Well, we must assume that laws of conservations are valid. So there must be something accumulating inside Earth that fuels the growth. Call it dark matter or dark energy or whatever. What is certain is that this thing is very weakly interacting with normal matter, and must have mass/energy and thus responds to the gravity field. That's a bit short to build a physical mechanism, isn't it? That's why I think it is more important to focus on the evidence of the growth as a first step.