By Ruiz-Lapuente P. (ed.)

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2000), one 22 Dark energy, gravitation and the Copernican principle considers beside the five-dimensional Einstein–Hilbert a four-dimensional term induced on the brane S= M52 2 R¯5 |g¯5 | d5 x + M42 2 R4 |g4 | d4 x. 25) There is a competition between these two terms and the five-dimensional term dominates on scales larger than rc = M42 /2M53 . The existence or absence of ghost in this class of models is still under debate. 2). As a conclusion, higher-dimensional models offer a rich variety of possibilities among which some may be relevant to describe a modification of general relativity on large scales.

The only viable such modification arises from βR 2 , which introduces a massive spin-0 degree of freedom. , 1996; Tomboulis, 1996) contain a massive spin-2 ghost. 3. A possibility may be to consider models designed such that their second-order expansion never shows any negative energy kinetic term. As recalled in EspositoFarèse and Bruneton (2007) and Woodard (2006), these models still exhibit instabilities, the origin of which can be related to a theorem by Ostrogradsky (1850) showing that their Hamiltonian is generically not bounded from below.

In that sense the CDM model is very economical since it reproduces all observations at the expense of a single new constant. 4 Beyond the Copernican principle As explained above, the conclusion that the cosmic expansion is accelerating is deeply related to the Copernican principle. Without such a uniformity principle, the reconstruction of the geometry of our spacetime becomes much more involved. 2 Modifying the minimal CDM 29 t r km um z+dz z Fig. 3. Left: Most low-redshift data are localized on our past light-cone.

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