we regularly equate heat with temperature without much consequence to our judgment, the latter can be described by a single number pertaining to a single object whereas the former – heat – is energy flowing from a hotter to a colder region of space (or the other way with the help of a heat pump). In essence, the amount of heat is a function of two differing temperatures. In turn it could matter, when looking for the “coolest” place, that we look not just for low temperatures but for lower temperatures within warmer surroundings. This is because it’s harder to maintain a lower temperature in such settings – for the same reason we use thermos flasks to keep liquids hot: if the liquid is exposed to the ambient atmosphere, heat will flow from the liquid to the air until the two achieve a thermal equilibrium.

An object is said to be cold if its temperature is lower than that of its surroundings. Vladivostok in Russia is cold relative to most of the world’s other cities but if Vladivostok was the sole human settlement and beyond which no one has ever ventured, the human idea of cold will have to be recalibrated from, say, 10º C to -20º C. The temperature required to achieve a Bose-Einstein condensate is the temperature required at which non-quantum-mechanical effects are so stilled that they stop interfering with the much weaker quantum-mechanical effects, given by a formula but typically lower than 1 K.

The deep nothingness of space itself has a temperature of 2.7 K (-270.45º C); when all the stars in the universe die and there are no more sources of energy, all hot objects – like neutron stars, colliding gas clouds or molten rain over an exoplanet – will eventually have to cool to 2.7 K to achieve equilibrium (notwithstanding other eschatological events).

This brings us, figuratively, to the Boomerang Nebula – in my opinion the real coolest lab in the universe because it maintains a very low temperature across a very large volume, i.e. its coolness density is significantly higher. This is a protoplanetary nebula, which is a phase in the lives of stars within a certain mass range. In this phase, the star sheds some of its mass that expands outwards in the form of a gas cloud, lit by the star’s light. The gas in the Boomerang Nebula, from a dying red giant star changing to a white dwarf at the centre, is expanding outward at a little over 160 km/s (576,000 km/hr), and has been for the last 1,500 years or so. This rapid expansion leaves the nebula with a temperature of 1 K. Astronomers discovered this cold mass in late 1995.

(“When gas expands, the decrease in pressure causes the molecules to slow down. This makes the gas cold”: source.)

The experiment to create a Bose-Einstein condensate in space – or for that matter anywhere on Earth – transpired in a well-insulated container that, apart from the atoms to be cooled, was a vacuum. So as such, to the atoms, the container was their universe, their Vladivostok. They were not at risk of the container’s coldness inviting heat from its surroundings and destroying the condensate. The Boomerang Nebula doesn’t have this luxury: as a nebula, it’s exposed to the vast emptiness, and 2.7 K, of space at all times. So even though the temperature difference between itself and space is only 1.7 K, the nebula also has to constantly contend with the equilibriating ‘pressure’ imposed by space.

Further, according to Raghavendra Sahai (as quoted by NASA), one of the nebula’s cold spots’ discoverers, it’s “even colder than most other expanding nebulae because it is losing its mass about 100-times faster than other similar dying stars and 100-billion-times faster than Earth’s Sun.” This implies there is a great mass of gas, and so atoms, whose temperature is around 1 K.

All together, the fact that the nebula has maintained a temperature of 1 K for around 1,500 years (plus a 5,000-year offset, to compensate for the distance to the nebula) and over 3.14 trillion km makes it a far cooler “coolest” place, lab, whatever.

Jun 18, 2020
Our universe, the poor man’s accelerator

The Hindu
March 25, 2014

On March 17, radio astronomers from the Harvard-Smithsonian Center for Astrophysics, Massachusetts, announced a remarkable discovery. They found evidence of primordial gravitational waves imprinted on the cosmic microwave background (CMB), a field of energy pervading the universe.

A confirmation that these waves exist is the validation of a theory called cosmic inflation. It describes the universe’s behaviour less than one-billionth of a second after it was born in the Big Bang, about 14 billion years ago, when it witnessed a brief but tremendous growth spurt. The residual energy of the Bang is the CMB, and the effect of gravitational waves on it is like the sonorous clang of a bell (the CMB) that was struck powerfully by an effect of cosmic inflation. Thanks to the announcement, now we know the bell was struck.

