CPT symmetry, analyticity and conformal symmetry: connecting particle physics to LCDM cosmology
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.