
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 
4 
The
Einstein–Langevin Equation: Functional Approach 

4.1 
Influence action for
semiclassical gravity 

4.2 
Influence action for stochastic gravity 

4.3 
Explicit form
of the Einstein–Langevin equation 
5 
Noise Kernel and PointSeparation 

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 
Discussion 
7 
Structure Formation 

7.1 
The model 

7.2 
The
Einstein–Langevin equation for scalar metric perturbations 

7.3 
Correlation
functions for scalar metric perturbations 

7.4 
Discussion 
8 
Black Hole
Backreaction 

8.1 
The model 

8.2 
CTP effective action for the black
hole 

8.3 
Near flat case 

8.4 
Near horizon case 

8.5 
The Einstein–Langevin
equation 

8.6 
Discussions 
9 
Concluding Remarks 
10 
Acknowledgements 

References 

Footnotes 