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We explain dark energy with equipartition theorem in string landscape.
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In this paper we introduce the fractional dark energy model, in which the accelerated expansion of the Universe is driven by a nonrelativistic gas (composed by either fermions or bosons) with a noncanonical kinetic term. The kinetic energy is inversely proportional to the cube of the absolute value of the momentum for a fluid with an equation of state parameter equal to minus one, and whose corresponding energy density mimics the one of the cosmological constant. In the general case, the dark energy equation of state parameter (times three) is precisely the exponent of the momentum in the kinetic term. We show that this inverse momentum operator appears in fractional quantum mechanics and it is the inverse of the Riesz fractional derivative. The observed vacuum energy can be obtained through the integral of the Fermi-Dirac (or Bose-Einstein) distribution and the lowest allowed energy of the particles. Finally, a possible thermal production and fate of fractional dark energy is investigated.
In this paper we study the evolution of cosmological perturbations in the presence of dynamical dark energy, and revisit the issue of dark energy perturbations. For a generally parameterized equation of state (EoS) such as w_D(z) = w_0+w_1frac{z}{1+z}, (for a single fluid or a single scalar field ) the dark energy perturbation diverges when its EoS crosses the cosmological constant boundary w_D=-1. In this paper we present a method of treating the dark energy perturbations during the crossing of the $w_D=-1$ surface by imposing matching conditions which require the induced 3-metric on the hypersurface of w_D=-1 and its extrinsic curvature to be continuous. These matching conditions have been used widely in the literature to study perturbations in various models of early universe physics, such as Inflation, the Pre-Big-Bang and Ekpyrotic scenarios, and bouncing cosmologies. In all of these cases the EoS undergoes a sudden change. Through a detailed analysis of the matching conditions, we show that delta_D and theta_D are continuous on the matching hypersurface. This justifies the method used[1-4] in the numerical calculation and data fitting for the determination of cosmological parameters. We discuss the conditions under which our analysis is applicable.
We study a phenomenological dark energy model which is rooted in the Veneziano ghost of QCD. In this dark energy model, the energy density of dark energy is proportional to Hubble parameter and the proportional coefficient is of the order $Lambda^3_{QCD}$, where $Lambda_{QCD}$ is the mass scale of QCD. The universe has a de Sitter phase at late time and begins to accelerate at redshift around $z_{acc}sim0.6$. We also fit this model and give the constraints on model parameters, with current observational data including SnIa, BAO, CMB, BBN and Hubble parameter data. We find that the squared sound speed of the dark energy is negative, which may cause an instability. We also study the cosmological evolution of the dark energy with interaction with cold dark matter.
We study the decay of gravitational waves into dark energy fluctuations $pi$, through the processes $gamma to pipi$ and $gamma to gamma pi$, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator $frac12 tilde m_4^2(t) , delta g^{00}, left( {}^{(3)}! R + delta K_mu^ u delta K^mu_ u -delta K^2 right)$, so that the recent observations force $tilde m_4 =0$ (or equivalently $alpha_{rm H}=0$). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to $tilde m_4^2$ generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on $tilde m_4^2$ comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable higher-derivative corrections.
An extension to the Einstein-Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, and written by of a vector $S^mu$. Then this torsion model, compliant with the Cosmological Principle, is made dynamical by introducing its quadratic, totally anti-symmetric derivative. The EC Lagrangian then splits up into the Einstein-Hilbert portion and a (mass) term $sim s_0^2$. While for the quintessence model, dark energy arises from the potential, here the kinetic term, $frac{1}{mu^2} dot{s}_0^2$, plays the role of dark energy. The quadratic torsion term, on the other hand, gives rise to a stiff fluid that leads to a bouncing solution. A bound on the bouncing solution is calculated.
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