The appearance of singularities in any physical theory is an indication that either something is wrong or we need to reformulate the theory itself. Singularities are like dividing something by zero. General relativity is one of those theories plagued by singularities and this problem is in existence because GR deals with universes that are zero in size (infinite densities). However, quantum mechanics suggests that there may be no such thing in nature as a point in spacetime, implying that space time is always smeared out occupying some minimum region. There fore we need a unification of Quantum mechanics with General relativity to resolve the singularity problem.
In
Quantum Gravity in a Nutshell1 I give out several solutions to the singularity problem. These are outlined below;
1. Evidence for Planck stars
2. Evidence for Maximal acceleration and
3. Minimal length
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