Abstract
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.
Highlights
The theorem states that any generator of the infinitely-dimensional coordinate transformation group is presented as series of commutators of generators from the conformal group C (1, 3) and the affine one A(4)
In paper [2], it was shown that any metric gravity theory can be viewed as a theory with a combined non-linear realization of conformal and affine symmetry
The other direction is to check if a given model with a non-linear symmetry realization has massless spin-2 degrees of freedom that could be associated with gravitons
Summary
Conformal symmetry occupies a special place in gravity physics due to the well-known. There are a few physical reasons to study models with non-linear realizations of the conformal symmetry. The first one is to search for models with a non-linear realization of the conformal symmetry which contain at least one scalar DoF and to verify its possibility to drive inflation. The other direction is to check if a given model with a non-linear symmetry realization has massless spin-2 degrees of freedom that could be associated with gravitons. Ψ and σ(α) ((α) = 0, · · · , 4) are scalar fields associated with target space coordinates on which the conformal symmetry acts non-linearly. (1) provides a model of five scalar fields subjected to a non-linear realization of the conformal symmetry. Degrees of freedom h(μ)(ν) are associated with the coset coordinates and their transformation under the non-linear conformal symmetry action is defined by the following formula:. We provide an expression for a covariant derivative of a vector field (A3) which defines such a coupling
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