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.

We study in some detail the properties of a previously proposed new class of string and brane models whose world-sheet (world-volume) actions are built with a modified reparametrization-invariant measure of integration and which do not contain any ad hoc dimensionful parameters. The ratio of the new and the standard Riemannian integration measure densities plays the role of a dynamically generated string or brane tension. The latter is identified as (the magnitude of) an effective (non-Abelian) electric field strength on the world-sheet or world-volume obeying the standard Gauss-law constraint. As a result a simple classical mechanism for confinement via modified-measure “color” strings is proposed where the colorlessness of the “hadrons” is an automatic consequence of the new string dynamics.

We propose a simple modified gravity model withoutany initial matter fields in terms of several alternative non-Riemannian spacetime volume elements within the metric (second order) formalism. We...

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant $p$-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally noninvariant) Nambu-Goto $p$ branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In $D=4$ the WILL membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on (straddles) the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps nontrivially around the compact (internal) dimensions and still describes massless mode dynamics in the noncompact (space-time) dimensions. Because of nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with nontrivial angular momentum, and with linear dependence between energy and angular momentum.