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Critical Gravity in Four Dimensions · Around

2011

Critical Gravity in Four Dimensions

Lu, H., Pope, C. N.

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We study four-dimensional gravity theories that are rendered renormalisable by the inclusion of curvature-squared terms to the usual Einstein action with cosmological constant.

By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless.
This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "New Massive Gravity" with a cosmological constant, in three dimensions.
We find that the on-shell energy for the remaining massless gravitons vanishes.

Built on

K.S. Stelle, Renormalization of higher derivative quantum gravity
1977
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K.S. Stelle, Classical gravity with higher derivatives
1978
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S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories
1982
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L.F. Abbott and S. Deser, Stability of gravity with a cosmological constant
1982
Earlier work this paper cites.
D.G. Boulware, G.T. Horowitz and A. Strominger, Zero energy theorem for scale invariant gravity
1983
Earlier work this paper cites.

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Then

D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point
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2008
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Y. Liu and Y.W. Sun, Note on new massive gravity in AdS 3 ,
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