Asymptotic safety in the f(R) approximation

Nov, 2012
66 pages
Published in:
  • JHEP 01 (2013) 108
e-Print:
Report number:
  • SHEP-12-26

Citations per year

201220152018202120240510152025
Abstract: (Springer)
In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R > 0. We confront these with the requirement that a fixed point solution be smooth and exist for all R ≥ 0. Singularities induced by cutoff choices force the earlier versions to have no such solutions. However, we show that the most recent version has a number of lines of fixed points, each supporting a continuous spectrum of eigen-perturbations. We uncover and analyse the first five such lines. Sensible fixed point behaviour may be achieved if one consistently incorporates geometry/topology change. As an exploratory example, we analyse the equations analytically continued to R < 0, however we now find only partial solutions. We show how these results are always consistent with, and to some extent can be predicted from, a straightforward analysis of the constraints inherent in the equations.
Note:
  • Latex, 66 pages, published version, typos corrected
  • topology: transition
  • fixed point
  • asymptotic safety
  • quantum gravity
  • gravitation: f(R)