Loop quantum gravity

The main idea behind loop quantum gravity is that spacetime, at it's fundamental level has a discrete and granular structure. Discrete means that space is made of a finite number of points. The building blocks of spacetime would be quanta of space. The proposal is that, at the Planck scale, 10^-35 meters, the scale of quantum gravity: spacetime has an elementary granular structure. The way the quantum state of spacetime is described mathematically is by a structure known as a spin network. A spin network is a graph with edges labeled by numbers. These numbers represent spin. Each quantum state of the geometry of space in loop quantum gravity is represented by a spin network. The idea was introduced by Roger Penrose about 30 years prior to the proposal of loop quantum gravity. Penrose believed that space had to be purely relational. The spin network was elaborated on by Carlo Rovelli and Lee Smolin, who showed that this, is the kind of structure that would naturally arise from a quantization of general relativity. These are representations of spacetime at the quantum scale. 

Loop quantum gravity is a background independent theory. It is not dependent on any preexisting coordinate system to make predictions. A background is the features of the universe that the model does not account for, however, is necessary to define some of it's properties. An example of a background dependent and a background independent theory is Newtonian physics (which is background dependent, as it makes use of the background) and General relativity (which is background independent, as it's geometry is not fixed, however, can evolve).