A satisfactory theoretical explanation for the current accelerated expansion of the Universe is an open question that indicates the necessity of new physics. Discovered in 1998 using type-Ia supernovae, the acceleration of the Universe is described by a fluid with negative pressure (dark energy, hereafter DE), whose simplest candidate is a cosmological constant ‘Λ’. However, the observed value of the vacuum energy (10¯47 GeV4) is extremely much smaller than any estimate of the zero-point energy of all modes of a field up to a cutoff scale. The lack of a good explanation for the origin of ‘Λ’ and its smallness leads to the search of alternative candidates, such as scalar or vector fields, metastable DE, holographic DE, interacting DE, usage of extra dimensions, among others.
DE has the unusual property that its pressure is negative, thus given the unsolved theoretical issues related to the origin of DE, one may wonder if it can be described by a matter with new properties. In the recent paper, Ricardo Landim introduced the fractional dark energy (FDE) model, in which the accelerated expansion of the Universe is driven by a non-relativistic gas (composed by either fermions or bosons) with a non-canonical kinetic term: an inverse momentum term.
The DE equation of state parameter ‘w’ is simply the power of the inverse momentum term and the resulting energy density ends up mimicking the one of the cosmological constant. The observed vacuum energy can be obtained from the integral of the corresponding Fermi-Dirac (or Bose-Einstein) distribution with an appropriate lower limit of integration, which is related to the minimum allowed energy of a FDE particle.
This non-canonical kinetic term is the eigenvalue of the inverse momentum operator, in the fractional quantum mechanics (FQM) framework. In this case, the operator is the inverse of the Riesz derivative, which in turn appears in the generalized Schodinger equation.
He also investigated a phenomenological decay of the FDE particles into another non-relativistic particle and showed that the phenomenological decay depends on the volume of the Universe or you can say on the FDE temperature (since V ~ T for w = – 1), which means that after the critical volume, the energy (𝜀 = C/p³) reaches a maximum and stops increasing, thus decaying to another non-relativistic particle. However, DE’s fate can be different if other mechanisms are evoked to avoid an infinite energy.
“When the FDE temperature reaches a critical value (Tc), the decay is turned on. A more detailed explanation of this phenomenon is expected to come from first principles and is subject of study in future work.”— Told Ricardo Landim, author of the study
Featured image: Parameter space in which the abundance of FDE in the non-relativistic regime (ε ∼ m) is equal to the one in the inverse momentum phase (ε ∼ C/p³). The particle is non-relativistic for m ≳ 1 GeV. © Ricardo Landim
Reference: Ricardo G. Landim, “Fractional Dark energy”, ArXiv, pp. 1-8, 23 Mar, 2021. https://arxiv.org/abs/2101.05072
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