How does the pericardium improve the efficiency of the heart?

By not interfering. A healthy pericardium is a very flexible, thin tissue that is "just there." it generally serves little purpose, other than to allow the chambers of the heart to expand outwards in a normal fashion, without resistance, as they fill with blood. If pericardium becomes inflamed, thickened or hardened, the heart loses this outward mobility, and pressure rises greatly as the heart tries to fill.