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 Mark Gordon were arrested in Brighton on Monday on suspicion of child neglect after several weeks avoiding the police, but the child was not with them.
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Detective Superintendent Lewis Basford said: “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 at yet.”