Applying Fractional Calculus in Cosmology
Details

Call:
PTCERN Call 2022/2

Academic Year:
2022

Domain:
Astroparticle Physics

Supervisor:
Paulo Moniz

CoSupervisor:
Seyed Meraj M. Rasouli

Institution:
Universidade da Beira Interior

Host Institution:
CMAUBI – Centro de Matemática e Aplicações

Abstract:
The research that will eventually be conducted to write a PhD thesis within this proposal involves using a seldom used mathematical technique in high energy physics, but only because the HEP community has not been aware. Otherwise, it has been employed in many domains of physics: e.g. including fractional calculus in atomic or solidstate physics. The possibilities are pretty interesting as far as gravitational settings are concerned. In this proposal, we will investigate (analytically as well as numerically) fractional differential calculus and subsequent equations that generalize wellknown frameworks in gravitational physics. We aim to consider the equations governing early universe either classically or from a quantum (semiclassically) perspective with several fractional derivatives. This may allow making predictions and contrast them to establish which limits or ranges for the fractional derivatives are permitted, given known gravitational data. Fractional quantum gravity is very much in its infancy, and many cases need to be investigated. Please note that, e.g. fractional uses of entropy and similar observables have found a correspondence in Barrow's proposals of entropy as fractal regions within suitable choices of parameters. Moreover, many models can still be established in the classical regime, which may have the ability to overcome the problems associated with standard counterparts. Can it be those gravitational physics, if using fractional calculus, even as phenomenological toy models will provide exciting and intriguing additional questions to address? Such a line is the course of the PhD research program.