Aspects of quadratic gravity
Abstract
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spintwo tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or antide Sitter, or by changing the longdistance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string or Mtheory. We demonstrate that string theory on noncompact $CY_3$ manifolds, like a line bundle over $\mathbb{CP}^2$, may indeed lead to gravity dynamics determined by a higher curvature action.
 Publication:

Fortschritte der Physik
 Pub Date:
 February 2016
 DOI:
 10.1002/prop.201500100
 arXiv:
 arXiv:1505.07657
 Bibcode:
 2016ForPh..64..176A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 24 pages, 2 figures, revised version contains additional references plus corrected typos