Gravitational Goldstone fields from affine gauge theory

We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due the partial isomorphism between $CA\left( 3,1\right) $ and the centrally extended $Sp\left( 8\right) $, we perform a nonlinear realization of the centrally extended (CE)$Sp\left( 8\right) $ in its se...

How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine symmetry in differential geometry is to define a Cartan connection on an affine bundle over spacetime. This is equivalent to (1) defining an affine connection on the affine bundle, (2) defining a zero section on the associated affine vector bundle...

We shall give dynamics to our spacetime manifold by first identifying the local affine symmetry as the characterizing symmetry for our geometry a'la Felix Klein, this symmetry is imposed on us by the Law of Inertia and the Law of Causality. We then prescribe 16 gauge vector bosons to this symmetry a'la Yang and Mills. The locally affine symmetric Yang-Mills Lagrangian in the presence of a background world metric, and the corresponding equations of motion, are respectively con...

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two--loop renormalizable effective actions. We use a key result from our partner work arXiv:0902.0911 that the classical Einstein gravity theory can be refo...

The Poincar\'e group can be interpreted as the group of isometries of a minkowskian space. This point of view suggests to consider the group of isometries of a given space as the suitable group to construct a gauge theory of gravity. We extend these ideas to the case of maximally symmetric spaces to reach a realistic theory including the presence of a cosmological constant. Introducing the concept of "minimal tetrads" we deduce Einstein gravity in the vacuum as a gauge theory...

A new geometric interpretation for General Relativity (GR) is proposed. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine connection can be interpreted as induced by a frame of reference (FR). Although the gravitational field equations are identical to Einstein's equations of GR, this formulation leads to a covariant tensor (instead of the pseudotensor) of energy-momentum of...

For the first time, we build a generalization of the $U(n)$ Yang-Mills theory obtained by abandoning the condition of covariant constancy of the Hermitian form in the fibers: $\nabla_a g_{\alpha\beta'} \ne 0$. So this theory is a simpler analogue of the well-known metric-affine gravity with $\nabla_a g_{bc} \ne 0$. In our case the connection $\nabla_a$ and the Hermitian form $g_{\alpha\beta'}$ are two independent variables, and the total curvature and the total potential are ...

In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what sense is gravity a gauge theory?" I will reformulate the theory of gravity in a general kinematical setting which highlights the presence of two Goldstone boson-like fields, and the occurrence of a gravitational Higgs phenomenon. The fact th...

We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.

The two-phase structure is imposed on the world continuum, with the graviton emerging as the tensor Goldstone boson during the spontaneous transition from the affinely connected phase to the metric one. The physics principle of metarelativity, extending the respective principle of special relativity, is postulated. The theory of metagravitation as the general nonlinear model GL(4,R)/SO(1,3) in the arbitrary background continuum is built. The concept of Metauniverse as the ens...