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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 Ã
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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