When I got home tonight I heard on BBC that Obama had retaken the oath of office, again administered by Chief Justice John Roberts. Since Roberts had flubbed it during the inaugguration ceremony. Obama's advisors wanted him to retake the oath just so there could not be complaints that his presidency was illegal. They wanted Obama to say the oath exactly as it is required by the Constitution.
Obama did not use a Bible this time, but did he say "So help me God?" There were only Whitehouse officials and four reporters present. I have not found an online report that answers that. Of course his inclination would be to include it, but since the purpose of the exercise was to get the words just as they are in the Constitution, it's just possible that they did it right.