Accelerating Expansion of Space-time and Geometry

 I was taking a coursera course on ancient philosophy and especially Stoicism in chapter 5 and found an interesting illustration of a Stoic idea about auxiliary and proximate causes in the context of fate and thought to apply some of it to cosmology. I wonder this;

A CYLINDER PUSHED WILL ROLL IN A STRAIT LINE WHILE A CONE PUSHED WITH THE SAME FORCE WILL CURVE. EINSTEIN'S GENERAL RELATIVITY EQUATIONS AND SOME CIRCUMSTANTIAL EVIDENCE SUGGEST THE UNIVERSE AT SOME STAGE WAS AT A SINGULARITY AND EXPANDED MORE OR LESS UNIFORMLY WITH A HYPERINFLATION FOR AN INSTANT. IT EXPANDED FURTHER FOR BILLIONS OF YEARS AND RECENTLY IS EXPANDING AT AN INCREASING PACE. MY QUESTION IS; COULD THE ACCELERATING EXPANSION BE DUE TO GEOMETRY? IS IT COMPARABLE AFTER A FASHION TO THE DIFFERENCE OF A CYLINDER AND SPHERE GIVEN A PUSH? COULD THE INCREASING PACE OF UNIVERSAL EXPANSION BE A RESULT OF GEOMETRY AND TIME RATHER THAN FORCE? GENERAL RELATIVITY DOES INDICATE THE CURVATURE OF SPACE-TIME.