## Cosmology, gravitational and high Energy physics

The cosmological standard model has a Big Bang origin. There are very general singularity theorems by Hawking and Penrose that generically predict the existence of singularities. More recently, work on their analytical structure has shown that the approach to the singularities is governed by reflection (Coxeter) groups, in what is called `cosmological billiards'. We have worked on generalisations of the standard model that can help circumvent singularities, both on the geometry and matter sides of the Einstein field equations, in particular anisotropic cosmologies (so-called Bianchi models) with scalar field matter.

We used Clifford algebra methods to implement conformal spacetime symmetry, which allows unified treatment of translations and rotations as a multiplicative group of versors. The stabiliser group of a specific vector gives the (hyperbolic) de Sitter space-time symmetry. Using a novel projection, we constructed from the de Sitter Killing vectors new sets of symmetric Killing vectors for Bianchi spacetimes, in particular a new

SU(2) × SU(2)-symmetric set for Bianchi IX, which is also symmetric in the three-dimensional coordinates x → y → z → x, in contrast to previously known ones.

In such a Bianchi IX (spherical) geometry, we have constructed a novel cosmological model, that – unusually – does not have a singularity at the ‘Big Bang’. This DLH model isotropises and inflates and thus has sensible late-time behaviour for a cosmological model; it fits current observations, and is thus a new candidate as a model for the early universe. In fact, our model predicts an observational phenomenon that the standard cosmological model is often argued to be statistically very unlikely to exhibit.

The DLH model warranted a comparison with a very pathological spacetime called Taub-NUT (both are Penrose type D), that is said to be ‘a counterexample to almost everything’. We found that the two spacetimes are related, but that Taub-NUT describes the geometry in an awkward way, whereas the DLH view seems a more natural view of the geometry, and is well-behaved both at the ‘Big Bang’ and as a late-time cosmological model.

In contrast, in the generic case in a wide range of gravitational theories (including General Relativity, Supergravity and string-derived models), there is a Big Bang singularity described by hyperbolic Coxeter groups, including the case of E_8 and its extensions.

SU(2) × SU(2)-symmetric set for Bianchi IX, which is also symmetric in the three-dimensional coordinates x → y → z → x, in contrast to previously known ones.

In such a Bianchi IX (spherical) geometry, we have constructed a novel cosmological model, that – unusually – does not have a singularity at the ‘Big Bang’. This DLH model isotropises and inflates and thus has sensible late-time behaviour for a cosmological model; it fits current observations, and is thus a new candidate as a model for the early universe. In fact, our model predicts an observational phenomenon that the standard cosmological model is often argued to be statistically very unlikely to exhibit.

The DLH model warranted a comparison with a very pathological spacetime called Taub-NUT (both are Penrose type D), that is said to be ‘a counterexample to almost everything’. We found that the two spacetimes are related, but that Taub-NUT describes the geometry in an awkward way, whereas the DLH view seems a more natural view of the geometry, and is well-behaved both at the ‘Big Bang’ and as a late-time cosmological model.

In contrast, in the generic case in a wide range of gravitational theories (including General Relativity, Supergravity and string-derived models), there is a Big Bang singularity described by hyperbolic Coxeter groups, including the case of E_8 and its extensions.