Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

Quasilocal conservation laws in cosmology: A first look

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

Substanzaktivität. Farbe als prima materia im Andachtsbild der Frühen Neuzeit

In devotional pictures of the Quattrocento by Giovanni di Francesco Toscani, Fra Angelico, Zanobi Strozzi, Benozzo Gozzoli, and Bartolomeo Caporali, floor and wall fields repeatedly appear as non-representational color grounds. They refer to a hitherto rather insufficiently analyzed multi-layered reflection of the design modes of the time. These surfaces only superficially resemble natural stone structures. Rather, they are coloristic protoforms of the pictorial figurations, which is why these color fields, apart from a theological sub-iconography, can also be understood as references to the substrate character of the color. By evoking spiral and snail shapes in addition to completely amorphous spots, they also seem to reflect the processes of rock formation as explored in Albertus Magnus’s De mineralibus. As a fluid matter that can develop spontaneously into any form in the sense of a painterly generatio spontanea, color finally approximates the Aristotelian concept of hylē. This contribution seeks to explore the exciting and dynamic relationship between matter and form in the quattrocentesque devotional picture. The color substance of the amorphous grounds is understood as an activated source material that is transformed into vivid forms by way of the respective artistic technē.

On Bianchi Type VI$$_0$$ Spacetimes with Orthogonal Perfect Fluid Matter

We study the asymptotic behaviour of Bianchi type VI$$_0$$ 0 spacetimes with orthogonal perfect fluid matter satisfying Einstein’s equations. In particular, we prove a conjecture due to Wainwright about the initial singularity on such backgrounds. Using the expansion-normalized variables of Wainwright–Hsu, we demonstrate that for a generic solution the initial singularity is vacuum dominated, anisotropic and silent. In addition, by employing known results on Bianchi backgrounds, we obtain convergence results on the asymptotics of solutions to the Klein–Gordon equation on all backgrounds of this type, except for one specific case.