Emergence of cosmic space and minimal length in quantum gravity: a large class of spacetimes, equations of state, and minimal length approaches

Abstract

We argue that the modified Landau-Raychaudhuri equations should first be analysed in a large class of spacetimes and in dependence on various equations of states, before endorsing any conclusion about (non) singular Big Bang. From the corrected entropy-area law in a large class of metrics, the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) approaches, and various equations of states, the modified Friedmann equations are derived. They are applied on Landau-Raychaudhuri equations in emergence of cosmic space framework from fixed point method. We show that any conclusion about (non) singular Big Bang is simply badly model-dependent, especially when utilizing GUP and MDR approaches, which can not replace a good theory for quantum gravity. We conclude that the various quantum gravity approaches, metrics and equations of state lead to different modifications in Friedmann and Landau-Raychaudhuri equations and thus to different (non) singular solutions for Big Bang theory.