Constance Marten and Mark Gordon have been further arrested on suspicion of gross negligence manslaughter as their baby remains missing.
The aristocrat and her partner were arrested in Brighton on Monday on suspicion of child neglect after several weeks avoiding the police, but the child was not with them.
The couple were detained after a 999 call by a member of the public who had seen media reports about the pair.
Detective Superintendent Lewis Basford said police had to consider the possibility that the child had “come to harm”, given the pair had now been in custody for a “significant period of time”.
The officer said: “We have had a significant period of time in custody facility with both Constance and Mark.
“At this time we have not furthered that information, which has now obviously led to the position where we feel that the risk is getting so great that we now have to consider the possibility that the baby has come to harm.”
He added: “I can confirm that they were initially arrested on suspicion of child neglect.
“I can now confirm that they have been further arrested on suspicion of gross negligence manslaughter and that they remain in custody at police stations in Sussex.
“The baby was not with them, and we have not found the baby as yet.”
The infant was born in early January and has had no medical attention since then, with his parents sleeping rough in freezing temperatures much of the time.
The police search for Marten, 35, and Gordon, 48, began on January 5 when their car was found on fire abandoned next to the M61 in Bolton.
They used taxis to first travel to Liverpool, then Harwich in Essex, and on to east London, before arriving in Sussex on January 8.
The couple avoided detection by only making payments in cash, hiding their faces on CCTV and often moving around at night or in the early hours of the morning.
They were finally arrested at about 9.30pm on Monday.
Marten, who is from a wealthy aristocratic family, was a promising drama student when she met Gordon in 2016.
Since then the couple have led an isolated life, and in September, as Marten’s pregnancy progressed, began moving around rental flats.
Gordon served 20 years in prison in the US for rape and battery committed when he was 14.
It is unknown if their baby was full-term or has any health issues.
