Initial Conditions on the Lattice

There are three kinds of initial conditions that need to be set for the lattice calculations. The first consists of the homogeneous values of the fields and derivatives. The second consists of the fluctuations of the fields and field derivatives. Finally, in an expanding universe the derivative of the scale factor, or equivalently the Hubble constant, needs to be set. Section 6.3.1 describes the setting of the homogeneous field and derivative components. In section 6.3.2 we derive equations for the field fluctuations and in section 6.3.3 we derive similar expressions for the fluctuations of the derivatives. Section 6.3.4 explains a slight modification of these equations required to preserve isotropy on the lattice. All of the calculations up to this point are done for three dimensional fluctuations. Section 6.3.5 generalizes the results for one and two dimensional lattices. In section 6.3.6 we derive an expression for the initial value of the Hubble constant in physical and program units. Finally section 6.3.7 gives a justification for an approximation used in setting the fluctuations of the derivatives.

Note that while the initializations described here all occur by default, you can choose to override them and use your own initializations in your model file. See section 4.2.2 for more details.

- Homogeneous Field and Derivative Values
- Initial Conditions for Field Fluctuations
- Initial Conditions for Field Derivative Fluctuations
- Standing Waves: Preserving Isotropy
- Initial Conditions in One and Two Dimensions
- The Initial value of the Hubble Constant
- The Adiabatic Approximation

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This documentation was generated on 2008-01-21