No abstract

A new equation of motion, which is derived previously by imposing Neumann boundary condition on cosmological perturbation equations (Shenavar 2016 a), is investigated. By studying the precession of perihelion, it is shown that the new equation of motion suggests a small, though detectable, correction in orbits of solar system objects. Then a system of particles is surveyed to have a better understanding of galactic structures. Also the general form of the force law is introduced by which the rotation curve and mass discrepancy of axisymmetric disks of stars are derived. In addition, it is suggested that the mass discrepancy as a function of centripetal acceleration becomes significant near a constant acceleration 2c 1 a 0 where c 1 is the Neumann constant and a 0 = 6.59×10 −10 m/s 2 is a fundamental acceleration. Furthermore, it is shown that a critical surface density equal to σ 0 = a 0 /G, in which G is the Newton gravitational constant, has a significant role in rotation curve and mass discrepancy plots. Also, the specific form of NFW mass density profile at small radii, ρ ∝ 1/r, is explained too. Finally, the present model will be tested by using a sample of 39 LSB galaxies for which we will show that the rotation curve fittings are generally acceptable. The derived mass to light ratios too are found within the plausible bound except for the galaxy F571-8.

The local stability of stellar and fluid discs, under a new modified dynamical model, is surveyed by using WKB approximation. The exact form of the modified Toomre criterion is derived for both types of systems and it is shown that the new model is, in all situations, more locally stable than Newtonian model. In addition, it has been proved that the central surface density of the galaxies plays an important role in the local stability in the sense that LSB galaxies are more stable than HSBs. Furthermore, the growth rate in the new model is found to be lower than the Newtonian one. We found that, according to this model, the local instability is related to the ratio of surface density of the disc to a critical surface density Σ crit . We provide observational evidence to support this result based on star formation rate in HSBs and LSBs.

Wheeler (1964) had formulated Mach's principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion which leads to a modified Poisson equation. In addition, a modified Hubble parameter is derived due to the presence of the new term. Moreover, it is proved that, without a cosmological constant, such model has a late time accelerated expansion with an equation of state converging to w < −1. Also, the luminosity distance in the present model is shown to differ from that of the ΛCDM model at high redshifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation-dominated era and then converges to zero at later times. Theoretical implications of Neumann boundary condition has been discussed and it is shown that by fixing the value of the conjugate momentum (under certain conditions) one could derive a similar version of modified dynamics. In a future work, we will confine the free parameters of the Neumann model based on Type Ia Supernovae, Hubble parameter data and the age of the oldest stars. *