Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the van Dam, Veltman, and Zakharov (vDVZ) discontinuity and the Boulware-Deser ghost were uncovered. These results are rederived in a pedagogical manner and the St\"uckelberg formalism to discuss them from the modern effective field theory viewpoint is developed. Recent progress of the last decade is reviewed, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra dimensions and brane worlds are reviewed.

Theoretical Aspects of Massive Gravity

Beyond the cosmological standard model

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

/pdf/renormalization-of-the-abelian-higgs-kibble-model-14fr0vp7oj.pdf

Renormalization of the Abelian Higgs-Kibble Model

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field. For scalar modes, the leading corrections to the R correlation function are found to be purely of the k-inflation type. For tensor modes the leading corrections to the correlation function arise from terms in the action that are quadratic in the curvature, including a parity-violating term that makes the propagation of these modes depend on their helicity. These methods are also briefly applied to nongeneric theories of inflation with an extra shift symmetry, as in so-called ghost inflation.

Effective field theory for inflation

We carry out the extension of the Ostrogradski method to relativistic field theories. Higher-derivative Lagrangians reduce to second differential order with one explicit independent field for each degree of freedom. We consider a higher-derivative relativistic theory of a scalar field and validate a powerful order-reducing covariant procedure by a rigorous phase-space analysis. The physical and ghost fields appear explicitly. Our results strongly support the formal covariant methods used in higher-derivative gravity.

/pdf/ostrogradski-formalism-for-higher-derivative-scalar-field-4khsnm2tbt.pdf

Ostrogradski formalism for higher-derivative scalar field theories

Conditions for the validity of (a weak version of) the Adler-Bardeen theorem for non-Abelian gauge theories are obtained. Its validity ensures that those theories in which the coefficient of the triangle anomaly vanishes at the one-loop level are anomaly free and therefore they are renormalizable and unitary. This result is based on the derivation of Slavnov-Taylor identities modified by the presence of anomalous terms and on a renormalization-group-like equation for the anomaly coefficient. In the derivation, the dimensional regularization scheme has been followed.

Non-abelian gauge theories and triangle anomalies

We present a general scheme for the nonlinear gauge realizations of spacetime groups on coset spaces of the groups considered In order to show the relevance of the method for the rigorous treatment of the translations in gravitational gauge theories, we apply it in particular to the affine group This is an illustration of the family of spacetime symmetries having the form of a semidirect productH ⊗ T, whereH is the stability subgroup andT are the translations The translational component of the connection behaves like a true tensor underH when coset realizations are involved

/pdf/nonlinear-gauge-realization-of-spacetime-symmetries-490uchz805.pdf

Nonlinear gauge realization of spacetime symmetries including translations

The (lower derivative) action, which describes the actual degrees of freedom of a (higher derivative) theory of gravity quadratic in the scalar and Ricci curvatures, is found. Key steps are a Legendre transform and a suitable diagonalization procedure. Some consequences of this insight are outlined.

Particle contents of higher-derivative gravity

The nonlinear local theory of the 4D conformal spacetime group is presented. Effective theories of gravity quadratic in curvatures may be viewed as nonlinear realizations of this group. We find that in the absence of torsion and under very general assumptions derived from the structure of the algebra, the symmetry takes the form of the simpler Weyl scale invariance and the resulting theory is Einstein's gravity with, generally, a cosmological constant.

http://iopscience.iop.org/article/10.1088/0264-9381/12/5/020/pdf

J. Julve

Papers

Ostrogradski formalism for higher-derivative scalar field theories

Non-abelian gauge theories and triangle anomalies

Nonlinear gauge realization of spacetime symmetries including translations

Particle contents of higher-derivative gravity

Nonlinear 4D conformal gauge spacetime symmetry