Abstract
One way to account for the acceleration of the universe is to modify general relativity, rather than introducing dark energy. Typically, such modifications introduce new degrees of freedom. It is interesting to consider models with no new degrees of freedom, but with a modified dependence on the conventional energy-momentum tensor; the Palatini formulation of f(R) theories is one example. Such theories offer an interesting testing ground for investigations of cosmological modified gravity. In this paper we study the evolution of structure in these ‘modified-source gravity’ (MSG) theories. In the linear regime, density perturbations exhibit scale dependent runaway growth at late times and, in particular, a mode of a given wavenumber goes nonlinear at a higher redshift than in the standard lambda-cold dark matter (ΛCDM) model. We discuss the implications of this behaviour and why there are reasons to expect that the growth will be cut off in the nonlinear regime. Assuming that this holds in a full nonlinear analysis, we briefly describe how upcoming measurements may probe the differences between the modified theory and the standard ΛCDM model.
Highlights
The concordance cosmological model describes a universe consisting of approximately5% ordinary matter, 25% dark matter, and 70% dark energy
Given the mysterious nature of dark matter and dark energy, and the fact that their existence is inferred exclusively through their gravitational effects, it is natural to wonder whether the apparent need for these components could be a sign that gravity is deviating from conventional general relativity (GR) on large scales
Dynamical measurements that are taken to imply the existence of dark matter generally refer to length scales of kiloparsecs or greater, while evidence for dark energy comes from the acceleration of the universe, a phenomenon characteristic of the present
Summary
The concordance cosmological model describes a universe consisting of approximately. 5% ordinary matter, 25% dark matter, and 70% dark energy. Since we have altered the right-hand side of Einstein’s equation without introducing any new degrees of freedom, it may be possible to account for the acceleration of the universe without dark energy while remaining consistent with conventional tests of GR. This idea has been realized in the form of the Palatini formulation of f (R) gravity. As Flanagan has shown [10], the equations of motion obtained by separately varying the metric and connection in an action of the form (1) leads to a theory with fewer degrees of freedom; there is no propagating scalar, only the massless spin-two graviton of ordinary GR. It is sufficiently difficult to find cosmological alternatives to general relativity that a simple explicit model can be useful in helping to focus efforts to distinguish between modified gravity and sources of dynamical dark energy
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