
Abstract 
1 
Overview 
2 
From Semiclassical to Stochastic Gravity 

2.1 
The
importance of quantum fluctuations 
3 
The Einstein–Langevin
Equation: Axiomatic Approach 

3.1 
Semiclassical gravity 

3.2 
Stochastic
gravity 

3.3 
Validity of semiclassical gravity 
4 
The EinsteinLangevin
Equation: Functional Approach 

4.1 
Influence action for semiclassical
gravity 

4.2 
Influence action for stochastic gravity 

4.3 
Explicit form of the
EinsteinLangevin equation 
5 
Noise Kernel and Point Separation 

5.1 
Point
separation 

5.2 
Stressenergy bitensor operator and noise kernel 
6 
Metric
Fluctuations in Minkowski Spacetime 

6.1 
Perturbations around
Minkowski spacetime 

6.2 
The kernels in the Minkowski background 

6.3 
The
Einstein–Langevin equation 

6.4 
Correlation functions for gravitational
perturbations 

6.5 
Stability of Minkowski spacetime 
7 
Structure Formation
in the Early Universe 

7.1 
The model 

7.2 
Einstein–Langevin equation for
scalar metric perturbations 

7.3 
Correlation functions for scalar metric
perturbations 

7.4 
Summary and outlook 
8 
Black Hole Backreaction and
Fluctuations 

8.1 
General issues of backreaction 

8.2 
Backreaction on
black holes under quasistatic conditions 

8.3 
Metric fluctuations of an
evaporating black hole 

8.4 
Other work on metric fluctuations but without
backreaction 
9 
Concluding Remarks 
10 
Acknowledgements 

References 

Figures 