# The Cosmological Bootstrap: a New Approach to the Primordial Universe

Lead Research Organisation:
University of Cambridge

Department Name: Applied Maths and Theoretical Physics

### Abstract

One of the most remarkable facts that has emerged from observations of the cosmos in the past few decades is that the distribution of stuff in the universe at intergalactic distances displays a shockingly high degree of regularity. This is true for everything we have observed: the galaxies that we see in the night sky and the Dark Matter that surrounds them; the photons in the cosmic microwave background, namely the faint afterglow of the universe' hot past, and the elusive neutrinos. Because our universe has been expanding for all of its observable history, we know for certain that this remarkable regularity must have been seeded during the first fraction of a second of the Big Bang. Our leading paradigm to describe that period in the history of the universe is called inflation and it posits that space expanded exponentially fast and small quantum fluctuations were stretched to cosmological size and eventually determined the spatial distribution of everything.

This picture of the very early universe has profound implications. First, it tells us that quantum mechanics, namely the set of physical laws that rule the atomic and subatomic scales and that enabled the digital age, is also the key to understanding the large cosmological distances of the observable universe. Second, this tells us that we can study the laws of physics at subatomic scale using cosmological surveys. Third, because the expansion of the universe is a gravitational phenomenon and since quantum mechanics must play a crucial role, we have the unique opportunity to learn about the holy grail of theoretical physics: quantum gravity.

In the past 30 years, people have made more and more elaborate models of inflation and the very early universe and they have compared them to observations. Unfortunately, despite the huge cosmological dataset at our disposal, it has become increasingly clear that there is a vast degeneracy in the space of models, which cannot be resolved by better observations. The key obstacle is that we have tried to model the evolution of the universe as time progresses, but that's not something we can observe today. All we can see is the end result of that evolution. A further obstacle is that the reliance on specific models has made it harder and harder to find general properties and patterns in the predictions of inflation.

The goal of this proposal is to devise a description of our primordial universe that does not involve time. In other words, we want to be able to predict what the possible outcomes and predictions of inflation are, without having to write down and solve all possible models. Rather, we want to rely exclusively on the pillars of our understanding of fundamental physics. These general principles, such as for example symmetries, unitarity and locality, sit at the core of our description of subatomic particles and should therefore be taken as a starting point for our understanding of the early universe.

To reach our goal of describing "time without time", we will import the approach and technology that has revolutionised our understanding of particle physics in the past two decades. This progress has not yet been transferred to the realm of cosmology, where it actually has the highest potential. Applying this approach to cosmology will allow me to predict the general, model-independent outcomes of inflation and more specifically the detailed statistical distributions that can be generated while being compatible with the laws of physics as we know them.

The output of this research will be a new understanding of how quantum mechanics works when combined with non-trivial gravitation backgrounds. It will open the door to use cosmological observations to discovering new particles beyond those that we know in the current standard model. We will be able to discover new forces at play in nature and perhaps even learn something about the perturbative regime of quantum gravity.

This picture of the very early universe has profound implications. First, it tells us that quantum mechanics, namely the set of physical laws that rule the atomic and subatomic scales and that enabled the digital age, is also the key to understanding the large cosmological distances of the observable universe. Second, this tells us that we can study the laws of physics at subatomic scale using cosmological surveys. Third, because the expansion of the universe is a gravitational phenomenon and since quantum mechanics must play a crucial role, we have the unique opportunity to learn about the holy grail of theoretical physics: quantum gravity.

In the past 30 years, people have made more and more elaborate models of inflation and the very early universe and they have compared them to observations. Unfortunately, despite the huge cosmological dataset at our disposal, it has become increasingly clear that there is a vast degeneracy in the space of models, which cannot be resolved by better observations. The key obstacle is that we have tried to model the evolution of the universe as time progresses, but that's not something we can observe today. All we can see is the end result of that evolution. A further obstacle is that the reliance on specific models has made it harder and harder to find general properties and patterns in the predictions of inflation.