Detecting these waves is difficult. In fact, astrophysicists used to think this day was many more years into the future. If it has come now, we must be thankful to human ingenuity. There is more work to be done, of course, because the results hold only for a small patch of the sky surveyed, and there is also data due from studies done until 2012 on the CMB. Should any disagreement with the recent findings arise, scientists will have to rework their theories.

Remarkable in other ways

The astronomers from the Harvard-Smithsonian used a telescope called BICEP2, situated at the South Pole, to make their observations of the CMB. In turn, BICEP2’s readings of the CMB imply that when cosmic inflation occurred about 14 billion years ago, it happened at a tremendous amount of energy of 10¹⁶ GeV (GeV is a unit of energy used in particle physics). Astrophysicists didn’t think it would be so high.

Even the Large Hadron Collider (LHC), the world’s most powerful particle accelerator, manages a puny 10⁴ GeV. The words of the physicist Yakov Zel’dovich, “The universe is the poor man’s accelerator”— written in the 1970s — prove timeless.

This energy at which inflation has occurred has drawn the attention of physicists studying various issues because here, finally, is a window that allows humankind to naturally study high-energy physics by observing the cosmos. Such a view holds many possibilities, too, from the trivial to the grand.

For example, consider the four naturally occurring fundamental forces: gravitation, strong and weak-nuclear force, and electromagnetic force. Normally, the strong-nuclear, weak-nuclear and electromagnetic forces act at very different energies and distances.

However, as we traverse higher and higher energies, these forces start to behave differently, as they might have in the early universe. This gives physicists probing the fundamental texture of nature an opportunity to explore the forces’ behaviours by studying astronomical data — such as from BICEP2 — instead of relying solely on particle accelerators like the LHC.

In fact, at energies around 10¹⁹ GeV, some physicists think gravity might become unified with the non-gravitational forces. However, this isn’t a well-defined goal of science, and doesn’t command as much consensus as it submits to rich veins of speculation. Theories like quantum gravity operate at this level, finding support from frameworks like string theory and loop quantum gravity.

Another perspective on cosmic inflation opens another window. Even though we now know that gravitational waves were sent rippling through the universe by cosmic inflation, we don’t know what caused them. An answer to this question has to come from high-energy physics — a journey that has taken diverse paths over the years.

Consider this: cosmic inflation is an effect associated with quantum field theory, which accommodates the three non-gravitational forces. Gravitational waves are an effect of the theories of relativity, which explain gravity. Because we may now have proof that the two effects are related, we know that quantum mechanics and relativity are also capable of being combined at a fundamental level. This means a theory unifying all the four forces could exist, although that doesn’t mean we’re on the right track.

At present, the Standard Model of particle physics, a paradigm of quantum field theory, is proving to be a mostly valid theory of particle physics, explaining interactions between various fundamental particles. The questions it does not have answers for could be answered by even more comprehensive theories that can use the Standard Model as a springboard to reach for solutions.

Physicists refer to such springboarders as “new physics”— a set of laws and principles capable of answering questions for which “old physics” has no answers; a set of ideas that can make seamless our understanding of nature at different energies.

Supersymmetry

One leading candidate of new physics is a theory called supersymmetry. It is an extension of the Standard Model, especially at higher energies. Finding symptoms of supersymmetry is one of the goals of the LHC, but in over three years of experimentation it has failed. This isn’t the end of the road, however, because supersymmetry holds much promise to solve certain pressing issues in physics which the Standard Model can’t, such as what dark matter is.

Thus, by finding evidence of cosmic inflation at very high energy, radio-astronomers from the Harvard-Smithsonian Center have twanged at one strand of a complex web connecting multiple theories. The help physicists have received from such astronomers is significant and will only mount as we look deeper into our skies.

Mar 25, 2014
The Big Bang did bang

The Hindu
March 19, 2014

On March 17, the most important day for cosmology in over a decade, the Harvard-Smithsonian Centre for Astrophysics made an announcement that swept even physicists off their feet. Scientists published the first pieces of evidence that a popular but untested theory called cosmic inflation is right. This has significant implications for the field of cosmology.

