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Unformatted text preview: B. Modifying general relativity A theory of massive gravity is a theory which propagates a massive spin 2 particle. The most straightforward way to construct such a theory is to simply add a mass term to the Einstein-Hilbert action, giving the graviton a mass m in such a way that GR is recovered as m ! 0. This is a modification of gravity, a deformation away from the elegant theory of Einstein. Since GR is the essentially unique theory of a massless spin 2 degree of freedom, it should be remembered that modifying gravity means changing its degrees of freedom. Despite the universal consensus that GR is a beautiful and accurate theory, there has in recent years arisen a small industry of physicists working to modify it and test these modifications. When asked to cite their motivation, they more often than not point to supernova data (Riess et al., 1998; Perlmutter et al., 1999) which show that the Universe has recently started accelerating in its expansion. If GR is correct, there must exist some dark energy density  $ 10À29 g=cm3 . The simplest interpretation is that there is a constant term à 2 in the Einstein-Hilbert action, which would give  $ MP Ã. To give the correct vacuum energy, this constant has to take 2 the small value Ã=MP $ 10À65 , whereas arguments from quantum field theory suggest a value much larger, up to the order of unity (Weinberg, 1989). It is therefore tempting to speculate that perhaps GR is wrong, and instead of a dark energy component, gravity is modified in the infrared (Deffayet, 2001; Deffayet, Dvali, and Gabadadze, 2002), in such a way as to produce an accelerating universe from nothing. Indeed many modifications can be cooked up which produce these so-called self-accelerating solutions. For example, one well-studied modification is to replace the Einstein-Hilbert Lagrangian with FðRÞ, a general function of the Ricci scalar (Sotiriou and Faraoni, 2008; De Felice and Tsujikawa, 2010), which can lead to self-accelerating solutions (Carroll et al., 2004, 2005). This modification is equivalent to adding an additional scalar degree of freedom. These cosmological reasons for studying modifications to gravity are often criticized on the grounds that they can take us only so far; the small value of the cosmological acceleration relative to the Planck mass must come from somewhere, and the best these modifications can do is to shift the finetuning into other parameters [see Batra et al. (2008) for an illustration in the FðRÞ scalar-tensor case]. While it is true the small number must come from somewhere, there remains hope that it can be put somewhere which is technically natural, i.e., stable to quantum corrections. Some small parameters, such as the ratio of the Higgs mass to the Planck mass in the standard model, are not technically natural, whereas others, such as small fermion masses, are technically natural, because their small values are stable Rev. Mod. Phys., Vol. 84, No. 2, April–June 2012 673...
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