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#' compute the comoving distance (transverse) [Mpc/h]
#'
#' @param z redshift upper limit
#' @param cosmo cosmological parameter list
#' @param z0 redshift lower limit
#' @param ... pass to integrate() to control integration accuracy.
#' @return Comoving distance from \eqn{z_0(=0)} to \eqn{z} [Mpc/h]
#' @seealso \code{\link{distance.comoving}}
#' @references Equation (16) in [H99]
#'
#' @examples
#' distance.transverse(0.1,parameter.fidcosmo)
distance.transverse <-
function(z, cosmo, z0=0, ...) {
dc <- distance.comoving(z, cosmo, z0=z0)
if (cosmo[['omegaK']] > 0){
parameter.DH * sinh(sqrt(cosmo[['omegaK']])*dc/parameter.DH) /
sqrt(cosmo[['omegaK']])
} else if (cosmo[['omegaK']] < 0){
parameter.DH * sin(sqrt(-cosmo[['omegaK']])*dc/parameter.DH) /
sqrt(-cosmo[['omegaK']])
} else {
dc
}
}
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