Constance Marten and Mark Gordon are held on suspicion of gross negligence manslaughter.
More than 200 police officers using dogs, thermal imaging cameras and drones are continuing their search for a missing baby as fears mount the infant might have come to harm.
The parents, Constance Marten and Mark Gordon, were arrested in Brighton on Tuesday on suspicion of gross negligence manslaughter.
They had been missing for 53 days.
A search for them began when their car was found on fire near Bolton. Police say Ms Marten had recently given birth.
They said the baby may have been born in the back of the vehicle, without a midwife or medical attention.
On Wednesday morning, officers from London Search and Rescue scoured Moulsecoomb Wild Park, around a mile from Stanmer Villas in Brighton where the couple were arrested.
The officers, whose jackets indicated some were dog handlers, searched under sticks and logs close to where the area meets Hollingbury Golf Course.
A uniformed officer was also seen standing at the entrance to the park.
On the previous day, allotments and the golf course were searched. A Facebook Group for the Roedale Valley allotments were told police had broken into every shed on the site in their search for the baby.
Ms Marten, 35, and Gordon – a convicted rapist and registered sex offender – were held on Monday after a member of the public saw them and called the police.
They were initially held on suspicion of child neglect, but were further arrested on suspicion of gross negligence manslaughter.
People charged with the offence could face up to 18 years in prison if found guilty over a death caused by negligent behaviour.
This is different to unlawful act manslaughter, where a prison term can be up to 24 years if someone is proven to have intentionally done something unlawful or dangerous that inadvertently caused death.
The couple remain in custody, but police said they had not provided any further information about the condition or whereabouts of the child.
Police do not know the sex of the baby.
In a statement released by police on Tuesday, Det Supt Lewis Basford urged the public to help with the search and report any potential sightings in Brighton and Newhaven.
He said: “I’d also ask people living in these areas to report any suspicious behaviour or items found in their gardens, outbuildings and sheds, between then and now.
“Equally if you are out walking in these areas and you discover something you think we should know about, please don’t hesitate to contact us, no matter how insignificant it may seem.”
A car belonging to Ms Marten and Gordon, 48, was found on fire on the side of the M61 motorway in Bolton on 5 January.
After their car was found on fire, police said the family left the scene and travelled to Liverpool, Essex, London and East Sussex.
They appeared to have covered their faces when in public, travelling at night and using cash to purchase supplies, in order to avoid being found.
Their home is in Eltham, in south-east London, but they have been living nomadically since September last year – when Ms Marten first started to show signs of pregnancy.
Police have not ruled out that someone could be looking after the baby – though they added this was unlikely.
Det Supt Lewis Basford said the risk to the baby – who is now thought to be about two months old – increased as time went on, particularly while the weather is cold.
He said that police must now “be open to the fact this may not end in the way we would like”.
Police previously said Ms Marten’s inherited wealth may have allowed the couple to remain at large for an extended period.
She is from a privileged background, having lived in a stately home growing up.
She became estranged from her family after meeting 48-year-old Gordon at drama school in 2016.
They believe the baby was alive at the time of the last previous sighting of the family in Newhaven, but little more is known about the family’s movements in the weeks since.
After the pair were found on Monday, Ms Marten’s estranged father Napier Marten told the Independent he felt “immense relief”, though this was “tempered by the very alarming news [her] baby has yet to be found”