## CAMB: equations and derivations

NEW Mathematica notebooks by Richard Shaw

CAMB uses variables derived from covariant quantities, and the
equations (in equations.f90) look superficially different from those
in CMBFAST using the synchronous gauge. 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. Potentially useful resources
in Maple 6 text format are:

- 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)

The last two files require the first one. The result produced by the
line of sight code differs from that in CAMB only by substitution of
the Friedmann equation. The above code all uses the zero acceleration (CDM) frame, which is equivalent to the synchronous gauge.
The initial conditions, initial power spectrum definition, and some
other useful relations are given in some provisional notes. This is mentioned here just in case it
is useful, even though they are very concise and un-perfected. If you
want to write some better docs do let me know!

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

There is also a separate theory page for vector modes.

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