Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied - Daniel L. Canedo; Paulo Moniz; Gil Oliveira-Neto (Fractal and Fractional, 2025)
In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant (<semantics>Λ</semantics>), and an ad-hoc potential. We employ the Riesz fractional derivative, which introduces a parameter <semantics>α</semantics>, where <semantics>1<α≤2</semantics>, in the WDW equation. We investigate numerically the tunneling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value of <semantics>α</semantics>, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value <semantics>α=2</semantics> (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for <semantics>Λ</semantics> (in a non-fractional conventional set-up) versus balancing, e.g., both <semantics>Λ</semantics> and <semantics>α</semantics> in the fractional framework.