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

Abstract

Models of geometric flows pertaining to ${\mathcal{R}}^2$ 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 ${\mathcal{M}}_n=SU(1,1+k)/U(1)\times SU(1+k)$ 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 $R^2$ 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.

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

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Cited by in corpus (14)

• Recovering a MOND-like acceleration law in mimetic gravity
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity
• Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems
• New evidence and analysis of cosmological-scale asymmetry in galaxy spin directions
• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Classical and quantum geometric information flows and entanglement of relativistic mechanical systems
• Geometric Flow of Bubbles
• Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
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• Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows