Towards a Modified Generalized Friedmann's Equation of an Anisotropic Universe

General Relativity solved many of the issues of gravity in the Newtonian regime. However, it brought forth its own problem: singularities, points of spacetime where all geodesics end. Their existence strongly implies the incompleteness of General Relativity, which Loop Quantum Gravity aims to resolve. This addition of Quantum Mechanics to General Relativity, in a setting in which the universe expands/contracts, has produced a 'quantum bounce' instead of the infamous Big Bang, which is mathematically encrypted in the modified Friedmann's equation. This result assumes a universe that is homogeneous and isotropic (i.e. same in all positions and directions). However, if the universe's size changes differently in each direction, the behavior of the universe is much harder to model with an equation. To solve this highly complex problem we worked with a slightly simplified model of Bianchi-I LRS spacetime in which two of the directional scale factors and their time evolutions are identical. We find an analytical form of the modified generalized Friedmann equation in this setting which is found to capture the numerical evolution to a high accuracy. Our results fill a long standing gap in understanding of anisotropic models in loop quantum cosmology and lay the foundation of finding similar governing equations in more general settings.