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Register a new userInfrared-modified gravities and massive gravitons
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V. A. Rubakov INR
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We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz--Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz-violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to interesting phenomenology.
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In a recent paper (arXiv: 0801.4566) it was shown that all global energy eigenstates of asymptotically $AdS_3$ chiral gravity have non-negative energy at the linearized level. This result was questioned (arXiv: 0803.3998) by Carlip, Deser, Waldron and Wise (CDWW), who work on the Poincare patch. They exhibit a linearized solution of chiral gravity and claim that it has negative energy and is smooth at the boundary. We show that the solution of CDWW is smooth only on that part of the boundary of $AdS_3$ included in the Poincare patch. Extended to global $AdS_3$, it is divergent at the boundary point not included in the Poincare patch. Hence it is consistent with the results of (arXiv: 0801.4566).
We reply to the recent criticism by Garriga and Tanaka of our proposal that quantum gravitational loop corrections may lead to a secular screening of the effective cosmological constant. Their argument rests upon a renormalization scheme in which the composite operator $(R sqrt{-g} - 4 Lambda sqrt{-g} )_{rm ren}$ is defined to be the trace of the renormalized field equations. Although this is a peculiar prescription, we show that it {it does not preclude secular screening}. Moreover, we show that a constant Ricci scalar {it does not even classically} imply a constant expansion rate. Other important points are: (1) the quantity $R_{rm ren}$ of Garriga and Tanaka is neither a properly defined composite operator, nor is it constant; (2) gauge dependence does not render a Greens function devoid of physical content; (3) scalar models on a non-dynamical de Sitter background (for which there is no gauge issue) can induce arbitrarily large secular contributions to the stress tensor; (4) the same secular corrections appear in observable quantities in quantum gravity; and (5) the prospects seem good for deriving a simple stochastic formulation of quantum gravity in which the leading secular effects can be summed and for which the expectation values of even complicated, gauge invariant operators can be computed at leading order.
It is shown that modified gravity theories with a Lagrangian composed of the three quadratic invariants of the Riemann curvature tensor are not appropriate. The field equations are either incompatible and/or irregular [like f(R)-gravities], or, if compatible, lead to the linear instability of polarizations relating to the Weyl tensor. A more relevant modification is the frame field theory, namely the best and unique variant of Absolute Parallelism; it has no free parameters (D=5 is a must) and no singularities arising in solutions. I sketch few remarkable features of this theory.
We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n>3. For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partially-massless case, where the duality has been previously discussed in covariant form only at the level of the equations of motion. The nature of the dual graviton is therefore clarified for all values of the mass and of the cosmological constant.
We discovered a chiral enhancement in the production cross-sections of massive spin-2 gravitons, below the electroweak symmetry breaking scale, that makes them ideal dark matter candidates for the freeze-in mechanism. The result is independent on the physics at high scales, and points towards masses in the MeV range. The graviton is, therefore, a warm dark matter particle, as favoured by the small scale galaxy structures. We apply the novel calculation to a Randall-Sundrum model with three branes, showing a significant parameter space where the first two massive gravitons saturate the dark matter relic density.
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