To understand the accelerating universe discovered observationally in 1998, we develop the scalar-tensor theory of gravitation originally due to Jordan, extended only minimally. The unique role of the conformal transformation and frames is discussed particularly from a physical point of view. We show the theory to provide us with a simple and natural way of understanding the core of the measurements, Λobs
for the observed values of the cosmological constant and today’s age of the universe both expressed in the Planckian units. According to this scenario of a decaying cosmological constant, Λobs
is this small only because we are old, not because we fine-tune the parameters. It also follows that the scalar field is simply the pseudo Nambu–Goldstone boson of broken global scale invariance, based on the way astronomers and astrophysicists measure the expansion of the universe in reference to the microscopic length units. A rather phenomenological trapping mechanism is assumed for the scalar field around the epoch of mini-inflation as observed, still maintaining the unmistakable behavior of the scenario stated above. Experimental searches for the scalar field, as light as ∼ 10−9
eV, as part of the dark energy, are also discussed.