It is known that Einstein equations can be derived from the proportionality between entropy and horizon area. However, it is also known that when quantum gravity effects are considered, a correction to the entropy logarithmic in horizon area appears.
Here, I will present quantum modified gravitational dynamics implied by this corrected entropy and discuss its main features. Furthermore, I will outline the application of the modified dynamics to cosmology, suggesting the replacement of the Big Bang singularity by a regular bounce.