On the Growth of Perturbations as a Test of Dark Energy
Abstract
The strongest evidence for dark energy comes presently from geometric techniques such as the supernova distance-redshift relation. By combining the measured expansion history with the Friedmann equation one determines the energy density and its time evolution, hence the equation of state. Because these methods rely on the Friedmann equation which has not been independently tested it is desirable to find alternative methods. We show that long-wavelength metric perturbations of a Robertson-Walker spacetime do not provide independent tests of general relativity unless significant shear stress is present on large scales. Assuming that sufficiently large patches of a perturbed spacetime evolve like separate Robertson-Walker universes allows one to reduce the metric, density, and velocity potential perturbations to quadratures. The general solution is given including curvature perturbations, entropy perturbations, and nonzero background curvature. Alternative cosmological-scale tests of gravity are proposed in terms of the constraint equations of general relativity.Keywords
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