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We examine the accuracy of the growth equation $\ddot{\delta} +2H\dot{\delta} - 4\pi G\rho\delta = 0$, which is ubiquitous in the cosmologicalliterature, in the context of the Newtonian gauge. By comparing the growthpredicted by this equation to a numerical solution of the linearized Einsteinequations in the $\Lambda$CDM scenario, we show that while this equation is areliable approximation on small scales ($k\gtrsim $h Mpc$^{-1}$), it can bedisastrously inaccurate ($\sim 10^4% $) on larger scales in this gauge. Wepropose a modified version of the growth equation for the Newtonian gauge,which while preserving the simplicity of the original equation, providesconsiderably more accurate results. We examine the implications of the failureof the growth equation on a few recent studies, aimed at discriminating generalrelativity 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, theyare not reliable on large scales or high redshifts, if one works in theNewtonian gauge. Finally, we discuss the growth equation in the synchronousgauge and show that the corrections to the Poisson equation are exactlyequivalent to the difference between the overdensities in the synchronous andNewtonian gauges.

On the dangers of using the growth equation on large scales in the Newtonian gauge