Dangers of using the growth equation on large scales in the Newtonian gauge

作者：Dent James B^*; Dutta Sourish

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2009, 79(6): 063516.

DOI：10.1103/PhysRevD.79.063516

We examine the accuracy of the growth equation delta+2H delta-4 pi G rho delta=0, which is ubiquitous in the cosmological literature, in the context of the Newtonian gauge. By comparing the growth predicted by this equation to a numerical solution of the linearized Einstein equations in the Lambda CDM scenario, we show that while this equation is a reliable approximation on small scales (k greater than or similar to h Mpc(-1)), it can be disastrously inaccurate (similar to 10(4)%) on larger scales in this gauge. We propose a modified version of the growth equation for the Newtonian gauge, which while preserving the simplicity of the original equation, provides considerably more accurate results. We examine the implications of the failure of the growth equation on a few recent studies, aimed at discriminating general relativity from modified gravity, which use this equation as a starting point. We show that while the results of these studies are valid on small scales, they are not reliable on large scales or high redshifts, if one works in the Newtonian gauge. Finally, we discuss the growth equation in the synchronous gauge and show that the corrections to the Poisson equation are exactly equivalent to the difference between the overdensities in the synchronous and Newtonian gauges.

• 出版日期2009-3