The argument that dimensionless constants are of the order 1 works well for the theories that have been tested experimentally so far. We don't know the value of

The argument that dimensionless constants are of the order 1 works well for the theories that have been tested experimentally so far. We don't know the value of the cosmological constant. I am not even certain that it is not exactly zero. But it's not dimensionless, it has dimension length^-2, and is usually expressed in the units of Planck's length (currently thought to be 10^-122 I think). If it indeed turns out to be not zero, it is a new fundamental constant, much like the gravitational constant or the speed of light. I didn't not understand your statement about EH action: the cosmological term there has a dimensionless coefficient of the order 1. Are you talking about some effective action, arising from a string theory model?