Density Perturbation and Preferential Coordinate Systems in an Expanding Universe

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Abstract
Under general coordinate conditions, the equation for density perturbation in an expanding universe has fictitious solutions. In order to exclude the fictitious solutions automatically, we adopt coordinate systems moving with the average distribution of matter; and we obtain some coordinate conditions which provide for these systems. These contain not only the so-called Lagrangian gauge but also new coordinate conditions. Under these conditions, the equation for spatially periodic density perturbation becomes a second-order differential equation with respect to time and reduces to Bessel's differential equation when the equation of state is of the form p/ε= const (p = pressure, ε= energy density).

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