2016/06/30 by Subhash Rajpoot, Sergiu I. Vacaru
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Ansatz #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Decoupling (probability) #Geometric flow #Gravitation #Invariant (physics) #Quantum gravity #Scalar (mathematics) #Scale invariance #Spacetime #Supergravity #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.aop.2017.06.016
published as Annals of Physics NY 384 (2017) 20-60 · v3 is accepted to AP NY, updated affiliation, and new references; Authors comments on "text overlap with arXiv:1409.7076 ...": together with [T. Gheorghiu et al. AP NY 369 (2016) 1], we present further developments of the published version of arXiv: 1409.7076 - cited several times, with repeating text and results by A. Kehagias, et al
openalex created_date 2016/07/22 · arxiv created 2017/06/28 · openalex publication_date 2017/07/03 · arxiv updated 2017/10/13 · openalex updated_date 2026/08/05
Models of geometric flows pertaining to R2 scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic to the Kählerian spaces Mn=SU(1,1+k)/U(1)× SU(1+k) as generalizations of the non-supersymmetric analogs with SO(1,1+k)/SO(1+k) manifolds. For curved superspaces with geometric evolution of physical objects, a complete supersymmetric theory has to be elaborated on nonholonomic (super) manifolds and bundles determined by non-integrable superdistributions with additional constraints on (super) field dynamics and geometric evolution equations. We also consider generalizations of Perelman's functionals using such nonholonomic variables which result in the decoupling of geometric flow equations and Ricci soliton equations with supergravity modifications of the R2 gravity theory. As such, it is possible to construct exact non-homogeneous and locally anisotropic cosmological solutions for various types of (super) gravity theories modelled as modified Ricci soliton configurations. Such solutions are defined by employing the general ansatz encompassing coefficients of generic off-diagonal metrics and generalized connections that depend generically on all spacetime coordinates. We consider nonholonomic constraints resulting in diagonal homogeneous configurations encoding contributions from possible nonlinear parametric geometric evolution scenarios, off-diagonal interactions and anisotropic polarization/ modification of physical constants. We also analyze the conditions under which such modified mimetic type theories and solutions reproduce the Starobinsky inflationary models in the double scalar approach.