Constance Marten and Mark Gordon have been further arrested on suspicion of gross negligence manslaughter as police search for their missing baby.
A vast outdoor area in Brighton is being searched, and police say the infant could still be alive.
But with no trace and temperatures falling, investigators fear the infant may have "come to harm".
The couple were arrested on Monday - initially on suspicion of child neglect - after being missing for 53 days.
They were held after a member of the public saw them in a shop, and called the police.
They remain in custody, but police said they had not provided any further information about the condition or whereabouts of the child.
The search for Ms Marten and Gordon - a convicted rapist and registered sex offender - began when their car was found ablaze by the side of a motorway on 5 January.