Seriously... Simplifying the Big Bang

Daniele Bertacca & Raul Jimenez, "New theory of gravitational waves holds key to the early universe"

Gravitational waves may resolve problems with the Big Bang theory

10 years ago, the detection of gravitational waves from a pair of colliding black holes revolutionised astronomy. Now, a team of physicists from Europe are proposing a new theory of gravitational waves with the potential to disrupt one of the key ideas in modern cosmology. Theoretical physicists Daniele Bertacca and Raul Jimenez argue the cosmic inflation paradigm has too many free parameters, and we are expanding the limits of our theories to fit the data. Bertacca and Jimenez propose a radical alternative: gravitational waves and their dynamics were key to the early universe and ultimately gave rise to galaxies, stars, and planets.

One, if not the, guiding principle in physics is that of the Ockham razor: the simplest model with the least number of parameters is the one that describes nature. A stronger view is that nature should not be described by models but by what we term “rigid theories,” a group of equations or concepts that do not contain any free parameters.

In physics, whenever we have found a theory that describes nature, it has been because of its “rigidity.” Newton's law of universal gravitation establishes that the force between two masses is inversely proportional to the square of the distance between two objects. This describes most data in the sky, and in a laboratory on Earth regarding the gravitational attraction between two masses. But why the square of the distance and not the cube of it, or 3.5 times it? The orbits of celestial objects would be different, but this would be purely an observational fact.

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In science, too much flexibility can be problematic, as it makes it difficult to know whether a model is actually predicting something or simply fitting data after the fact.

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Indeed, Newton's law is just, a very clever, fit to Kepler's data. It is not surprising then that the new tools in the field of computer science like neural networks and large language models can easily find Newton’s law from observations of the orbits of celestial objects; after all they are the universal interpolator in the body of (scanned) human knowledge.

However, Newton's law is not rigid. Instead we must look to Einstein’s gravity, which can also explain why the exponent in Newton's law is two. Einstein’s theory of general relativity has been remarkably successful in explaining a wide range of astronomical and physical phenomena that could not be understood with Newtonian gravity. One of its earliest triumphs was accurately accounting for the anomalous precession of Mercury’s perihelion, a long-standing puzzle that classical mechanics failed to resolve. The theory also predicted the existence of black holes—regions of spacetime where gravity is so strong that nothing, not even light, can escape—which have since been observed through their effects on nearby matter and, more recently, by direct imaging by the Event Horizon Telescope. General relativity further anticipated the bending of light by massive objects, known as gravitational lensing, which is now a powerful tool in cosmology for mapping dark matter and studying distant galaxies. Finally, the prediction of gravitational waves—ripples in spacetime produced by violent cosmic events—was spectacularly confirmed a century later with their direct detection by LIGO, providing some of the most striking evidence yet for Einstein’s revolutionary theory.

Motivated by the search for a rigid theory of the early universe, we have started a program in which we have aimed to identify those aspects of a theory of the universe that are guaranteed, i.e. will happen no matter what, like the fact that an apple will fall towards the center of the Earth.

Our new study, which includes Prof. Raúl Jiménez of Barcelona University, Dr. Daniele Bertacca and Prof. Sabino Matarrese of Padua University and Dr. Angelo Ricciardone of Pisa University, published in the Physical Review Journals, introduces a radical shift in how we might understand the earliest moments after the Big Bang, without relying on free parameters.

For decades, cosmologists have been working on a model, the "inflationary paradigm", that suggests the universe expanded at an incredible rate in the very early universe, explaining everything we observe today. This theory was invented to solve several problems in the standard Big Bang model, such as why the universe looks so uniform (the horizon problem) and why it appears so flat (the flatness problem). It proposes that the universe underwent a brief period of extremely rapid expansion in its earliest moments, stretching out any initial irregularities. This rapid inflation also provides a mechanism for the origin of the tiny quantum fluctuations that later grew into galaxies and cosmic structure. But there's a problem: this theory includes too many free parameters that can be adjusted at will. In science, too much flexibility can be problematic, as it makes it difficult to know whether a model is actually predicting something or simply fitting data after the fact.

The never ending adjustment of free parameters within the inflationary theory has a very checkered history. The most “infamous” event was when the BICEPS experiment wrongly claimed a detection of the sought after primordial gravitational wave background created by inflation. The claim was that tensor modes in the CMB due to gravitational waves had been detected at a given value and thus the energy scale of inflation, one of the many free parameters in the theory, determined. This resulted in inflationary models being vindicated for a given set of free parameters. After the BICEPS result was shown to be mislabelled dust, one would have hoped the inflationary paradigm would have been put under stress, but no, the parameters were just adjusted. Indeed, in its present form it can fit any future observation of the early universe.

Our approach was different. We posed the following question: starting from a well-established cosmic state whose properties are well known and has only the energy scale of the vacuum as a free parameter, a symmetric universe with positive cosmological constant, known as de Sitter space, what were the unavoidable consequences of such a space-time?

Because of quantum mechanics, one is guaranteed to have fluctuations of the de Sitter space-time metric, and hence gravitational waves. However, unlike changes in a scalar or vector field, these fluctuations are quadrupoles where spacetime is stretched in one direction and squeezed in the perpendicular, like rugby balls. These quadrupole fluctuations, while guaranteed, are not good at describing our mostly scalar universe.

Gravitational waves are transverse quadrupole waves If a wave passes through the ring of:

The passage of a gravitational wave through a ring of test particles (Source Living Reviews in Relativity).

So here is when complexity and non-linearities come to the rescue. While studying second order perturbation theory of these tensor fluctuations we realised that one could produce scalar perturbations as well. This was interesting as we could connect the tensor world of space-time to the scalar world of the matter we are made of, i.e. we only need a number to describe perturbations in the universe and not a tensor.

Further, these scalar perturbations turn out to be exponentially enhanced over the tensor perturbation. Starting from a low level of primordial fluctuations, just one part in a hundred thousand, one has to only produce a tiny level of scalar over-densities in order to makes this second order feedback loop dominate. As a result of this connection, the observed and measured level of primordial fluctuations by cosmic microwave background experiments determines the energy scale of de Sitter space-time, constraining the space-times only free parameter.

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We could connect the tensor world of space-time to the scalar world of the matter we are made.

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In our picture, de Sitter space can be considered as a Bose-Einstein condensate of gravitons (the mediator of gravity force in quantum theories of gravitation). It is this condensate and its quantum correlations that provide a natural way for the inflationary expansion of the universe to end and enter a radiation-dominated era. It is the vacuum energy of de Sitter that drives inflation.

In particular, we believe that within the cosmological horizon, due to the intrinsic nonlinear dynamics of gravity, the unstable de Sitter symmetry will be broken at a finite time. From that moment, quantum effects become so incredibly strong that they lead the universe itself into a quantum chaotic system, moving the system from near equilibrium state described by the Bose-Einstein condensate of gravitons to a totally out-of-equilibrium quantum s.ystem.

Unlike the textbook theories of inflation, our model doesn't rely on speculative fields like the inflaton. Rather, it suggests that natural quantum oscillations of space-time itself, gravitational waves, were sufficient to trigger the tiny density differences that ultimately gave rise to galaxies, stars, and planets. These gravitational ripples evolve nonlinearly, meaning they interact and build complexity over time, leading to testable predictions that researchers can now compare with real data.

These new results demonstrate that we may not need speculative ingredients to explain the cosmos, but only a deep understanding of gravity and quantum physics. If the model holds true, it could mark a new chapter in the way we think about the birth of the universe