On the Quantum Improved Affine Gravity

Improvement of the classical gravity with the running gravitational coupling obtained from asymptotically safe gravity, is a good way of considering the effects of quantum gravity. This is usually done for metric theories of gravity. Here we investigate the effects of such an improvement for pure affine theories of gravity. To motivate the approach, we first consider the effects of quantum improvement on the connection using metric theory and investigate the effects on the causal structure of black hole solution. Next in the framework of Schr\"odinger-Eddington affine theory, the general way of affine improvement is presented and a spherically symmetric solution is obtained and compared with other ways of improvement.