A new perspective on the origin of the universe! The universe unfolds: time disappears in the Big Bang?

Understanding the origin of the universe has always been the ultimate question for mankind. Although the inflation theory of the very early universe has achieved great success, people can only test the two-point correlation function predicted by it in experiments, and their theoretical understanding remains at an early stage. In response to this, physicists proposed the so-called "cosmic self-expansion" from a new perspective of "theoretical self-consistency".

Amazingly, in this theory of the origin of the universe, time does not exist.

Written by Wang Donggang (Stephen Hawking Centre for Theoretical Cosmology, Department of Applied Mathematics and Theoretical Physics, University of Cambridge)

For those of us who believe in physics, the distinction between past, present, and future is nothing more than a stubborn illusion.

— Albert Einstein, 1955

In a sense, cosmology is the ultimate archaeology.

Archaeologists have unearthed fossils and traces left by our ancestors in ancient times to restore human activities tens of thousands of years ago, and then infer the origin and evolution of civilization. The "fossils" that cosmologists are looking for are in the sky. Due to the limited speed of light, when we use telescopes to capture the faint light from distant galaxies tens of billions of light years away, we are also peeking at what the universe looked like tens of billions of years ago. Based on these astronomical observations, cosmologists can reconstruct the 13.8 billion years of evolution of the universe itself:

Everything is the ashes of the Big Bang. The first hydrogen elements were formed in the high-temperature plasma soup, then electrons were captured by atomic nuclei, and photons began to shuttle freely. As space continued to expand, the universe slowly cooled, and stars and galaxies continued to be born and die over the long billions of years.

Therefore, both "down-to-earth" archaeology and "looking up at the stars" cosmology are sciences about time.

As we continue to trace back, before the formation of the Earth, the solar system, and even the Milky Way, before the birth of the first ray of light in the universe, and even before the appearance of the extremely hot plasma fireball of the Big Bang universe, until the beginning of everything, the curiosity of physicists hopes to touch the starting point of time. In recent years, a series of cutting-edge studies called "cosmological bootstrap" Note 1 have shown that the origin of our universe may be a history without time.

From quantum fluctuations to galaxies

As for the beginning of everything, we still have to start from the "beginning". At present, our most successful description of the very early universe is the so-called cosmic inflation theory. According to this theory, the universe experienced an extremely violent exponentially accelerated expansion in a very short period of about 10-32 seconds at the beginning of the Big Bang, which can be roughly regarded as the de Sitter spacetime in general relativity. This theory was proposed by cosmologists such as Alan Guth and Andrei Linde in the early 1980s, and it solved many initial condition problems in the traditional Big Bang universe in one fell swoop and attracted widespread attention. However, the achievements of the inflation theory go far beyond this.

In the summer of 1982, soon after inflation was proposed, Stephen Hawking convened the three-week Nuffield Symposium on the Very Early Universe in Cambridge. The focus of this legendary meeting was on quantum effects in inflationary cosmology. Five groups of cosmologists independently performed theoretical calculations , and they finally reached a consensus: when quantum mechanics is taken into account, inflation theory provides a surprising but convincing explanation for the origin of everything in the universe.

Before introducing the conclusion, we first note that one of the most notable characteristics of the infant universe is that it is "small". At the beginning of inflation, the diameter of today's observable universe was even less than 10-30 meters, which is much smaller than all currently known elementary particles. Therefore, in addition to the general theory of relativity that describes the expansion of the universe, the quantum field theory that governs the microscopic world also plays a pivotal role in inflation. In quantum physics, vacuum is a subtle concept. It is not empty as we usually imagine, but is filled with ever-changing quantum fluctuations at all times and places, like ripples on the water, fluctuating. Usually these fluctuations are constantly generated on a microscopic scale and then quickly annihilated, and do not directly affect the macroscopic world we are familiar with.

In the inflation theory, the space-time background is expanding at a rapidly accelerating rate. These quantum fluctuations, which should have died out on their own in the microscopic world, are instantly stretched to the macroscopic level, becoming the initial uneven distribution of matter in the infant universe - there is more cosmic matter at the peak of the fluctuations, while the universe at the trough is relatively empty. At first, the amplitude of these fluctuations was also very small. In the subsequent long history of expansion, gravity began to slowly but continuously direct a "Matthew effect" on a cosmic scale - more and more matter gathered in dense areas, while less dense areas became more and more empty. After billions of years of evolution, these dense areas gradually formed various celestial bodies that are currently distributed throughout the universe, as well as large-scale structures spanning tens of billions of light years.

