http://arxiv.org/abs/1810.05001
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 $\Lambda CDM$ 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.
H. Shenavar and K. Javidan
Tue, 18 Jun 19
45/73
Comments: The model is discussed in more details. Data analysis of the model will be presented in future. Includes 23 pages and 9 figures
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