A Modified Dynamical Model of Cosmology I Theory

Hossein Shenavar,Kurosh Javidan

doi:10.3390/universe6010001

Abstract

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 a 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 Λ C D M 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 the Neumann boundary condition have 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 hype Ia Supernovae, Hubble parameter data, and the age of the oldest stars.

Highlights

The question of the existence of dark matter and dark energy and their implications at different cosmic scales has been the dominant subject of the contemporary cosmology
Theoretical implications of the Neumann boundary condition have been discussed, and it is shown that, by fixing the value of the conjugate momentum, one could derive a similar version of modified dynamics
One could mention the discussion between de Sitter and Einstein on this matter, which could be considered as the root of relativistic cosmology

Summary

Introduction

The question of the existence of dark matter and dark energy and their implications at different cosmic scales has been the dominant subject of the contemporary cosmology. The main argument in favor of these two components is that their presence would solve some otherwise baffling discrepancies between observations and predictions of general relativity (GR). See References [1,2] These predictions are mostly based on the zero- and first-order perturbation equations of GR field equations. See References [3,4,5,6,7] for reviews on perturbation method in general relativity. The presence of the dark matter particles could explain most notably, among other phenomena, the growth of structures in the universe, the stability of gravitating systems, the rotation curves of spiral galaxies, and the missing mass problem in gravitational lensing. See References [1,8,9]

Objectives

Findings

Discussion

Conclusion