Figure 1. The universe is like an ultimate amplifier, which takes billions of years to transform quantum fluctuations in the microscopic world into galaxies and galaxy clusters on a macroscopic scale. The large-scale distribution of matter today hides the secrets of the universe's infancy, and the key to deciphering this secret is the "cosmological correlation function."

This is the shocking conclusion of the Nuffield conference - everything from superclusters and galaxies to the solar system and the Earth, and even ourselves, originates from microscopic quantum fluctuations in the vacuum during the inflation period. "Putting Mount Sumeru in a mustard seed" is a Buddhist saying that was originally full of speculative meanings and is most intuitively reflected here. This theory, later called the "cosmological perturbation theory", successfully used the quantum physics of the microscopic world to explain the distribution of matter on a cosmic scale, and was later considered by many physicists to be one of the most elegant and wonderful stories in the history of science.

The success of inflation and cosmological perturbation theory has greatly inspired the study of very early cosmology in the past four decades. In this theoretical picture, the "fossils" formed by quantum fluctuations during inflation are also called primordial perturbations, which are the seeds for the formation of the large-scale structure of matter in the universe today. The statistical correlation of the spatial distribution of these "fossils", the so-called "cosmological correlation function", is the core prediction of inflation. Therefore, by looking for correlations in the large-scale distribution of matter in the universe, we can test the theory by astronomical observations. Later, with the detailed measurements of temperature fluctuations in the cosmic microwave background radiation since the 1990s, the simplest prediction of inflation and cosmological perturbation theory - the two-point correlation function, has been tested very accurately.

This is just the beginning. In comparison, higher-order cosmological correlation functions contain much richer information about the very early universe, such as the triangle (three-point correlation) and quadrilateral (four-point correlation) in Figure 1. In principle, by fully understanding the statistical information of the large-scale distribution of matter in the universe, we can restore the inflation process and explore the mysteries of the beginning of creation.

The Universe Unfolds: Where Is Time?

Deciphering the origin of the universe from ancient correlation functions is a great ideal, but the reality is very bleak. First of all, we have not yet detected statistical correlations beyond the two-point function. Although there are more and more targeted sky surveys, how to dig out this information from the ancient universe from the massive amount of observational data is like panning for gold in the desert, which is still full of challenges.

At the same time, our theoretical understanding of cosmological correlation functions is still in its infancy.

Specifically, the difficulty of the problem here is the quantum field theory under de Sitter spacetime. Unlike the flat spacetime background we are familiar with, the quantum effects under the background of accelerated expansion are much more complicated. In order to obtain the cosmological correlation function predicted by inflation, we need to track the complete time evolution of quantum fluctuations during inflation, traverse all possible histories and sum them up. Even for the simplest physical process (as shown in Figure 2), its theoretical calculation is still daunting.

Figure 2. Feynman diagram in de Sitter spacetime. Quantum fluctuations during inflation formed tiny inhomogeneities, which became the seeds for the formation of galaxies and other structures in the subsequent billions of years of evolution. The superposition of countless such events formed statistical correlations in the spatial distribution of the primordial disturbances. In this process, new physics during inflation, such as heavy particles (purple solid line in the figure), left traces in the cosmological correlation function like fossils.

In recent years, theorists have begun to look at this thorny problem from a different perspective: the time evolution during inflation is too complicated, and all we can detect are the "fossil" remains at the end of inflation, so can we directly work on the final observable quantity - the cosmological correlation function? At first glance, it seems unlikely, but "theoretical self-consistency" provides another possible starting point: we can construct a variety of inflation histories, but only some of them are self-consistent in theory, and the other part violates certain basic principles of physics, such as space-time symmetry (physical laws remain unchanged at different space-time positions), unitary (information conservation) and locality (no long-range interaction). This tentative idea was unexpectedly successful: in many cases, the predictions of inflation theory can be completely constrained by these basic principles!

That is to say, no matter how the evolutionary history of the universe is, "theoretical self-consistency" itself may be sufficient to determine the results of the correlation function. This new perspective is called "cosmological bootstrap".

