Quantum Fractionary Cosmology: K-Essence Theory

Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann-Lema <^> ss tre-Robertson-Walker (FLRW) model (radiation and inflation-like epochs, for example), appears naturally. In the classical analysis, the kinetic energy of scalar fields can falsify the standard matter in the sense that we obtain the time behavior for the scale factor in all scenarios of our Universe by using the Hamiltonian formalism, where the results are analogous to those obtained by an algebraic procedure in the Einstein field equations with standard matter. In the case of the quantum Wheeler-DeWitt (WDW) equation for the scalar field closed integral, a fractional differential equation of order beta = 2 proportional to/ 2 proportional to-1 is obtained. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; that is to say, when w X is an element of [-0, 1], the order belongs to the interval 1 <= b <= 2, and when wX is an element of[-1, 0), the order belongs to the interval 0 < beta <= 1. The corresponding quantum solutions are also given.

Automated summary

Using a specific quantum K-essence scalar field, we demonstrate the presence of a fractional differential equation in the scalar field variable within the quantum formalism, particularly in certain epochs of the FLRW model. In classical analysis, the kinetic energy of scalar fields can falsify standard matter and provide similar results to the algebraic procedures in the Einstein field equations. The quantum Wheeler-DeWitt equation yields a fractional differential equation with an order proportional to/ 2 proportional to-1, and the corresponding quantum solutions are provided.