Inflation and Fractional Quantum Cosmology

The Wheeler–DeWitt equation for a flat and compact Friedmann–Lemaître–Robertson–Walker cosmology at the pre-inflation epoch is studied in contexts of standard fractional quantum cosmology. Working within semiclassical regime applying Wentzel-Kramers-Brillouin (WKB) approximation, we show that some fascinating consequences are obtained our simple scenario completely different from their corresponding counterparts: (i) conventional de Sitter behavior inflationary universe constant potential replaced by power-law inflation. (ii) non-locality Riesz’s derivative produces inflation depends on fractal dimension spatial section space-time, independent energy scale inflaton.