The Lorentz Curve Model applied to the Macrocosm and the Microcosm

In the Lorentz curve model (LCM) presented in this paper, the time dependence L(t) of the dark energy and the frequency dependence t(w) of the cosmic proper time can be derived from the three measured values for the current age t0 of our observable universe, for the so-called cosmological ‘constant’ L0 and for the current temperature T0 of the cosmic microwave background radiation (CMB). In the LCM, L(t) follows a first Lorentz curve and t(w) a second Lorentz curve. The inverse function of t(w) gives w(t), i.e. - roughly speaking - the time dependence of the angular frequency of the Planck-distributed CMB. Formulated more precisely, the quantity w(t) indicates where the Planck-distributed CMB reaches its maximum value at the respective cosmic proper time t. This in turn gives rise to e, the shortest unit of time that cannot be further divided, and tmax, which is proportional to the maximum radius of our observable universe. The value for the rest mass mMa of the lightest neutrino results from e and tmax, which can be used not only to calculate the rest masses of all three left-handed neutrinos, but also to explain how large the individual ratios of the three weaker fundamental forces of nature are. In addition, with the help of the value of mMa and within the LCM, a proposal for solving the mass hierarchy problem of elementary particles with rest masses is ventured. The invariant tmax can be expressed not only by the measured values t0, w(t0) = w0 and the invariant e, which is a simple function of the measured values L0 and t0, but also by Sommerfeld's fine structure constant a, the Planck mass mPl, three fundamental particle rest masses, namely mStrange of the strange quark, mEl of the electron and mMa, and by e. In addition to the time dependencies L(t) and w(t), the following time dependencies are derived: T(t), M(t), S(t) and H(t), where T(t) is the time dependent temperature of the CMB, M(t) is the time dependent fermionic total mass of the universe, S(t) is the time dependent total entropy of the universe and H(t) is the time dependent Hubble parameter. With H(t) it is possible to solve the horizon problem of the standard model of cosmology and to calculate the contribution ΩL of the dark energy to the energy balance of the universe normalised to 1. With L(t), M(t), Ṡ(t) = dS(t)/dt, w(t), H(t) and T(t), the ratio of the contribution Ωdm of the so-called dark ‘matter’ to the contribution Ωfe of the total fermionic mass of the universe can be calculated where Ωdm and Ωfe are also normalised to 1. This solves within the LCM, together with the measured value for Ωfe of about 0.049 ± 0.001, the flatness problem of the standard cosmological model. According to the LCM, there is no singularity at the Big Bang. Likewise, according to the LCM, our observable universe is and will not be infinitely large. The LCM combines Einstein's GRT with quantum theory (QT) in a remarkably simple way and shows the structure of the universe by computing the values of the fundamental constants of physics. For L(t) the LCM yields the following result for t >> e in Planck units: L(t) = r(t)·e-2, where r(t) is the time dependent density of the universe and is given by the sum of its fermionic fraction rfe(t) and its bosonic fraction rbos(t).Keywords: Lorentz curve model, Big Bang, dark energy, dark matter, neutrino rest masses, cosmic microwave background radiation, Hubble parameter, fermionic mass of the universe, entropy of the universe, Hawking-like radiation, dynamic universal black hole, mini black holes, horizon problem, flatness problem, mass hierarchy problem, problem of the cosmological constant, the fundamental constants of physics, the time dependent density of the universe.