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Symmetries and Degrees of Freedom in Cosmic Epochs of Accelerated Expansion

Periodic Reporting for period 1 - SymAcc (Symmetries and Degrees of Freedom in Cosmic Epochs of Accelerated Expansion)

Reporting period: 2019-10-01 to 2021-09-30

From light to water we are surrounded by waves. Our understanding of waves also works into our understanding of fundamental matter, such as electrons. We study properties of matter from elements to light as fields with quantum nature. Yet it matters on what geometry we consider these fields to be. Particle physics experiments agree with the results of quantum field theory on flat spacetime geometry. Yet we are faced with questions beyond the reach of quantum field theory on flat spacetime at very high energies and on curved backgrounds.

Observations on cosmic scales point out that we live in a curved universe with changing curvature throughout its history. A specific curved geometry, referred to as de Sitter has relevance to our universe twice in its history, at primordial times and in the current cosmic epoch. This proposal asks what degrees of freedom a de Sitter spacetime can host, and how to recognize them in cosmological setups? The proposal works towards the answer by introducing "late-time operators" and considers the correlation functions of these late-time operators as their relation to observational signatures.

A guiding fact is that physical laws are independent from the coordinates used in setting up our investigation. We refer to this freedom to choose coordinates as symmetries. Different geometries possess different symmetries with different physical results. This project addresses physical degrees of freedom on de Sitter by focusing on its symmetries.

The results of the proposal have implications on our understanding of the universe we live in. These results enlighten us about the similarity and differences of physics between the scales of particles and cosmic events and between geometries of different curvature. Quite excitingly they contribute to our understanding of established techniques and their range of applicability.

The overall objective of this proposal is to investigate how to capture effective degrees of freedom for cosmological setups in a way they can be reassessed by methods of holography. Holography is a contemporary tool that address gravitational theories from the perspective of conformal field theories, field theories that have symmetries associated with rescaling of coordinates. Not all geometries possess such symmetries, called conformal symmetries and it is an ongoing effort to understand the full stretch of holography. de Sitter spacetime, does have conformal symmetries and provides an interesting venue of testing the generality of holography where in return holography can give us further insight in interpreting observational signatures from cosmology.
The unitary irreducible representations of the de Sitter group have long ago been established in mathematics literature, starting with the works of Harish-Chandra. Making use of this literature we identified degrees of freedom at the late-time boundary of de Sitter in terms of these unitary irreducible representations which we refer to as late-time operators. We also worked out how they contribute to quantities calculated in quantum field theory and holography that have connection to observable quantities, in terms of two-point functions. Our results have been composed into two papers with open access, one published by a refereed journal and the second to be submitted to a refereed journal; presented as seminars and talks at conferences and workshops and made accessible to the public through a public talks and two short movies on Youtube, accessible through the project's webpage. We also organized an online workshop on Holography bringing together experts in the field. During the workshop we discussed our project results with other participants.
The project’s goal was to make use of holography in a cosmological setting, namely on de Sitter. To reach the overall objective of investigating how to capture effective degrees of freedom for cosmological setups in a way they can be reassessed by methods of holography, we had to understand what are the allowed ingredients in de Sitter holography. These are operators with scaling dimensions and specific correlation functions in holography belong to the conformal field theory, but their properties are encoded in the gravitational theory on the curved geometry, which in our case is the de Sitter geometry. By studying unitary irreducible representations of the de Sitter group and how they manifested themselves at the late time boundary, which is a set up that address early universe cosmology, we managed to gather clues about the holographic nature of de Sitter, and initiate a discussion on how these clues can show up in cosmological studies. As explicit results we provided a list of operators, the late-time operators, with their scaling dimensions and two-point functions for scalar fields on de Sitter.
the late-time operators