We consider an $f(Q,T)$ type gravity model in which the scalar non-metricity $Q_{αμν}$ of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $w_μ$. The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function $f(Q,T)$, and we compare the predictions of the theory with the standard $Λ$CDM model.
We introduce a new Weyl-invariant and generally-covariant vector-tensor theory with higher derivatives. This theory can be induced by extending the mimetic construction to vector fields of conformal weight four. We demonstrate that in gauge-invariant variables this novel theory reduces to the Henneaux-Teitelboim description of the unimodular gravity. Hence, compared with the standard general relativity, our new higher derivative vector-tensor theory has only one new global degree of freedom - the cosmological constant. Finally we discuss potential extensions of this vector-tensor theory.
We discuss the cosmological evolution of the Weyl conformal geometry and its associated Weyl quadratic gravity. The Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity; this happens after the Weyl gauge field ($ω_μ$) of scale symmetry, that is part of the Weyl geometry, becomes massive by Stueckelberg mechanism and then decouples. This breaking is a natural result of the cosmological evolution of Weyl geometry, in the absence of matter. Of particular interest in the analysis is the special limiting case of Weyl integrable geom…
These are lectures for students at the summer school conducted by the Faculty of Fundamental Sciences, Bauman Moscow State Technical University at 2022.
We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gau…
We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-aether theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.
We apply singularity analysis to investigate the integrability properties of the gravitational field equations in Weyl Integrable Spacetime for a spatially flat Friedmann--Lemaître--Robertson--Walker background spacetime induced with an ideal gas. We find that the field equations possess the Painlevé property in the presence of the cosmological constant and the analytic solution is given by a left Laurent expansion.
We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic …
We consider a non-minimally coupled curvature-matter gravity model (NMC) with a Weyl connection, a theory referred to as non-minimally coupled Weyl connection gravity (NMCWCG). The Weyl connection is an affine connection that is not compatible with the metric, and involves a vector field. Assuming a vacuum expectation value for the vector field and a matter Lagrangian that only contains the contributions of the vacuum energy, we show that the model admits solutions in the space-form with a reference curvature that can be fine-tuned to much smaller values than the contribution of the matter fie…
In this work, we study the issue of the past and future cosmological singularities in the context of the fourth-order conformal Weyl gravity. In particular, we investigate the emergent universe scenario proposed by Ellis {\it et al}, and find the stability conditions of the corresponding Einstein static state using the fixed point approach. We show that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable emergent states for an FRW universe with both the positive and negative spatial curvatures. This represents that…
The standard electroweak theory of leptons and the conformal groups of spacetime Weyl's transformations are at the core of a general relativistic, conformally covariant scalar tensor theory aimed at the resolution of the most intriguing enigma of modern Physics: the cosmological constant paradox (hereafter: Lambda paradox. A Higgs mechanism within a spontaneous symmetry breaking process offers formal connections, via an effective potential V(eff), between some relevant properties of the elementary particles and the dark energy content of the Universe. The nonintegrable application of the Weyl'…
We examine the Weyl double copy relation for vacuum solutions of the Einstein equations with a cosmological constant using the approach we previously described, in which the spin-1/2 massless free-field spinors (Dirac-Weyl fields) are regarded as basic units. Based on the exact non-twisting vacuum type N and vacuum type D solutions, the finding explicitly shows that the single and zeroth copies fulfill conformally invariant field equations in conformally flat spacetime. In addition, irrespective of the presence of a cosmological constant, we demonstrate that the zeroth copy connects Dirac-Weyl…
We investigate the cosmological evolution for the physical parameters in Weyl integrable gravity in a Friedmann--Lema\^ıtre--Robertson--Walker universe with zero spatially curvature. For the matter component, we assume that it is an ideal gas, and of the Chaplygin gas. From the Weyl integrable gravity a scalar field is introduced by a geometric approach which provides an interaction with the matter component. We calculate the stationary points for the field equations and we study their stability properties. Furthermore, we solve the inverse problem for the case of an ideal gas and prove that t…
The homogeneous and isotropic cosmological model in the Weyl conformal geometry is considered. We showed that, despite the conformal invariance, the dust matter is allowed in such a universe. It is shown that the number of dust particles is not conserved, i. e., they are continuously produced. The general form of the law for their creation is found.
In the present article, we show that a simple modification to the Einstein-Hilbert action can explain the possibility of mutual interaction between the cosmic fluids. That is achieved considering the Weyl Integrable Spacetime in the background of a nonflat Friedmann-Lemnaître-Robertson-Walker geometry for the universe. We show that widely-known phenomenological interacting cosmological scenarios can naturally appear in this context. We then performed the dynamical system analysis of the underlying cosmological scenario and explored many possibilities extracted from this gravitational theory.
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 the Chern-Simons current instead of the vector field used 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 Lagran…
We consider quadratic gravity with only Ricci squared and Weyl squared kinetic terms at tree-level, coupled to specific numbers of infinite towers of free scalars, Weyl fermions and gauge bosons in four dimensions. We show that predictable cosmological and Newton constants are induced at 1-loop. This result is cross-checked using both the heat kernel method and Adler's approach.
In this thesis, we attempt to gain a more complete insight into Double Layer Theories in Weyl Gravity. In order to do this, we first establish the premise of Weyls Theory, including its provenance, development and flaws. This is all discussed in the first five chapters of the thesis. After having established Weyls Infinitesimal geometry and his gauged (scalar-tensor) gravity theory, we move onto the topic at hand, namely, Double Layers. We define the action to be used and describe the volume of integration (especially the Singular Hyper Surface) across which the action principle is setup. We d…
