Fractional Einstein-Hilbert Action Cosmology

Abstract

We propose a new type of cosmological model derived from the fractional variational principle when it is applied to the gravitational sector of action functional. In contrast to the fractional cosmological model developed earlier by the author from a fractional total action, in our new model the continuity equation remains valid in its usual form. For this model, a lot of exact solutions are obtained from a specific ansatz which is proposed for the cosmological term in this paper. Several examples arising from the given variations of the Hubble parameter with time are provided. Besides, we suggest an original interpretation of the main equations for our model. It supposes that the effective cosmological term could arise as a result of kinematical induction through the non-zero Hubble parameter. With the help of particular example, we demonstrate how this approach could lead our model quite closer to the real behavior of the universe.

12 pages, 8 figures; some references added

References in corpus (12)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Case for a Positive Cosmological Lambda-term
• Statefinder -- a new geometrical diagnostic of dark energy
• Evolution of the Scale Factor with a Variable Cosmological Term
• Fractal universe and quantum gravity
• Quantum field theory, gravity and cosmology in a fractal universe
• Cosmological Models with Fractional Derivatives and Fractional Action Functional
• A two measure model of dark energy and dark matter
• Fractional Action Cosmology: Emergent, Logamediate, Intermediate, Power law Scenarios of the Universe and Generalized Second Law of Thermodynamics
• Fractional Action Cosmology with Power Law Weight Function
• Interacting dark energy models in fractal cosmology

Cited by in corpus (18)

• Cosmology under the fractional calculus approach
• Testing Fractional Action Cosmology
• Revisiting Fractional Cosmology
• Fractional-order derivatives in cosmological models of accelerated expansion
• Exact solutions and cosmological constraints in fractional cosmology
• Estimated Age of the Universe in Fractional Cosmology
• Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe
• Fractional Scalar Field Cosmology
• Emergence of fractal cosmic space from fractional quantum gravity
• Cosmology with an Effective $\Lambda$-Term in Lyra Manifold
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• Fractional Bosonic Strings
• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• On observational signatures of multi-fractional theory
• Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action
• Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation
• Cosmology of fractional gravity