Conformal Nature of the Universe - 2012

New techniques for obtaining the complete set of analytic solutions of the usual cosmological equations continue to shed new light on various aspects of cosmology. This approach, which was developed with a locally Weyl invariant formulation of gravity in 3+1 dimensions, was inspired by the 2T-physics formulation of all physics in 4+2 dimensions. I will first give a review of the general aspects of the analytic cosmological solutions, including recent work with Shi-Hung Chen, Paul Steinhardt and Neil Turok, on geodesic completeness through the singularity and the nature of the Big Crunch/Big Bang transition. Then I will include the full Standard Model, and discuss how the instability of the Higgs potential and the conditions for the electroweak phase transition develop slowly during cosmological evolution of the universe, thus understanding that the electroweak phase transition is not "spontaneous" and the Standard Model is not decoupled from gravity or cosmology. This scenario, which is currently being developed further, is the natural cosmological consequence of coupling the Standard Model to Gravity by imposing Weyl symmetry, a feature that is required if 2T-physics in 4+2 dimensions is considered as the starting point. There are no dimensionful parameters, not even the Newton constant. Emergent dimensionful scales are dynamical during the evolution of the universe.

I show how the local Lorentz and/or diffeomorphism invariances may be broken by a varying c, softly or harshly, depending on taste. Regardless of the fundamental implications of such dramas, these  symmetry breakings may be of great practical use in cosmology. They may solve the horizon and flatness problems. A near scale-invariant spectrum of fluctuation may arise, even without inflation. Distinct imprints may be left, teaching us an important lesson: our foundations may be flimsier than we like to think.

We present a new model of inflation which does not rely on fundamental scalar fields.  The theory is a conformally invariant gauge field theory minimally coupled to massless fermions.  At the beginning of inflation, the conformal symmetry is dynamically broken by a BCS condensation of the fermions, leading to a spontaneously violation of conformal symmetry.  A quasi de-Sitter inflationary regime is driven by the interaction between a homogenous plasma dynamo between the gauge, gravitational and condensate field.  Unique observational consequences of this model are twofold : (1) The sourcing of B-mode vorticity fluctuations in upcoming CMB powerspectra. (2) A possible inflationary Baryogenesis mechanism connected to the initial conditions of inflation.

I will describe an approach to the problem of time that uses dust as a time variable. The canonical theory is such that there is a true Hamiltonian with spatial diffeomorphisms as the only gauge symmetry. This feature, and the form of the Hamiltonian, suggest a model for non-perturbative quantum gravity that is computationally accessible using the formalism of loop quantum gravity.  

We comment on a certain partially reduced phase space quantisation of general relativity conformally coupled to a scalar field, and its extension to standard model matter fields. The partially reduced phase space is reached by trading the Hamiltonian constraint for the generator of local conformal transformations on all phase space variables, inspired by the ideas of shape dynamics, and constructing conformally invariant connection variables. Furthermore, we review this trading of symmetries from the gauge fixing/unfixing perspective, which is dual to the concept of a linking theory. Finally we point out possible applications and open problems.

The pseudo-conformal scenario is an alternative to inflation in which the early universe is approximately described by a conformal field theory in Minkowski space. Crucially, the cosmological background spontaneously breaks the flat space so(4,2) conformal algebra down to its so(4,1) de Sitter subalgebra, causing conformal-weight-0 fields to acquire a scale invariant spectrum of perturbations. This framework is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. After reviewing the salient features of the model, I will describe a DBI realization of the pseudo-conformal scenario, in which scale-invariance is further protected by an additional shift symmetry acting on the weight-0 field.