Quantum Gravity Effects in Cosmology

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The goal of this proposal is to study quantum gravity effects in the early universe as predicted by loop quantum gravity. Beyond the difficulties related to developing an appropriate mathematical framework, a major obstruction to constructing a successful theory of quantum gravity is that there has been essentially no guidance from experiments or observations like those that played a central role in the development of quantum mechanics. One main objective for this proposal is to start addressing this problem by deriving loop quantum gravity predictions that can realistically be tested by observations of the cosmic microwave background, the faint afterglow of the big bang that has now been measured in incredible detail.******In addition, in general relativity singularities are known to arise in cosmological and black hole space-times, at which point the theory breaks down. It is widely believed that this is an indication that quantum gravity effects should be important in these regions and hopefully remove the singularities. Indeed, this is what has been shown to happen for some simple space-times in loop quantum cosmology, but it is important to determine whether the singularities that arise in more realistic space-times are also resolved by quantum gravity effects. The second objective of this proposal is to answer this question.******To be specific, I will work on two key open problems concerning loop quantum gravity and its cosmological sector. First, I will determine how to encode generic cosmological perturbations within the framework of full loop quantum gravity, and find the equations that govern their dynamics. I will then use these results to compute how loop quantum gravity effects may modify the predictions of general relativity, and compare these predictions to measurements of the cosmic microwave background. Second, I will study in detail the quantum gravity dynamics of a family of space-times, known as Bianchi space-times, that according to the Belinski-Khalatnikov-Lifshitz conjecture may determine quantum gravity effects in a wide range of space-time regions where the curvature becomes very large.******By providing predictions of loop quantum gravity effects in the early universe and giving a quantitative study of potential singularity resolution in a wider family of space-times than before, this project will give new insights into quantum gravity and can be expected to spur further important research in the field.