Axionic cosmological constant

Abstract

We propose a novel higher-derivative, Weyl-invariant and generally-covariant theory for the cosmological constant. This theory is a mimetic construction with gauge fields playing the role of dynamical variables. These fields compose Chern-Simons current instead of the vector field in the Henneaux and Teitelboim formulation of the unimodular gravity. The equations of motion exactly reproduce the traceless Einstein equations. We demonstrate that, reformulated in Weyl-invariant variables, this novel theory reduces to standard general relativity with the cosmological constant as a Lagrange multiplier. This Lagrange multiplier has an axion-like coupling.

Disforming to Conformal Symmetry

“…This raises an interesting question whether all types of such restricted variations of the metric can be realized through some metric transformation. For instance, unimodular restriction on variation of the metric (3.15) has been realized through different mimetic transformations involving vector fields [40,41].…”

Losing the trace to find dynamical Newton or Planck constants

“…Combing unimodular gravity with theories where Newton constant is another global degree of freedom is the key element of the vacuum sequester proposal, [4,34,36]. A novelty with respect to vacuum sequester works [34-36, 41, 45-47] is that following [25] we also use normal Yang-Mills gauge fields instead of more exotic three and four forms to specify a new measure for the action integral. Moreover, in our formulation the Lagrange multiplier fields from these setups look like axions and can even have normal kinetic terms.…”

“…Moreover, one could avoid the Lagrange multiplier and formulate unimodular gravity as a higher-derivative and Weyl-invariant theory for a vector field [24] or for a gauge field [25], see also [30]. One can also describe this dynamics by a covariant action containing a three-form as in e.g.…”

“…An action similar to (53) was used in [34,35] for local version of the vacuum energy sequester [36]. On the other hand, following (25) from [25] one can exchange the vector C µ with a Chern-Simons current of a gauge field A µ and obtain…”

Generalized unimodular gravity as a new form of k -essence

“…As in other models with spontaneously broken symmetries, it is always possible to embed GUMG theory into a fully covariant framework by means of additional fields. For instance, UMG theory can be covariantized by means of a vector field [6,25], via four Stueckelberg fields [26] or in terms of a gauge field [27]. Examples of covariantization also include Lorentz-invariant formulation of Horava gravity by means of the chronon field [28] and covariant versions of massive gravity in terms of Stueckelberg scalar fields [10,11,29].…”