Abstract
Applying the exact renormalization group method to search the non–Gaussian fixed points of gravitational coupling, is frequently followed by two steps: cutoff identification and improvement. Although there are various models for identifying the cutoff momentum by some physical length, saving the general covariance should be considered as an important property in the procedure. In this paper, use of an arbitrary function of curvature invariants for cutoff identification is suggested. It is shown that the field equations for this approach differs from the ones obtained from the conventional cutoff identification and improvement, even for non–vacuum solutions of the improved Einstein equations. Indeed, it is concluded that these two steps are correlated to each other.
Highlights
Finding a consistent quantum gravity theory which fulfills the cornerstones of general relativity and quantum mechanics, simultaneously, is still a big challenge for theoretical physicists
The Weinberg’s asymptotic safety conjecture is able to save the theory from divergences, if its running coupling constants tend to a non–Gaussian fixed point at the UV limit
Exact renormalization group method is a successful method in search for such a non–Gaussian fixed point
Summary
Finding a consistent quantum gravity theory which fulfills the cornerstones of general relativity and quantum mechanics, simultaneously, is still a big challenge for theoretical physicists. To apply the theory to physical phenomena, fully quantum effective action is needed, which is not available This functional renormalization group method is usually followed by two steps: cutoff identification and improvement. Improving the coupling constant of the classical theory to the running one, the quantum corrections of this method at the low energy could be studied. Since these coupled steps could seriously affect the general covariance of the action and the background independence of the theory, they need more studies. The classical action S which is considered as an initial condition is the one with the coupling constant improved to running unspecified one Applying this initial condition to ERGE, ends to multi β–functions which are running couplings’ evolution equations. The improved Friedman equation for a flat cosmological model filled with cosmological constant is studied and the last section is dedicated to a conclusion on this identification method
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