The universe has turned out to be simpler than expected on small and large scales. This encourages us to build unified theories connecting particle physics to the LCDM model. Instead of postulating an ``attractor” phase such as inflation, prior to the hot big bang, we extrapolate the observed universe all the way back to the initial singularity. If the hot plasma in the early universe is perfectly conformal radiation, the singularity is only conformal and one can analytically extend cosmic spacetime and matter through it into a ``mirror” universe on the other side. The universe is then CPT symmetric. We calculate the gravitational entropy for cosmologies with radiation, matter, Lambda and space curvature, finding that thermodynamics favours flat, homogeneous and isotropic universes like ours. To maintain conformal symmetry we include unusual Dim-0 (dimension zero) fields, whose unique physical state is the vacuum. They improve the Standard Model’s (SM’s) coupling to gravity, by cancelling the SM’s vacuum energy and two local “Weyl” anomalies due to gauge fields and fermions. They also cancel the acausal, nonanalytic behaviour introduced into the graviton propagator by loops of SM particles. Cancellation requires (and predicts) precisely 3 generations of SM fermions, each with a RH neutrino, and that the Higgs is composite. One of the RH neutrinos, if stable, is then the simplest-yet proposed viable candidate for the dark matter. Galaxy surveys including EUCLID and LSST will allow precise tests soon. Finally, and most exciting, Dim-0 fields have scale-invariant fluctuations in the vacuum. These source curvature perturbations in the early universe. We recently calculated their power spectrum, ab initio, in terms of Standard Model couplings at the Planck scale. Subject to some theoretical assumptions, the amplitude and spectral tilt closely match the observations, with no free parameters. (See arXiv:2302.00344and references therein).

We show how Feynman's path integral for quantum mechanics may be defined without a Wick rotation to imaginary time. Instead, we employ analytic continuation (and Cauchy's theorem) in the complexified space of paths being integrated over. We outline an existence proof and describe applications to both nonrelativistic quantum mechanics and to interference patterns due to gravitational microlensing in radio astronomy. [please email a.held@imperial.ac.uk for zoom link or password]

Tom Kibble was a pioneer of the symmetry breaking paradigm in fundamental physics. His view of physics is exceptionally broad, and Tom also led efforts to see how to test ideas of grand unification through exploring their consequences for the very early universe. Over time, this led to new paradigms for cosmology, like cosmic inflation, with a plethora of observational tests. In this talk, I shall review some of Tom's cosmological innovations and also look forward to new and even more fundamental paradigms capable of tackling the big bang singularity. [Symmetry and Fundamental Physics - Tom Kibble at 80]

Neil Lambert (KCL) 'From D-branes to M-branes', David Tong (DAMTP) 'Quantum vortex strings' plus several presentations by PhD students on their work. Ends at 14:15. See www.mth.kcl.ac.uk/'tilde'anderl/LMSpremeeting/