In theoretical physics, this type of method, collectively referred to as Bootstrap (usually translated as "self-bootstrapping", see Note 1), has successful precedents, such as S-matrix bootstrap in the study of elementary particle scattering amplitudes and conformal bootstrap in conformal field theory. The bootstrap method in cosmology was first proposed by Nima Arkani-Hamed, Daniel Baumann, Hayden Lee and Guilherme Pimentel in 2018 [1] . Subsequently, many colleagues including the author systematically studied the constraints of various basic principles on cosmological correlation functions. This emerging research direction has flourished in the past few years [2].

The most amazing thing about this new theoretical description is that time disappears! Because we focus on the cosmological correlation function, we have selected a specific time slice at the end of inflation, and there is indeed only space on this slice, without time. However, this theory without time successfully describes the prediction of inflation! For cosmology, a science about time, "time" itself is invisible in the theory of the origin of the universe, which sounds like an absurd result. Is it really as Einstein said more than half a century ago, that time does not exist and everything is our illusion?

The concept of "timeless history" in the self-development of the universe is actually very old. Its essence is closely related to the holographic principle in quantum gravity research. In recent years, various signs have shown that "time" and "space" themselves may not be basic, but rather "emerge" as derived concepts from some more basic physical reality.

We have already had a certain understanding of the "emergence of space" in holographic theory. As early as 1997, theoretical physicist Juan Maldacena proposed the famous "AdS/CFT correspondence". AdS stands for anti-de Sitter spacetime, which is a type of spacetime background that is completely different from our real universe (see Figure 3, left). In this theoretical conception, Maldacena pointed out that the gravity inside the AdS space is equivalent to the conformal field theory (CFT) on the boundary in a complex but subtle way. In other words, the low-dimensional boundary of the AdS spacetime is like a holographic screen, containing the physics of the higher-dimensional internal space. The emergence of the "AdS/CFT correspondence" provides a concrete example for the study of quantum gravity and the nature of spacetime. After more than 20 years of in-depth exploration, theoretical physicists have gradually figured out that the quantum entanglement in the boundary theory constructs the spatial distance inside the AdS, so space itself may not be fundamental, but emerges from the entanglement.

Figure 3. The emergence of space in anti-de Sitter spacetime (left); the emergence of time in de Sitter spacetime (right).

So what about "time"? In the description of the holographic principle, "time" has completely different properties from "space". As early as the beginning of the proposal of AdS/CFT, theoretical physicists have tried to extend the holographic principle to the de Sitter spacetime, which is closer to the real universe we live in, the so-called "de Sitter Holography". To this day, this idea has not been successfully realized. One difficulty is that in the de Sitter spacetime, the original low-dimensional boundary (holographic screen) becomes a specific time slice in the future (such as the moment when inflation ends), and the dimension extended in the internal spacetime changes from space to time (see Figure 3), but we don't know how to understand the emergence of the time dimension.

The emergence of cosmic bootstrapping undoubtedly provides new ideas for the "emergence of time" and "de Sitter holography". We can review the connection between cosmic bootstrapping and traditional time evolution methods in dealing with cosmological correlation functions. At this time, people found that the historical process during inflation was described by the spatial correlation of the primordial perturbations on the future boundary. Specifically, when we change the form of the cosmological correlation function on the future boundary, we are actually exploring the flow of time in the past in de Sitter spacetime (see Figure 3, right); different cosmic evolution histories give different statistical correlations on the future boundary. Recently, Nima Arkani-Hamed et al. further pointed out that the passage of time itself is equivalent to the mathematical structure called "kinematic flow" in the correlation function [3, 4].

These intriguing new developments make possible results that previously seemed outlandish - describing the origin and evolution of the universe in a theory without time. Perhaps, at the most fundamental level, the past 13.8 billion years have been history without time!

The dawn of new physics

In the development of theoretical physics, conceptual innovation is always exciting, but we also need to be aware that the research direction of cosmic self-expansion is still in its infancy. We have not yet established a holographic theory of cosmology, and we do not know why time is fundamentally different from space; if time is emergent, then what is the real physical reality behind it? There is still a long way to go to gain a clear understanding of these deep-seated questions.

At the same time, this interesting new idea of ​​cosmic self-expansion is not just a new story of inflation theory at the conceptual level, its research also has important "practical" value for high-energy particle physics.

