# String theory used to describe the expanding universe

We know that the universe is expanding, and our understanding of nature based on general relativity and the standard model of elementary particles is consistent with this observation. However, these theories of particles and their interactions break down when we try to apply them to the physical phenomena that occurred in the first moments after the Big Bang, which prevents us from reaching a complete understanding of the evolution of the universe.

Our theories fail because the temperature and density of matter right after the Big Bang was so high that a concept called quantum gravity is needed to describe the physical processes that have taken place. The problem is that this theory requires a unification of general relativity and quantum mechanics. Although not yet fully understood, there are viable candidates for a theory of quantum gravity, such as string theory.

To solve the problem of unknown quantum gravitational effects in the early universe, a team of theoretical physicists from Japan applied a technique inspired by string theory known as holographic duality. This allowed them to perform calculations using methods familiar from elementary particle physics rather than the incredibly complex calculation usually required in quantum gravity applications.

**String Theory Quantum Gravity**

The most difficult problem one encounters in finding a correct theory of quantum gravity is the lack of experimental data. The fundamental interactions are generally studied with elementary particle accelerators, which smash together beams of particles moving at speeds close to the speed of light. From the velocities of the particles born in these collisions and the angles at which they depart, scientists can extract valuable information about their fundamental interactions.

The key problem here is that the gravitational effects in most elementary particle interactions are negligible (but not under the extreme conditions of the early universe!), and they cannot be measured using accelerators. modern. For example, the gravitational attraction between two electrons is more than 42 orders of magnitude weaker than the electromagnetic repulsion between them. For this reason, studies of quantum gravity have so far only been theoretical.

For decades, the most promising approach to quantum gravity has been string theory, the main postulate of which is that elementary particles are not pointlike, but are tiny oscillating strings. The unique vibrational modes of these strings give rise to a different elementary particle, such as electrons, quarks, and yet-to-be-observed gravitons, which should mediate gravitational interactions in the same way photons mediate electromagnetic interactions.

Unfortunately, our current understanding of string theory is incomplete and does not allow us to quantitatively study many quantum gravitational effects.

**Taming string theory with holographic duality**

Although string theory has not yet reached its full potential, research in this area has led to the development of many theoretical tools that can be used outside of it. The most radical and powerful, although not fully proven, is known as duality or holographic correspondence.

The holographic hypothesis claims that events inside a region of space that involve quantum gravity and are described by string theory can also be described by a gravityless quantum theory defined on the surface of that region. . The last the theory is easy enough to deal with, and we have learned a great deal about such theories by studying electromagnetic, weak and strong interactions.

The existence of this duality means that for every measurable quantity in quantum gravity theory, there must be an analogue in the gravityless alternative. The validity of holographic duality has been verified by hundreds of research papers through direct calculations of various quantities on both sides of duality.

Since 1997, when the first version of the holographic correspondence was offers by Juan Maldacena, many other pairs of theories related by this equivalence have been discovered and analyzed, but the rule that a higher-dimensional space includes gravity and a lower-dimensional space does not always remain satisfied.

Some of these quantum gravity theories are known to be related to string theory, while the others’ connection to strings has yet to be discovered but is generally believed to exist.

**Studying the expanding universe with holography**

An unfortunate feature of the holographic approach in the study of quantum gravity in the real world is that in most known examples of duality, the higher dimensional theory mathematically describes quantum gravity in what is called the anti-de Sitter space, which does not resemble our expanding universe, and whose geometry corresponds to what mathematicians call “de Sitter space”.

The remarkable achievement of the new study is that the authors were able to find a non-gravitational theory equivalent to quantum gravity in a universe quite similar to our own. The most important difference is that it has only three dimensions – two spatial directions and one temporal dimension – unlike our own universe, which is four-dimensional (three spatial dimensions and one temporal dimension).

“Gravity in three dimensions is much simpler than in four,” said Tadashi Takayanagi, a professor at the Yukawa Institute for Theoretical Physics and one of the study’s authors. “However, we believe that the basic mechanism of how holography works in de Sitter space should not be dimension-dependent.”

The new theory is proposed as an equivalent of quantum gravity in a lower-dimensional expanding universe defined in a spatial dimension and a time dimension, known as the Wess-Zumino-Witten model.

Although the three-dimensional universe they discuss doesn’t look exactly like our own, the authors believe their work is an important step toward understanding quantum gravity in the real world.

“Since we don’t know the basic mechanics of how holography works in de Sitter spaces at all, it’s useful to start by constructing the simplest example, as we have done in this work,” said said Takayanagi. “At the same time, it helps us to check whether or not holographic duality exists for de Sitter spaces. Moreover, in our simple mode, we can take into account quantum corrections [to general relativity].”

As usual in this branch of theoretical physics, scientists did not prove duality because to do so they would have to calculate all possible physical quantities on both sides of the correspondence and compare the results. Instead, they calculated a few and found an exact match from which they concluded their guess was correct.

Most of the authors’ calculations ignored quantum effects on the gravitational side of duality and taking them into account will be the course of future work. If the scientists succeed, they plan to generalize their results and apply them to our four-dimensional universe.

“If we can understand this question from our three-dimensional example, we hope

one can generalize the results to higher dimensions and ultimately dispute

problem of explaining the emergence of our four-dimensional universe,” Takayanagi concluded.

*Reference: Yasuaki Hikida, et al., CFT duals of Sitter’s three-dimensional gravity, Journal of High Energy Physics, (2022). DO I:* *10.1007/JHEP05(2022)129*

*Image credit: Johnson Martin*