# Cosmology as a CFT1

Over the last decades, the emergence of conformal symmetry in gravitational systems has provided a powerful tool to investigate new aspects in classical, semi-classical and quantum general relativity.

Slow-roll single-field inflation constitutes the main paradigm of the Early Universe. But this model suffers from a number of conceptual issues that naturally lead to the consideration of multifield models of inflation with curved field space, that have recently been under scrutiny as realistic realizations of high-energy physics in the Early Universe. I will show that the non-trivial internal geometry reshuffles observational predictions from inflation, at the level of the background (geometrical destabilisation of inflation), of linear

The idea that low energy fields such as Gravitons or Axions can be thought of as composite particles has been entertained since a long time. We revisit this idea motivated by the AdS/CFT correspondence. We focus in the case of axions and show that hidden sectors coupled to SM fields may provide an emergent axionic field that is a composite of the hidden fields (instanton density). This is a more general phenomenon beyond holographic theories. We study the general properties of such an "emergent axion", without a PQ symmetry. The construction goes beyond

Inflation, an era of accelerated expansion of the universe prior to the radiation phase, constitutes the paradigm of primordial cosmology. Within this paradigm, the simplest single-field slow-roll models economically explain all curent data. However, the sensitivity of inflation to Planck scale physics, and the fact that ultraviolet completions of inflation invariably involve extra fields coupled to the inflaton, indicate that these models constitute at best a phenomenological description that emerges from a more realistic physical framework.

The observed accelerated expansion of the Universe opens up

the possibility that general relativity is modified on cosmological

scales. While this has motivated the theoretical study of many

alternative theories that will be tested by the next generation of

cosmic large-scale structure surveys, I will show that the recent

observations of gravitational waves by LIGO/Virgo has dramatic

consequences on these theories.

Mergers of compact objects, such as black holes and neutron stars, have been nicknamed *standard sirens*, by analogy with electromagnetic standard candles, because their waveform directly gives access to their distance. When an electromagnetic counterpart is observed, such sources thus allow us to construct a *Hubble diagram*, just as supernovae. Recently, the gravitational-wave Hubble diagram has been argued to be a key probe of alternative theories of gravity, such as *Horndeski models*.

Asymptotically flat spacetimes admit both supertranslations and Lorentz transformations as asymptotic symmetries known as BMS symmetries. Furthermore, they admit super-Lorentz transformations, namely superrotations and superboosts, as outer symmetries associated with super angular momentum and super-center-of-mass charges. In this talk, we present the flux-balance laws for all such (extended) BMS charges in terms of radiative multipole moments at future null infinity.