# Cosmological Constant on the LHS of Einstein's Field Equation

The cosmological constant seems to be normally described as an energy (repulsive force, Dark Energy) of Space-Time. I was just wondering, if we were to interpret the cosmological constant as being geometrical (i.e. put it on the LHS of the equation), how would it be described. Would it correspond to an exponential increase in the 'stretch' of Space-Time from any given reference frame, or is it more subtle than that?

• Einstein did originally see it as a modification to the LHS. If you think of the GR Lagrangian as a series in R, the cosmological constant is just the first term in the series $R^0$. The physics is the same if its put on the LHS or RHS. May 29, 2015 at 0:39
• @physicsphile The mathematical effect is the same, but the physics of what's causing it is different. With dark energy the cosmological constant is a dynamical effect caused by a uniform filler, under Einstein's original interpretation it is purely kinematic. So the difference is similar to Lorentz's ether vs special relativity. Compared to standard GR one could say that in GR with CC space is 'internally stretchy'. May 29, 2015 at 3:38
• @Conifold I disagree with your ether analogy. The ether is disfavored observationally and theoretically compared to relativity. While in the CC case there is no strong experimental or physical argument that favors the term being on the LHS or RHS of the equation. May 30, 2015 at 2:01
• I'm wondering if there is any the mathematics of the Cosmological Constant can be viewed as the dimensions of spacetime having a natural exponential stretch (i.e. if you lay out a set of rulers and clocks in a line in space, these rulers and clocks will be dilated such that the dilation increases exponentially with the distance from the observer). May 30, 2015 at 17:12