Since the 19th century^{e} In the century, the development of mathematical physics had shown that although gravity, heat and magnetism or even fluid mechanics were different physical phenomena, they had in common a certain number of mathematical equations which in their term , THE. PhysicistPhysicist Call the partial differential equation of the potential, playplay and waves for the main names so we can draw inspiration from the problem of calculating the gravity field to solve the flow problem.the windthe wind For example around an airplane wing.

Cess AnalogiesAnalogies Others are true for equations, which allows physicists, as Richard Feynman explained in his famous course, to master many elements of different physical theories by reducing them to a few canonical mathematical physics problems. One should not surrender to the growing sea of knowledge. There are still limits and the last universal physicist was, almost, undoubtedly. Enrico FermiEnrico Fermi and Leo Landau, more than 60 years ago.

All of this applies equally well.AstrophysicsAstrophysics Compared to geophysics, researchers face similar questions and phenomena that call for invariant methods, especially for nonlinear phenomena, and account for the sensitivity of certain equations to initial conditions, such as That scientists say again. Jargon

Let’s take a few simple examples. When we consider The wavesThe waves If the water surface is weak or the air flow around the wing of an airplane is slow, we can consider linear wave equations, which means that the sum of two solutions of these linear equations is simply added to the other. There is a solution. Often, for example, summation of simple sine and cosine functions is sufficient.

But when the water surface is agitated during a StormStormThe equations we must use, for example to explain the existence of rogue waves, are no longer linear. Solving them requires the use of new mathematical methods which we therefore call “non-perturbative” or rely on them. Digital simulationDigital simulation With the powerful ComputersComputers.

However, with non-linear equations, so-called chaotic phenomena can appear which exhibit the well-known sensitivity to initial conditions. This phenomenon is often called the butterfly effect.

Weather forecasting continues to improve, but despite considerable advances in science and technology, there is still a limit to predicting the future. This limitation is due to chaos theory, the idea that the flapping of a butterfly’s wings in Brazil can cause a tornado in Texas. Although it may seem a bit exaggerated, chaos theory can have a powerful effect on weather forecasting, but meteorologists have ways to reduce its effects and improve forecasts. To get a fairly accurate French translation, click on the white rectangle at the bottom right. Then the English subtitles should appear. Then click on the nut on the right side of the rectangle, then on “Subtitles” and finally on “Auto Translate”. Select “French”. © The Met Office, the UK’s national weather service

## A chaotic universe, from the Big Bang to meteorology

We found with chaos theory and computer simulations that an error, at a density as small as the perturbation of the butterfly’s flight and vitessevitesse The local wind of the place where the butterfly flies will lead it. MeteorologyMeteorology Fast forward to the future where the presence or absence of that butterfly flight could make the difference between someone’s existence or not. StormStorm On the given date. As we cannot know with such precision that the state ofEnvironmentEnvironment Everywhere on the planet, essentially any climate prediction objective has only a very limited value over time.

It turns out that we have been able to compare our behavior for decadesSpace timeSpace time is described by the nonlinear equation of General relativityGeneral relativity with the behavior of fluids described by the nonlinear Navier-Stokes equations, so that we discuss e.g.foamfoam The quantum of spacetime and that we can bring the equivalent of fluid turbulence to spacetime in chaos theory and cosmology.

gave Standard Cosmological ModelStandard Cosmological Model It also implicitly assumes that it is well-rounded by a theory that has not yet been demonstrated, but is confirmed by observations of famous people. Fossil radiationFossil radiation as well as some properties of the large-scale structure of the distribution The galaxyThe galaxy. It is inflationary theory that assumes very early in history. the cosmosthe cosmos There was an observable, rapid phase of expansion, but the gap was very short and transient.

Join Perimeter Institute Hawking Chair in Cosmology and Science Communication Katie Mack on an incredible journey through the universe in our new series, *Cosmology 101*. In this episode, we learn how the discovery of the Cosmic Microwave Background (CMB) validated the Big Bang theory and led to the development of the concept of cosmic inflation. Explore the ongoing challenges and debates in cosmology as scientists strive to uncover the true nature of the early universe and the origins of cosmic structure. To get a fairly accurate French translation, click on the white rectangle at the bottom right. Then the English subtitles should appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Auto-Translate”. Select “French”. © *Perimeter Institute for Theoretical Physics*

## A zoo of possible inflation theories

Inflation theory comes in several possible versions that have been proposed over time such as two AstronomersAstronomers The Russians Alexei Starobinsky and Andre Linde proposed a chaos theory of inflation that naturally leads to the concept of eternal inflation, which Futura discussed with Max Tegmark. As Andre Linde clearly shows in his open access work, speculation in particle physics Standard modelStandard model Advanced Physics EnergiesEnergies make the existence of a phase of inflation almost inevitableUniverseUniverse Initially this is accompanied by quantum fluctuations/oscillations that leave traces in fossil radiation and its origin. The matterThe matter. Often, we postulate the existence of a new scalar field cousin to the famous Braut-Englert-Higgs boson and call itInflationInflation. However, it is not easy to infer the existence and state of the current observable universe from possible Infield fields. In some cases, inflation is not strong enough and in others, the universe shrinks too quickly. The Big BangThe Big Bang.

Here again the question arises as to whether we should use a perturbative or a non-perturbative approach to possible inflation models, and this is the question that a group of researchers, members of the CNRS at the Paris Institute of Astrophysics The team evaluated using numerical simulations. including the medalists of bronzebronze of CNRS 2024 Sebastien Renaux-Patel)) and Johns Hopkins University (United States), as can be seen in the open access publication. *arXiv*.

Sébastien Renaux-Petel spoke to us about cosmology in 2014 when we were wondering if we had discovered the signature of gravitational waves from inflation, which unfortunately was not the case. © *Ideas in science*

## Predictions from superstring theory?

As explained in a press release by the CNRS, the astronomers discovered that the small quantum fluctuations whose effects we know can be amplified by the inflationary phase of the inflationary theory. must also be enhanced by non-linear phenomena, the importance of which we did not know. Noteworthy first, that emergingemerging with oscillations in the inflaton field model and which can be estimated Superstring theorySuperstring theory.

Just as in the case of the butterfly effect in meteorology, many different evolutions from the initial state of the universe at the beginning of the Big Bang would have been possible and may have occurred in the multiverse. In any case, it opens up new perspectives on possible predictions of universes that could emerge from the effects of chaos in the physics of the inflationary phase, assuming it exists.

The article, now published in Popular. *physical examination letters,* explains the following: ” *We show that small-scale quantum fluctuations, amplified by the oscillating feature, can significantly affect the fate of the entire universe, sometimes preventing inflation from ending. This *“The Butterfly Effect of Inflation”* Demonstrates the need for non-disruptive processing in observational systems. This marks the beginning of a new era in the exploration of the early universe, reminiscent in some ways of the important implications of chaotic phenomena.* »

The CNRS press release added that the researchers “ *have shown that in some theories the entire universe may be stuck in a state of eternal inflation, inhospitable to life. In other cases, quantum fluctuations can trigger formation. Black holesBlack holes fromto fallto fall pockets of the universe. These black holes are not typical stellar remnants: there is not a collapsed core inside. The starThe starbut a whole parallel universe! This work marks a breakthrough in the study of the ancient universe, using non-perturbative methods at the interface between CosmologyCosmologyChaos Theory and Computational Sciences *».

Remarkably, it is possible. Gravitational wavesGravitational waves Detectors associated with these new effects are accessible to programs such as those using pulsars.