The goal of this proposal is to devise a description of our primordial universe that does not involve time. In other words, we want to be able to predict what the possible outcomes and predictions of inflation are, without having to write down and solve all possible models. Rather, we want to rely exclusively on the pillars of our understanding of fundamental physics. These general principles, such as for example symmetries, unitarity and locality, sit at the core of our description of subatomic particles and should therefore be taken as a starting point for our understanding of the early universe.

To reach our goal of describing "time without time", we will import the approach and technology that has revolutionised our understanding of particle physics in the past two decades. This progress has not yet been transferred to the realm of cosmology, where it actually has the highest potential. Applying this approach to cosmology will allow me to predict the general, model-independent outcomes of inflation and more specifically the detailed statistical distributions that can be generated while being compatible with the laws of physics as we know them.

The output of this research will be a new understanding of how quantum mechanics works when combined with non-trivial gravitation backgrounds. It will open the door to use cosmological observations to discovering new particles beyond those that we know in the current standard model. We will be able to discover new forces at play in nature and perhaps even learn something about the perturbative regime of quantum gravity.

### Organisations

## People |
## ORCID iD |

Enrico Pajer (Principal Investigator) |

### Publications

Bonifacio J
(2023)

*The graviton four-point function in de Sitter space*in Journal of High Energy Physics
Bonifacio J
(2021)

*From amplitudes to contact cosmological correlators*in Journal of High Energy Physics
Cabass G
(2022)

*Bootstrapping large graviton non-Gaussianities*in Journal of High Energy Physics
Cabass G
(2023)

*Parity violation in the scalar trispectrum: no-go theorems and yes-go examples*in Journal of High Energy Physics
Cabass G
(2022)

*Bootstrapping large graviton non-Gaussianities*
Goodhew H
(2021)

*Cutting cosmological correlators*in Journal of Cosmology and Astroparticle Physics
Goodhew H
(2021)

*The Cosmological Optical Theorem*in Journal of Cosmology and Astroparticle Physics
Hillman A
(2022)

*A differential representation of cosmological wavefunctions*in Journal of High Energy Physics
Hillman A
(2022)

*A differential representation of cosmological wavefunctions*
Jazayeri S
(2021)

*From locality and unitarity to cosmological correlators*in Journal of High Energy PhysicsDescription | In HEP 11 (2023) 038, we were able to identify a specific signal left over from the first fraction of the big bang in the form of a difference in teh distribution of matter in the universe between how we see it and how it would look like in a mirror. We showed that a potential detection of this signal would rule out the vast majority of models of the very universe we have to date and point to the existence of new particles beyond those already known or a drastic change in the current leading model. In JHEP 06 (2023) 020 we studied the consequence a important principle of the laws of physics: you cannot affect the past. This simple principle, known in the field as the requirement of "causality" has deep implications for all predictions from the quantum theory and for cosmology. We systematically studied the implication of causality for an object called the "wave function" from which all statistical prediction of a relativistic quantum field theory can be derived. |

Exploitation Route | We established some essential results that will dramatically limit the set of possible models of the early universe and the laws of physics during that period. |

Sectors | Other |

Description | Our results answer some of the deepest questions about the laws of nature and origin of the structure we observe in the universe. |

Description | Biweekly International virtual journal club |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Professional Practitioners |

Results and Impact | I organized a biweekly journal club held virtually to discuss recent research progress on the topic of the grant both by our team and by other teams at international institutions. The regular meeting has started in 2020 and runs virtually on the platform Zoom. We have had an average of 20-30 participants at every event and about 20 events per year, with short breaks for the summer and winter holidays. The participants of the meeting come from many international organizations including the University of Cambridge (my group), the university of Amsterdam (NL), University of Leiden (NL), Cornell University (USA), the univesity of Chicago (USA), the University of Pisa (IT), Sharif University (Iran), the Instute d'astrophysicque Paris (FR), the Ecole Politechnicque Federal de Laussanne (CH) just to name a few. The meeting usually involves an short organized presentation about the topic of the grant (the cosmological bootstrap) and an informal discussion of reseach publication that are of relevance. Attendees are PhD students, postdocs and faculty members at research institutions. |

Year(s) Of Engagement Activity | 2020,2021,2022 |

URL | https://www.benty-fields.com/manage_jc?groupid=443 |