There is no real research done on this. However, you should NOT use a memory foam mattress topper for your baby. Why? Because she may suffocate. Unlike normal foam, memory foam is not permeable to air. The structure is just too dense, despite the “open cell” label on some brands, and air cannot flow through a memory foam topper. That means if your baby turns to lie face down on the foam topper, she cannot breathe. Furthermore, she is probably too weak to easily turn herself face up again.
This advice is not just for babies. It holds true for any young child who becomes invalided (temporarily or not) through a serious illness. She may be too weak to move, but if through some bad luck, she manages to turn face down on the memory foam mattress pad, she will likely suffocate just like a baby.