Stochastic Selection of Cosmological Constant in Chaotic Inflation: A String Theory Landscape Approach

b. Inflaton motion equation with quantum fluctuations:

+3H+V()=(t),(t)(t)=H342(tt)   +3H+V()=x(t),x(t)x(t)=4p2H3d(tt)

2.2 Distribution of L in Landscape

a. Modified Bousso-Polchinski formula:

k=012i=1Nniqi2,niZ k=L021i=1Nniqi2,niZ

b. Anthropic probability: P()exp(242MPl4V())(max)   P()exp(V()24p2MPl4)(LmaxL)

3. Numerical Simulation

3.1 Simulation Protocol

a. Input:

1 Parameter string theory (qi,A,B,a,b)   qi,A,B,a,b) of Calabi-Yau compactification.

2 Stochastic initial conditions for  .