The 35-year-old actor exchanged vows with Smith in Hawaii on January 4, reported Daily Express.
"She had her hand on her stomach most of the time and looked like she had a little bump," a source said.
Bartha had proposed to Smith last year.
The wedding ceremony did not have more than 20 people, but Reese Witherspoon and her husband Jim Toth attended the nuptial.
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