2012 673 under quantum corrections a rule of thumb is

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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 appears. 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 areas. 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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This document was uploaded on 09/28/2013.

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