Gauging the Maxwell Extended GLn,R and SLn+1,R Algebras

We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in D space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a suitable contraction of generalized algebras. The extended Lie algebras could be useful in the construction of generalized gravity theories and the objects that couple to them. We also consider the gravitational dynamics of these algebras in the framework of the gauge theories of gravity. By adopting the symmetry-breaking mechanism of the Stelle–West model, we present some modified gravity models that contain the generalized cosmological constant term in four dimensions.

Two Approaches to Hamiltonian Bigravity

Bigravity is one of the most natural modifications of General Relativity (GR), as it is based on the equivalence principle. However, its canonical structure appears rather complicated because of the unusual form of the interaction between two metrics. As a consequence, there are different approaches that are difficult to compare in detail. This work is a first attempt to obtain a synthetic picture of the Hamiltonian formalism for bigravity. Here, we are trying to combine two rather different approaches to gain a binocular view of the theory. The first publications on the subject were based on metric formalism. It was proved that both massive gravity and bigravity with de Rham–Gabadadze–Tolley (dRGT) potential were free of Boulware–Deser (BD) ghosts. This proof was based on the transformation of variables involving a 3×3-matrix which could be treated as the root of a quadratic equation involving two spatial metrics and a new 3-vector introduced instead of the standard shift variable. Therefore, this matrix occurred as an implicit function of the abovementioned variables. After a substantial amount of time, it became possible to calculate the algebra of constraints in full using this method. However, in another approach also based on metric variables and implicit functions, similar calculations were completed earlier. It is not a new matrix, but the potential itself has been taken as an implicit function of two spatial metrics and four functions constructed of two pairs of lapses and shifts. Finally, a straightforward route to canonical bigravity is to apply tetrad (or vierbein) variables. The matrix square root involved in the dRGT potential can be explicitly extracted if tetrads fulfill the symmetry condition. A full treatment has been developed in first-order formalism by treating tetrads and connections as independent variables. In that case, the theory contains many more variables and constraints than in metric formalism. An essential simplification occurs in second-order vierbein formalism. The potential is given explicitly as a polynomial of bilinear combinations of the two tetrads. The 3×3-matrix introduced in the pioneer papers can be expressed explicitly through canonical coordinates, and the celebrated transformation of variables arises in the Dirac constraint analysis.

Gravity Models with Nonlinear Symmetry Realization

Validity of three gravity models with non-linear realization of conformal symmetry previously discussed in literature is addressed. Two models are found to be equivalent up to a change of coset coordinates. It was found that models contain ghost degrees of freedom that may be excluded by an introduction of an additional symmetry to the target space. One model found to be safe in early universe. The others found to lack spin-2 degrees of freedom and to have peculiar coupling to matter degrees of freedom.

On massive Nambu-Goldstone fields

We consider two theories undergoing the same spontaneous symmetry breaking pattern but with different representations of an order parameter under the Lorentz group. The effective description of the first theory includes a massive Nambu-Goldstone field, while in the second example it is absent. Based on this, we clarify the physical meaning of massive Nambu-Goldstone fields as non-radial modes needed to describe the fluctuations of an order parameter. The connection with the inverse Higgs phenomenon is also discussed.

Acausality of massive gravity

We show, by analyzing its characteristics, that the ghost-free, 5 degree of freedom, Wess-Zumino massive gravity model admits superluminal shock wave solutions and thus is acausal. Ironically, this pathology arises from the very constraint that removes the (sixth) Boulware-Deser ghost mode.