If my line of calculations in my preliminary studies on CDTT theory is correct, then this theory may show when the late-time inflation started. This calculational result is derived from taking a certain form for the curvature scalar being a function of the cosmic time. This form of the curvature scalar takes on singular value not at t=0, rather when t is inversely proportional to the mu-mass parameter in the CDTT theory. Such form is based on the asymptotic form of the CDTT potential and presents that at the said value of t when the curvature scalar is singular the corresponding Hubble parameter approaches a constant (de Sitter form), and if taken to be related to the sqr.rt. of the cosmological constant then using a rough data on such constant, given that the universe is more than 12billionyears old, then the late-time inflation may have started not less than 4billionyears ago as it went to power-law inflation then.
K, thanks... :)