Dark Energy and Superfluid Cosmology

and radiation $R$ such that we have $\Omega = \frac{3H_0^2}{8\pi G} + \frac{M_{a0}}{a^3} + \frac{R_{a0}}{a^4}$; (2.14) so that $\Omega + \Omega_M + \Omega_R + \Omega_K = 1$; (2.15) where $\Omega_K = \frac{k}{a_0^2 H_0^2}$. 2.3 A revisitation of dark energy Given the experimental observations and preliminary mathematical analyses, the possible physico-mathematical solutions proposed to explain the existence of dark energy can be summarized as follows[18]: 1. There exists a cosmological constant that acts in an anti-gravitational sense leading to an accelerated expansion of the Universe. This is a simple solution, but no real physical motivation beyond pure and simple experimental observation justifies its introduction. 2. The vacuum has a non-zero energy charge. Mathematically this is a solution equivalent to the cosmological constant, certainly would be motivated, as well as experimentally by the Casimir effect. However, every attempt to estimate this energy with the classical techniques of Quantum Field Theory has led to errors of many orders of magnitude. 3. Existence of scalar fields that have led to a period of cosmic acceleration. Among these theories falls the theory of inflation. 4. A new gravitational physics far from General Relativity.³ Which mathematically is equivalent to asking again for the non-zero existence of a cosmological constant. From a certain point of view, both points 2 and 3 are in the direction of an investigation of the superfluidity of space-time. In fact, the works of Klinkhamer[24] and Volovik[7] start from the microscopic investigation of the vacuum based on the analogy of superfluid $^3He$, while the works of Huang et al[6] are in the direction of introducing a complex scalar field responsible for cosmic acceleration and which makes the vacuum superfluid. In particular, Huang[4] has shown that by inserting a complex scalar field with a potential given by: $$V(\phi) = c_a^3 M(\alpha, \beta, z)^{-1/2}|\phi|^2 - \frac{1}{2}\varepsilon_0^2 a^2 |\phi|^2 - 1; \quad (2.16)$$ where $M(\alpha,\beta,z)$ is the Kummer function given by: $$M(\alpha,\beta,z) = \sum_{n=1}^{\infty} \frac{\Gamma(\alpha+n)}{\Gamma(\alpha)} \cdot \frac{\Gamma(\beta)}{\Gamma(\beta+n)} \cdot \frac{z^n}{n!}; \quad (2.17)$$ with $\Gamma(0) = 1$ and $\Gamma(n) = (\alpha+1)\cdots(\alpha+n-1)$, it is possible to proceed with a numerical integration to obtain an evolution of the Hubble constant given by: $$H \propto h_0 t^{-p}; \quad (2.18)$$ and an evolution of the scale factor: $$a(t) \propto \exp(t^{1-p}), \quad 0 < p < 1; \quad (2.19)$$ compatible with an acceleration of the expansion of the Universe caused by dark energy. 2.4 Dark matter and superfluid dynamics A galaxy in the cosmic superfluid can be modeled as a vortex that therefore drags with it part of the superfluid forming a halo that can be gravitationally perceived as dark matter. Suppose that the superfluid interacts with matter according to a coupling constant $\lambda$, and let $\omega$ denote the angular velocity of the galaxy and $r$ the distance from the center. Then in the Newtonian limit the nonlinear Klein-Gordon equation can be written as: $$\square\phi(1-2U) + \nabla^2\phi + \dot{U}\dot{\phi} + \nabla U \nabla \phi - \frac{m^2c^2}{\hbar^2}\phi - \frac{F_0^2}{\hbar^2}(i\dot{\phi} + \omega r \nabla \phi) = 0; \quad (2.20)$$ where the gravitational potential $U$ is given by: $$U(x) = -G\int \frac{\rho_{gal}+\rho_s d^3y}{|x-y|}; \quad (2.21)$$ Figure 2.5: Simulation of the evolution of two galaxies. Numerical simulation of the evolution of two colliding galaxies in a 2D superfluid. The galactic halos move in accordance with superfluid dynamics[30]. with the density due to the galaxy given by $\rho_{gal} = M_{galaxy}$ and that of the cosmic superfluid by $\rho_s = |\phi|^2 + \nabla\phi \cdot \nabla\phi + \frac{2m^2c^2}{\hbar^2}|\phi|^2 + F_0^2$. Numerical simulations with $\rho \approx 10^{-35} cm^{-3}$, $F_0 \approx 1.5 \times 10^{27} cm^{-1}$ and $\lambda \approx 3.6 \times 10^{-105}$ have led to results consistent with the dynamics of galaxies in the presence of dark matter as demonstrated by the figures. 3 Energy, space-time and information A crucial element in the cosmological vision outlined in the introduction is that the vortices produced in the superfluid space-time are produced by a Force which ultimately is a Conscious Power that becomes Being-Wisdom-Energy. Such a vision is still very far from being able to find a coherent mathematical systematization according to the current scientific approach. The physics required for such systematization presupposes a notable advancement in the treatment of observer physics to the point of being able to trace back again the fundamental categories of physical thought to the four fundamental ones: space, time, energy and consciousness. Current cosmological research indeed does not take consciousness into consideration, but is orienting itself toward studying the connections between energy, space-time and information. It is clear that information constitutes the ideal candidate to realize a bridge in this type of study insofar as information presupposes a consciousness capable of receiving or producing it and at the same time requires energy to be conserved and transmitted. Research in this field is still at a seminal and highly speculative stage, we want to report here only some insights that seem promising. 3.1 Energy and information Since Brillouin's first writings, information is classified in...