Abstract
We consider a modified gravity plus single scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. As shown in a previous paper, the pertinent scalar-field dynamics provides an exact unified description of both dark energy via dynamical generation of a cosmological constant, and dark matter as a “dust” fluid with geodesic flow as a result of a hidden Noether symmetry. Here we extend the discussion by considering a non-trivial modification of the purely gravitational action in the form of $$f(R) = R - \alpha R^2$$ generalized gravity. Upon deriving the corresponding “Einstein-frame” effective action of the latter modified gravity-scalar-field theory we find explicit duality (in the sense of weak versus strong coupling) between the original model of unified dynamical dark energy and dust fluid dark matter, on one hand, and a specific quadratic purely kinetic “k-essence” gravity–matter model with special dependence of its coupling constants on only two independent parameters, on the other hand. The canonical Hamiltonian treatment and Wheeler–DeWitt quantization of the dual purely kinetic “k-essence” gravity–matter model is also briefly discussed.
Highlights
A unified treatment of dark energy and dark matter was proposed in the “Chaplygin gas” models [7,8,9,10]
In this paper we study a class of generalized models of gravity interacting with a single scalar field employing the method of non-Riemannian volume-forms on the pertinent spacetime manifold, i.e., generally covariant integration measure densities independent of the standard Riemannian one given in terms of the square root of the determinant of the metric [26,27,28,29]. (For further developments, see Ref. [30].) In this general class of models, called “two-measure gravity theories”, the non-Riemannian volume-forms are defined in terms of auxiliary maximal-rank antisymmetric tensor gauge fields (“measure gauge fields”)
In the present paper we have discussed in some detail the main properties of a generalized model of gravity interacting with a single scalar field, where we have employed the method of non-Riemannian spacetime volume-forms constructed in terms of auxiliary maximal-rank tensor gauge fields (“measure” gauge fields)
Summary
A unified treatment of dark energy and dark matter was proposed in the “Chaplygin gas” models [7,8,9,10]. Recently a lot of interest has been attracted by the so-called “mimetic” dark matter model proposed in [21,22] The latter employs a special covariant isolation of the conformal degree of freedom in Einstein gravity, whose dynamics mimics cold dark matter as a pressureless “dust”. In this paper we study a class of generalized models of gravity interacting with a single scalar field employing the method of non-Riemannian volume-forms on the pertinent spacetime manifold, i.e., generally covariant integration measure densities independent of the standard Riemannian one given in terms of the square root of the determinant of the metric [26,27,28,29]. The introduction of the two integration measures (one standard Riemannian and the other a non-Riemannian one) opens the possibility to obtain both dark energy and dark matter from a single scalar field dynamics, as already observed in Ref. In Ref. [32] we have gone further and have discovered the fundamental reason that a class of mod-
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