Sound Wave in the Backreaction Affected Spacetime in Analogue Gravity Based on Number-Conserving Approach

It is shown that the sound wave in the backreaction affected dynamical spacetime follows the equations for a massive scalar field in a analogue spacetime using number-conserving approach. Even with backreaction, the analogue metric is in the same form to the case without backreaction. The sound velocity, fluid density, and fluid velocity are defined with small correction to include the backreaction effect. Moreover, the modification of classical fluid dynamical equations by the backreaction introduces spacetime dependent mass. For a finite-size homogeneous quasi-one dimensional Bose gas, we find that the backreaction increase the UV divergence of the equal position correlation function. Moreover, in this model, we see that the backreaction increase the correlation in a finite region and decrease the correlation in far region.