Quantum Turbulence and Universal Cavitation in Cosmological Superfluids

From (1.15) the critical distance for vortex reconnection is inversely proportional to velocity, i.e. $\propto 1/v$.

4.2 Cosmological equations in case of quantum turbulence

To model a Universal Cavitation phenomenon in the cosmological superfluid we must introduce the following variables with the following equations of motion:

A complex scalar field $\Psi = F(x)e^{i\Phi(x)}$ that represents the wave function of the superfluid.
The density of vortex lines in space $\ell(t)$ whose evolution is regulated by Vinen's equation in (4.2) and which in the Robertson-Walker metric becomes (4.3) $\dot{\ell} = 3H\ell + A\ell^{3/2} - B\ell^2$.
The scale factor $a(t)$ coming from the Robertson-Walker metric defined in (2.7) with equations of motion regulated by Einstein's equations in (2.6) where the momentum-energy Tensor must be derived considering the modulus of the scalar field $T_F$, the momentum energy given by the vortex system $T_\ell$ and the ordinary momentum energy $T_m$ given by the sum of the contributions of matter, radiation and vacuum energy, i.e. $T_{tot} = T_F + T_\ell + T_m$. (4.7)
Matter density $\rho_m$ regulated by the identity $DT_{tot} = 0$.

Having made these premises, defining the energy density $\rho$ from the contributions of matter, scalar field and vortices according to

$$\rho = \rho_\Phi + \rho_v + \rho_m; \quad (4.8)$$

and the pressure $p$ as

$$p = p_\Phi + w_0\rho_m; \quad (4.9)$$

where $w_0$ takes values $-1, 0, 1/3$ in the three cases of vacuum energy, pressureless particles and radiation, we obtain the following cosmological equations that replace Friedmann's in (2.11) and (2.12)[30]

$$\dot{H} = -\frac{\kappa}{2} - \frac{\kappa}{a^2}(\rho + p); \quad (4.10)$$ $$\ddot{F} = -3H\dot{F} - \frac{F}{v^2} - \frac{1}{2}\frac{\partial V}{\partial F}; \quad (4.11)$$ $$\dot{\rho}_v = -3H\rho_v + 3^{3/2}\ell_v - 2\ell_v; \quad (4.12)$$

to which must be added the constraint

$$H^2 + \frac{\kappa}{a^2} - \frac{2\kappa\rho}{3} = 0: \quad (4.13)$$

4.3 Astronomical observations

Seeking observational confirmations on the superfluid constitution of spacetime we can turn to the observation of non-thermal emission filaments present in the Galaxy. These photons observed by the Very Large Array[48] do not come from any thermal emission and the origin of this emission is still partially unknown. From figure 4.2 it is hypothesizable to think of the origin of these filaments as produced by quantized vortex lines orthogonal to the rotation plane of the Galaxy. This suggestive observation would confirm the hypothesis of a superfluid spacetime in which the Galaxy would orbit like a 3D vortex.

Another possible experimental confirmation could come from the analysis of particular voids in galactic distributions[49] as in figure 4.4 that recall matter distributions coming from the superposition of quantized vortices in a superfluid.

5 Universal evolution

Starting from E. Schrödinger's ideas[50] in 1943, the idea is currently widespread that one of the elements that discriminate organisms with respect to mechanisms is the local violation of the second law of thermodynamics[53]. Organisms are in fact characterized by a local negentropy or syntropy, with respect to mechanisms that are characterized by a continuous increase in the entropy of the system. This is due to the fact that organisms cannot in any way be considered an isolated system. Indeed, one of the three fundamental characteristics that characterize a living being together with evolution and reproduction is metabolism which presupposes a dynamic exchange with a larger system in which the organism lives.

In all processes sustained and stably at negative entropy, a principle is evident which is that of finality. For example, the nutrients that circulate in maternal blood actually go to form precisely the structure of the unborn child. The material configuration of the eyes is extremely particular and manifests the purpose or end of vision and is the current result of a long evolution. An evolution is only possible when a purpose or objective of evolution[54] and a source of free energy to be able to operate this evolution[53] are present. In the case of life on Earth, the evolution of all...