CAMB: equations and derivations

CAMB uses variables derived from covariant quantities, and the equations (in equations.f90) look superficially different from how sometimes written in the synchronous gauge. There is a symbolic equation notebook (using sympy) giving all the main perturbation equations (there are also Mathematica notebooks by Richard Shaw). The latest line of sight and non-flat integration (plus other things) are covered in the latest paper.

The equations in the form used by CAMB are derived and presented in Antony's thesis, though the notation there is somewhat unconventional, see also the references in the Readme.

The initial conditions, initial power spectrum definition, and some other useful relations are given in the notes.

Older potentially useful resources in Maple 6 text format are (now largely replaced by the symbolic module, symbolic equation notebook above and initial conditions derivation in the series notebook):

• Scalar equations definitions and equations
• Line of sight scalar source term derivation
• Initial conditions - derivation of the 5 regular series solutions for the scalar perturbations
  Note that there is a bug in Maple 7/8- the initial conditions code does not work because dsolve fails. Use Maple 6.
• CMB lensing derivation of lensed correlation function results (.mws file)

There is also a maple file of the scalar perturbation equations in an arbitrary frame here.