Constance Marten and Mark Gordon have been further arrested on suspicion of gross negligence manslaughter, police have said.
They were arrested in Brighton on Monday on suspicion of child neglect after being spotted by a member of the public just before 9.30pm.
Police said more than 200 officers were involved in an urgent operation to find their baby and have been searching allotments and woodland in the city.
A helicopter, sniffer dogs and drones are also involved as the area widens to include the South Downs towards Newhaven – where the couple were previously spotted.
It’s believed they had been living rough in a tent and moving frequently to avoid being found.
In an update this afternoon, officers said the couple had also been arrested on suspicion of gross negligence manslaughter.
Marten, 35, and Gordon, 48, were reported missing on 5 January after their car caught fire on the M61, near Bolton.
They were spotted numerous times around the UK in the days that followed, including in Liverpool, Essex, south London and East Sussex.
Concerns about their baby grew as it’s not thought to have had any medical care.
Marten, who is from a wealthy family, is said to have lived an isolated life with Gordon – a convicted sex offender – since 2016.
Met Police Detective Superintendent Lewis Basford said the couple had not yet given them information about the child’s whereabouts – not even its gender.
“We now have to consider the possibility that the baby has come to harm,” he told reporters.
However, he added that they were still focussed on trying to find the baby alive.
Chief Superintendent James Collis, from Sussex Police, said the search area was “extensive” and appealed for people to contact them urgently if they have any information.