The results also highlight a deep connection between the force of gravitation and quantum mechanics. This has been the subject of one of the most enduring quests in physics.

Marc Kamionkowski, professor of physics and astronomy at Johns Hopkins University, said the results were a “smoking gun for inflation,” at a news conference. Avi Loeb, a theoretical physicist from Harvard University, added that “the results also tell us when inflation took place and how powerful the process was.” Neither was involved in the project.

Rapid expansion

Cosmic inflation was first hypothesized by American physicist Alan Guth. He was trying to answer the question why distant parts of the universe were similar even though they couldn’t have shared a common history. In 1980, he proposed a radical solution. He theorized that 10-36 seconds after the Big Bang happened, all matter and radiation was uniformly packed into a volume the size of a proton.

In the next few instants, its volume increased by 1078 times – a period called the inflationary epoch. After this event, the universe was almost as big as a grapefruit, expanding to this day but at a slower pace. While this theory was poised to resolve many cosmological issues, it was difficult to prove. To get this far, scientists from the Centre used the BICEP2 telescope stationed at the South Pole.

BICEP (Background Imaging of Cosmic Extragalactic Polarization) 2 studies some residual energy of the Big Bang called the cosmic microwave background (CMB). This is a field of microwave radiation that permeates the universe. Its temperature is about 3 Kelvin. The CMB consists of electric (E) and magnetic (B) fields, called modes.

Polarized radiation

Before proceeding further, consider this analogy. When sunlight strikes a smooth, non-metallic surface, like a lake, the particles of light start vibrating parallel to the lake’s surface, becoming polarized. This is what we see as glare. Similarly, the E-mode and B-mode of the CMB are also polarized in certain ways.

The E-mode is polarized because of interactions with scattered photons and electrons in the universe. It is the easier to detect than the B-mode, and was studied in great detail until 2012 by the Planck space telescope. The B-mode, on the other hand, can be polarized only under the effect of gravitational waves. These are waves of purely gravitational energy capable of stretching or squeezing the space-time continuum.

The inflationary epoch is thought to have set off gravitational waves rippling through the continuum, in the process polarizing the B-mode.

To find this, a team of scientists led by John Kovac from Harvard University used the BICEP2 telescope from 2010 to 2012. It was equipped with a lens of aperture 26 cm, and devices called bolometers to detect the power of the CMB section being studied.

The telescope’s camera is actually a jumble of electronics. “The circuit board included an antenna to focus and filter polarized light, a micro-machined detector that turns the radiation into heat, and a superconducting thermometer to measure this heat,” explained Jamie Bock, a physics professor at the California Institute of Technology and project co-leader.

It scanned an effective area of two to 10 times the width of the Moon. The signal denoting effects of gravitational waves on the B-mode was confirmed with a statistical significance of over 5σ, sufficient to claim evidence.

Prof. Kovac said in a statement, “Detecting this signal is one of the most important goals in cosmology today.”

Unified theory

Despite many physicists calling the BICEP2 results as the first direct evidence of gravitational waves, theoretical physicist Carlo Rovelli advised caution. “The first direct detection is not here yet,” he tweeted, alluding to the scientists only having found the waves’ signatures.

Scientists are also looking for the value of a parameter called r, which describes the level of impact that gravitational waves could have had on galaxy formation. That value has been found to be particularly high: 0.20 (+0.07 –0.05). This helps explain why galaxies formed so rapidly, how powerful inflation was and why the universe is so large.

Now, astrophysicists from other observatories around the world will try to replicate BICEP2’s results. Also, data from the Planck telescope on the B-mode is due in 2015.

It is notable that gravitational waves are a feature of theories of gravitation, and cosmic inflation is a feature of quantum mechanics. Thus, the BICEP2 results show that the two previously exclusive theories can be combined at a fundamental level. This throws open the door for theoretical physicists and string theorists to explore a unified theory of nature in new light.

Liam McAllister, a physicist from Cornell University, proclaimed, “In terms of impact on fundamental physics, particularly as a tool for testing ideas about quantum gravity, the detection of primordial gravitational waves is completely unprecedented.”

Mar 19, 2014