An Alternative to Dark Matter?A Cosmological Model of Galaxy Rotation Using Cosmological Gravity Force, F<sub>Λ</sub> (ALW)

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time was developed to determine precise, realistic values for a number of cosmological parameters, such as energy, cosmological constant Λ, curvature of space k, energy density ρΛe, etc. Several starting assumptions were put forth in order to solve these equations. The current version of the model partially explains several of the observed phenomena that raise questions. Numerical application of the model has yielded the following results, among others: Initially, during the Planck era, at the very beginning of Planck time, tp, the universe contained a single photon at Planck temperature and Planck energy in the Planck volume. During the photon inflation phase (before characteristic time ~10-9 [s]), the number of photons increased at each unit of Planck time and geometrical progression ~n3, where n is the quotient of cosmic time over Planck time (t/tp). Then, the primordial number of photons reached a maximum of ~1089, where it remained constant. Such geometric growth in the number of photons can bring a solution to the horizon problem through photon-photon exchange and a photon energy volume that is in phase with that of the universe. The age of the universe in cosmic time that is in line with positive energy conservation (in terms of conventional thermodynamics) and the creation of proton, neutron, electron, and neutrino masses, is ~76 [Gy]. The predicted total mass (p, n, e and n), based on the Maxwell-Juttner relativistic statistical distribution, is ~7 × 1050 [kg]. The predicted cosmic neutrino mass is ≤ 8.69 × 10−32 [kg]. (≤ 48.7 [keVc−2]) if based on observations of SN1987A. The temperature variation of the cosmic microwave background (CMB), as measured by Planck, can be said to be partially due to energy variations in the universe (DE/E) during the primordial baryon synthesis (energy jump from the creation of protons and neutrons), through a process called baryon asymmetry and the Maxwell-Juttner relativistic distribution. In this model, what is usually referred to as dark energy actually corresponds to the energy of the universe that has not been converted to mass, and which acts on the mass created by the mass-energy equivalence principle and the cosmological gravity field, FΛ, associated with the cosmological constant, which is high during primordial formation of the galaxies (<1 [Gy]). A look at the Casimir effect makes it possible to estimate a minimum Casimir pressure and thus determine our possible relative position in the universe at cosmic time 0,1813 (t0/tW = 13,8 [Gy]/76,1[Gy]). Therefore, from the observed age of 13,8 [Gy], we can derive a possible cosmic age of 76,1 [Gy]. That energy of the universe, when taken into consideration during the formation of the first galaxies (< 1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses. Indeed, such residual, non-baryonic energy, when considered in Newton’s gravity equation, adds the term FΛ(r), which can partially explain, without recourse to dark matter, the rotations of some galaxies, such as M33, UGC12591, UGC2885, NGC3198, NGC253, DDO161, UDG44, the MW and the Coma cluster. Today, that cosmological gravity force is in the order of 1026 times smaller than the conventional gravity force. The model predicts an acceleration of the mass in the universe (q ~ −0.986); the energy associated with curvature Ek is the driving force behind the expansion of the universe, rather than the energy associated with the cosmological constant EΛ. An equation to determine expansion is obtained using the energy form of the Friedmann equation relative to Planck power and cosmic time or Planck force acting at the frontier of the universe. Finally, the model partly explains the value a0 of the MOND theory. Indeed, a0 is not a true constant, but depends on the cosmological constant at the time the great structures were formed (~1 [Gy]), as well as an adjustment of the typical mass and dimension of those great structures, such as galaxies. The constant a0 is a different expression of the cosmological gravity force as expressed by the cosmological constant, Λ, acting through the mass-energy equivalent during the formation of the structures. It does not put in question the value of G.

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