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A Fibonacci-like universe expansion on time-scale

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  • Postavaru, Octavian
  • Toma, Antonela

Abstract

The time scale Fibonacci sequences satisfy the Friedmann–Lemaître–Robertson–Walker (FLRW) dynamic equation on time scale, which are an exact solution of Einstein’s field equations of general relativity for an expanding homogeneous and isotropic universe. We show that the equations of motion correspond to the one-dimensional motion of a particle of position F(t) in an inverted harmonic potential. For the dynamic equations on time scale describing the Fibonacci numbers F(t), we present the Lagrangian and Hamiltonian formalism. Identifying these with the equations that describe factor scales, we conclude that for a certain granulation, for both the continuous and the discrete universe, we have the same dynamics.

Suggested Citation

  • Postavaru, Octavian & Toma, Antonela, 2022. "A Fibonacci-like universe expansion on time-scale," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009735
    DOI: 10.1016/j.chaos.2021.111619
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    References listed on IDEAS

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    1. Andrew J. Fleming, 2002. "Plant mathematics and Fibonacci's flowers," Nature, Nature, vol. 418(6899), pages 723-723, August.
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