Conformal gravity and extensions of critical gravity Academic Article uri icon


  • Higher-order curvature corrections involving the conformally invariant Weyl-squared action have played a role in two recent investigations of four-dimensional gravity: in critical gravity, where they are added to the standard cosmological Einstein-Hilbert action with a coefficient tuned to make the massive ghostlike spin-2 excitations massless, and in a pure Weyl-squared action considered by Maldacena, where the massive spin-2 modes are removed by the imposition of boundary conditions. We exhibit the connections between the two approaches, and we also generalize critical gravity to a wider class of Weyl-squared modifications to cosmological Einstein gravity where one can eliminate the massive ghostlike spin-2 modes by means of boundary conditions. The cosmological constant plays a crucial role in the discussion, since there is then a "window" of negative mass-squared spin-2 modes around AdS 4 that are not tachyonic. We also construct analogous conformal and nonconformal gravities in six dimensions. 2011 American Physical Society.

published proceedings


altmetric score

  • 2.5

author list (cited authors)

  • Lue, H., Pang, Y. i., & Pope, C. N.

citation count

  • 74

publication date

  • September 2011