English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Models of geometric flows pertaining to $\mathcal{R}^2$ scale invariant(super) gravity theories coupled to conformally invariant matter fields areinvestigated. Related to this work are supersymmetric scalar manifolds that areisomorphic to the K\"{a}hlerian spaces $\mathcal{M}_n=SU(1,1+k)/U(1)\timesSU(1+k)$ as generalizations of the non-supersymmetric analogs with$SO(1,1+k)/SO(1+k)$ manifolds. For curved superspaces with geometric evolutionof physical objects, a complete supersymmetric theory has to be elaborated onnonholonomic (super) manifolds and bundles determined by non-integrablesuperdistributions with additional constraints on (super) field dynamics andgeometric evolution equations. We also consider generalizations of Perelman'sfunctionals using such nonholonomic variables which result in the decoupling ofgeometric flow equations and Ricci soliton equations with supergravitymodifications of the $R^2$ gravity theory. As such, it is possible to constructexact non-homogeneous and locally anisotropic cosmological solutions forvarious types of (super) gravity theories modelled as modified Ricci solitonconfigurations. Such solutions are defined by employing the general ansatzencompassing coefficients of generic off-diagonal metrics and generalizedconnections that depend generically on all spacetime coordinates. We considernonholonomic constraints resulting in diagonal homogeneous configurationsencoding contributions from possible nonlinear parametric geometric evolutionscenarios, off-diagonal interactions and anisotropic polarization/ modificationof physical constants. We also analyze the conditions under which such modifiedmimetic type theories and solutions reproduce the Starobinsky inflationarymodels in the double scalar approach.

On Supersymmetric Geometric Flows and $\mathcal{R}^2$ Inflation From Scale Invariant Supergravity