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After an extensive introduction to the asymptotic safety approach
to quantum gravity, this thesis explains recent key advances
reported in four influential papers. Firstly, two exact solutions
to the reconstruction problem (how to recover a bare action from
the effective average action) are provided. Secondly, the
fundamental requirement of background independence in quantum
gravity is successfully implemented. Working within the derivative
expansion of conformally reduced gravity, the notion of
compatibility is developed, uncovering the underlying reasons for
background dependence generically forbidding fixed points in such
models. Thirdly, in order to understand the true nature of
fixed-point solutions, one needs to study their asymptotic
behaviour. The author carefully explains how to find the asymptotic
form of fixed point solutions within the f(R) approximation.
Finally, the key findings are summarised and useful extensions of
the work are identified. The thesis finishes by considering the
need to incorporate matter into the formalism in a compatible way
and touches upon potential opportunities to test asymptotic safety
in the future.
After an extensive introduction to the asymptotic safety approach
to quantum gravity, this thesis explains recent key advances
reported in four influential papers. Firstly, two exact solutions
to the reconstruction problem (how to recover a bare action from
the effective average action) are provided. Secondly, the
fundamental requirement of background independence in quantum
gravity is successfully implemented. Working within the derivative
expansion of conformally reduced gravity, the notion of
compatibility is developed, uncovering the underlying reasons for
background dependence generically forbidding fixed points in such
models. Thirdly, in order to understand the true nature of
fixed-point solutions, one needs to study their asymptotic
behaviour. The author carefully explains how to find the asymptotic
form of fixed point solutions within the f(R) approximation.
Finally, the key findings are summarised and useful extensions of
the work are identified. The thesis finishes by considering the
need to incorporate matter into the formalism in a compatible way
and touches upon potential opportunities to test asymptotic safety
in the future.
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