Rabbenu Gershom issued a takkana that it’s assur to read someone else’s mail. Included in this ban is looking at any information that a person prefers remain private, e.g. looking at private documents, health or legal records, and credit reports. The prohibition applies even if the person looking at these items does not plan on acting on the information that he sees, but is merely curious, or is interested in finding out what other people think and write about him, etc. Definitely looking in someone’s phone without their reshut is against this issur.
Rambam paskens that one’s personal, private space/property is inviolate and cannot be invaded (Hilkhot Malveh Ve loveh 2:2). A cell phone can and should be seen as someone’s personal space, even if cell phones are metaltelin.