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Unformatted text preview: under quantum corrections. A rule of thumb is that a small
parameter is technically natural if there is a symmetry that
appears as the small parameter is set to zero. When this is the
case, symmetry protects a zero value of the small parameter
from quantum corrections. This means corrections due to the
small parameter must be proportional to the parameter itself.
In the case of small fermion masses, it is chiral symmetry that
appears, whereas in the case of the Higgs mass and the
cosmological constant, there is no obvious symmetry that
Of course, there is no logical inconsistency with having
small parameters, technically natural or not, and nature may
explain them anthropically (Barrow and Tipler, 1988), or may
just employ them without reason. But as practical working
physicists, we hope that it is the case that a small parameter is
technically natural, because then there is hope that perhaps
some classical mechanism can be found that drives the
parameter toward zero, or otherwise explains its small value.
If it is not technically natural, any such mechanism will be
much harder to ﬁnd because it must know about the quantum
corrections in order to compensate them.
One does not need a cosmological constant problem,
however, to justify studying modiﬁcations to GR. There are
few better ways to learn about a structure, whether it is a car, a
computer program, or a theory, than to attempt to modify it.
With a rigid theory such as GR, there is a level of appreciation
that can be achieved only by witnessing how easily things can
go badly with the slightest modiﬁcation. In addition, deforming a known structure is one of the best ways to go about
discovering new structures, structures which may have unforeseen applications.
One principle that comes into play is the continuity of
physical predictions of a theory in the parameters of the
theory. Surely, we should not be able to say experimentally,
given our ﬁnite experimental precision, that a parameter of
nature is exactly mathematically zero and not just very small.
If we deform GR by a small parameter, the predictions of the
deformed theory should be very close to GR, to the extent that
the deformation parameter is small. It follows that any undesirable pathologies associated with the deformation should
cure themselves as the parameter is set to zero. Thus, we
uncover a mechanism by which such pathologies can be
cured, a mechanism which may have applications in other
Massive gravity is a well-developed case study in the
infrared modiﬁcation of gravity, where all of these points
are nicely illustrated. Purely from the consideration of degrees of freedom, it is a natural modiﬁcation to consider,
since it amounts to simply giving a mass to the particle which
is already present in GR. In another sense, it is less minimal
than FðRÞ or scalar-tensor theory, which adds a single scalar
degree of freedom, because to reach the ﬁve polarizations of
the massive graviton we must add at leas...
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