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We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach…
We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the…
The Ricci iteration is a discrete analogue of the Ricci flow. We give the first study of the Ricci iteration on a class of Riemannian manifolds that are not K\"ahler. The Ricci iteration in the non-K\"ahler setting exhibits new phenomena.…
We present a set of equations describing the evolution of the scalar-type cosmological perturbation in a gravity with general quadratic order curvature coupling terms. Equations are presented in a gauge ready form, thus are ready to…
Let $N$ be a Riemannian, neutral or Lorentzian $4$-dimensional space form. In this paper, the expressions of the equations of Gauss, Codazzi and Ricci of a space-like or time-like surface in $N$ given in [7] are naturally understood in…
We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential…
A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…
General relativity can be cast as a gauge theory by introducing a tetrad field and a spin-connection. This formalism was extended by replacing the tetrad field with a mixed tensor field independent of the metric tensor in order to develop a…
We calculate renormalized Higgs boson couplings with gauge bosons and fermions at the one-loop level in the model with an additional isospin singlet real scalar field. These coupling constants can deviate from the predictions in the…
The background field equations for homogeneous and isotropic spacetime are derived in conformal scalar-tensor gravity. The background temporal evolution is entirely driven by the dynamical evolution of the scalar field, i.e. particle…
The dynamic status of scalar fields is studied in the Hamiltonian approach to the General Relativity. We show that the conformal coupling of the scalar field violates the standard geometrical structure of the Einstein equations in GR and…
We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov-Hausdorff topology, under a suitable rescaling, to an Einstein metric on the…
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…
This paper undertakes a conceptual re-examination of several foundational elements of cosmology through the lens of spacetime symmetries. A new derivation of the Friedmann-Lema\^itre-Robertson-Walker metric is obtained by a careful…
Using the tool of Hodge-Morrey decomposition of forms, we prove a new decomposition of symmetric rank-2 tensors on Ricci flat manifolds with boundary. Using this we reconstruct a new cosmological perturbation theory that allows for the…
Field theory including Supersymmetry and Bose Fermi Symmetry is an active subject of particle physics and cosmology. Recent and expected observational evidence gives indicators for the creation and destruction of normal and supersymmetric…
On Hermitian manifolds, the second Ricci curvature tensors of various metric connections are closely related to the geometry of Hermitian manifolds. By refining the Bochner formulas for any Hermitian complex vector bundle (Riemannain real…
The field equations in FRW background for the so called C-theories are presented and investigated. In these theories the usual Ricci scalar is substituted with $f(\mathcal{R})$ where $\mathcal{R}$ is a Ricci scalar related to a conformally…
The Weyl-Weinberg-Salam model is presented. It is based on the local conformal gauge symmetry. The model identifies the Higgs scalar field in SM with the Penrose-Chernikov-Tagirov scalar field of the conformal theory of gravity. Higgs…
A cosmological model based on two scalar fields is proposed. The first of these, $\varphi$, has mass $\mu$, while the second, $\chi$, is massless. The pair are coupled through a ``Higgs portal''. First, we show how the model reproduces the…