Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections

Marcelo Amaral, Raymond Aschheim, Laurentiu Bubuianu, Klee Irwin, Sergiu Vacaru, Daniel Woolridge (2016)The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic / (super) cluster / filament / polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

arXiv:1611.05295v1 [physics.gen-ph] 7 Nov 2016Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections Marcelo M. Amaral Quantum Gravity Research; 101 S. Topanga Canyon Blvd # 1159. Topanga, CA 90290, USA emails: marcelo@quantumgravityresearch.org Raymond Aschheim Quantum Gravity Research; 101 S. Topanga Canyon Blvd # 1159. Topanga, CA 90290, USA email: raymond@quantumgravityresearch.org Laurenţiu Bubuianu TVR Iaşi, 33 Lascǎr Catargi street, 700107 Iaşi, Romania email: laurentiu.bubuianu@tvr.ro Klee Irwin Quantum Gravity Research; 101 S. Topanga Canyon Blvd # 1159. Topanga, CA 90290, USA email: klee@quantumgravityresearch.org Sergiu I. Vacaru Quantum Gravity Research; 101 S. Topanga Canyon Blvd # 1159. Topanga, CA 90290, USA and University "Al. I. Cuza" Iaşi, Project IDEI 18 Piaţa Voevozilor bloc A 16, Sc. A, ap. 43, 700587 Iaşi, Romania email: sergiu.vacaru@gmail.com Daniel Woolridge Quantum Gravity Research; 101 S. Topanga Canyon Blvd # 1159. Topanga, CA 90290, USA email: dan@quantumgravityresearch.org November 7, 2016 1 Abstract The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theo- ries, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravita- tional and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration func- tions and constants. The coefficients of metrics and connections for such cosmological configu- rations depend, in general, on all spacetime coordinates and can be chosen to generate observ- able (quasi)