When it comes to particle physics, the first thing that comes to mind may be colliders, such as the Large Hadron Collider (LHC) at CERN. Even in many hardcore science fiction novels, giant colliders have become a "necessity" on the road to evolving into advanced civilizations. For example, in "The Three-Body Problem", the first goal of the "sophists" after arriving on Earth is to disrupt high-energy particle collision experiments; and hundreds of years later, humans have built a "heliocentric accelerator" in the orbit of Jupiter to develop their own basic science. The development of civilization is indeed inseparable from a deep understanding of the microscopic structure of matter, but in the real world, it is becoming increasingly difficult to build large colliders, which has become a major challenge for the development of particle physics.

Interestingly, cosmology may provide a new opportunity for high-energy physics experiments. As mentioned above, when inflation occurred, the universe was at an extremely microscopic scale. The energy scale at that time could be as high as 10^13 GeV, far exceeding the energy scale of any large particle collider on the ground. Therefore, inflation itself can be regarded as a natural high-energy physics laboratory. With the help of increasingly precise cosmological observations, we can extract the "fossil" signals left over from ancient times and explore the new physics of that time.

The most intuitive presentation of this idea is a type of primordial signal called a "cosmological collider" [5, 6] Note 3. In this theoretical conception, the existence of high-energy particles during inflation (such as the purple line in Figure 2) affects the "shape" of the primordial disturbance, leaving a characteristic imprint in its three-point connection that has been preserved to this day. The idea is similar to an accelerator on the ground, except that the particle collision occurs in the infancy of the universe, and the detected signal becomes an ancient photon originating from the depths of the universe.

Figure 4. Schematic diagram of the concept of a cosmological collider. The particle "collisions" in the early inflation left special "shapes" in the distribution of matter on a cosmic scale; and in astronomical observations (such as the Planck satellite microwave background radiation data in the figure), people can look for these ancient traces and then explore the mass and spin of those extremely high-energy particles and other physical information.

In the study of cosmological colliders, the theoretical breakthroughs brought about by the bootstrap method have played an important guiding role. Because it involves heavy particles during inflation, traditional time evolution calculations are very complicated and usually only produce approximate results. The bootstrap method itself is a powerful analytical calculation tool that allows us to solve the strict analytical predictions of cosmological collider signals for the first time. In recent years, the author and his collaborators have used the bootstrap method to examine the various possibilities of cosmological colliders [8, 9] and derived a complete set of analytical results. Because it no longer relies on specific models, the bootstrap method also provides a systematic classification of the characteristic signals in these cosmological correlation functions, greatly enriching the predictions of inflation theory.

Some people may say that the theory is interesting, but is it really possible to detect a cosmological collider? Looking for extremely weak signals from billions of years ago in actual astronomical observations sounds like a fantasy.

Never underestimate the speed of scientific development, especially since cosmology itself is in the golden age of great discoveries! With the help of the complete theoretical predictions given by the bootstrap method, we can already look for signals of cosmological colliders in existing astronomical observation experiments. Recently, Matias Zaldarriaga, a cosmologist at Princeton, and his collaborators have used the BOSS galaxy survey data to conduct observational tests on such predictions [10] . At the same time, I collaborated with my observational cosmology colleagues at the University of Cambridge to use the microwave background radiation data of the Planck satellite for the first time [11]. After systematic scanning and screening, we found a suspected signal with a confidence level of about 2 sigma in the Planck data. Is this a real high-energy particle signal or a statistical fluctuation in the observational data? Only further testing in the future can determine it. But as a preliminary analysis, it has to be said that this result has exceeded expectations.

This encouraging progress is of course due to the rapid development of new technologies in cosmological experiments and data analysis. In the next decade, new microwave background radiation experiments will begin high-precision observations, such as the Ali CMB observation project in Tibet, China, and the Simons Observatory and CMB-S4 internationally. At the same time, multiple large-scale structure observation experiments in the universe (such as SphereX, Euclid, LSST, etc.) are about to start. The massive data brought by these projects will undoubtedly significantly improve the accuracy of observations, making it possible to truly discover heavy particle signals in cosmological colliders.

In the slightly more distant future, astronomers hope to detect neutral hydrogen radio signals from the early universe before the formation of galaxies. Such signals are very weak, but widespread in the universe, and are called 21 cm lines because of their characteristic wavelength of about 21 cm. They can help us draw a detailed map of the distribution of matter in the dark time of the universe, and then achieve precise measurements of cosmological correlation functions, which is an excellent window to peek into the predictions of inflation theory. Therefore, future observations of the 21 cm line can greatly promote the development of cosmology. Through this, we may not only be able to detect new high-energy physics in the infant universe, but may even eventually uncover the mystery of the origin of time.

At this point, our chat should come to an end. Finally, let us expand our thinking and imagine the basic physics research in a hundred years: by then, humans will have a deeper understanding of the microscopic structure of matter and the nature of space and time, but new experimental equipment will be needed to test high-energy theories. By then, should our descendants build a giant collider on the scale of the solar system as described in science fiction?

Perhaps the 21cm line array on the far side of the moon is a more worthy option : )

Notes

1. Regarding the translation of the word Bootstrap, its original meaning is the shoelaces at the back of the boots. It is widely known because of the English idiom "Pull yourself up by the bootstrap" (pull yourself up by the bootstrap without relying on external help). At first, this sentence was intended to satirize ridiculous and impossible things, but later its meaning became inexplicably inspiring: no matter how difficult it is, you can succeed by relying on yourself. In theoretical physics, Bootstrap is generally translated as "self-lifting", which means that the laws of physics can be completely determined by the most basic principles and theoretical self-consistency without additional help. Similarly, Cosmological Bootstrap can be translated as "cosmological bootstrap" or "cosmic self-emerging". Because it is closely related to "the Emergence of Time" in concept, this article adopts the latter translation, which means "unfolding" or "presenting".

2. The five groups of physicists are: Viatcheslav Mukhanov and Gennady Chibisov; Stephen Hawking; Alexey Starobinksy; Alan Guth and So-Young Pi; James Badeen, Paul Steinhardt and Michael Turner. Mukhanov and Chibisov did not attend the Cambridge Nuffied seminar.

3. The concept of cosmological collider was proposed by Nima Akani-Hamed and Juan Maldacena in 2015[5] . It is worth noting that Professor Xingang Chen of Harvard University and Professor Yi Wang of Hong Kong University of Science and Technology made very important foundational contributions to the development of this concept in their 2009 article[6]. Professor Xian Yuzhongzhi of Tsinghua University also conducted systematic and in-depth exploration of this emerging direction [7].

References

[1] N. Arkani-Hamed, D. Baumann, H. Lee, and GL Pimentel, “The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities,” JHEP 04 (2020) 105.

[2] D. Baumann, D. Green, A. Joyce, E. Pajer, GL Pimentel, C. Sleight, and M. Taronna, “Snowmass White Paper: The Cosmological Bootstrap,” in 2022 Snowmass Summer Study. 3, 2022.

[3] N. Arkani-Hamed, D. Baumann, A. Hillman, A. Joyce, H. Lee, and GL Pimentel, “Kinematic Flow and the Emergence of Time,” arXiv:2312.05300 [hep-th].

[4] N. Arkani-Hamed, D. Baumann, A. Hillman, A. Joyce, H. Lee, and GL Pimentel, “Differential Equations for Cosmological Correlators,” arXiv:2312.05303 [hep-th].
[5] N. Arkani-Hamed and J. Maldacena, “Cosmological Collider Physics,” arXiv:1503.08043 [hep-th].
[6] X. Chen and Y. Wang, “Quasi-Single Field Inflation and Non-Gaussianities,” JCAP 04 (2010) 027.

[7] X. Chen, Y. Wang, and Z.-Z. Xianyu, “Standard Model Background of the Cosmological Collider,” Phys. Rev. Lett. 118 (2017) no. 26, 261302.
[8] GL Pimentel and D.-G. Wang, “Boostless cosmological collider bootstrap,” JHEP 10 (2022) 177.
[9] D.-G. Wang, GL Pimentel, and A. Achucarro, “Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisited,” JCAP 05 (2023) 043.
[10] G. Cabass, OHE Philcox, MM Ivanov, K. Akitsu, S.-F. Chen, M. Simonovic, and
M. Zaldarriaga, “BOSS Constraints on Massive Particles during Inflation: The Cosmological Collider in Action,” arXiv:2404.01894.

[11] W. Sohn, D.-G. Wang, J. Fergusson, EPS Shellard, “Searching for Cosmological Collider in the Planck CMB Data,” arXiv:2404.07203.

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