# open the input file
open(IN,"file") or die;
#
# open a temporary output file ( you could also use the
# -i "inplace edit feature", see perldoc perlrun )
#
open(OUT,">file.$$") or die;
#
# print the contents of IN to OUT,
# adding your additional line if we
# see $dom as the first chars of the line
# \Q and \E to quotemeta the domain since
# it probably contains metachars like "."
#
while (<IN>) {
    print OUT;
    if (/^\Q$dom\E\s/) {
          print OUT "$user\@$dom\t$user\n";
    }
}
# close both files and overwrite
# IN with OUT via rename().
close IN;
close OUT;
rename("file.$$","file") or die;