In the FRW model with Euclidean 3-space, k=0 in the first Friedmann equation makes the density(times a constant) directly related to the Hubble parameter. The Hubble parameter is the time derivative of the scale factor divided by the scale factor itself. My question is: does a Euclidean geometry of the space, being scale invariant, put any constraint on the nature of the scale factor function a(t)? Wouldn't Euclidean scale invariance indicate that the a(t) function for the flat case could only be linear in t, since the scale invariance of the space(not only of the Friedmann equations like in the general case) and thus of the proper distance invariant makes the scale function of t indifferent to any power of t? DISCLAIMER:I know a linear scale factor ("coasting universe") has been discarded observationally, and if my reasoning was sound it would seem to imply the flat FRW model has been observationally discarded, but I'm not asking about that, so please just concentrate on refuting mathematically my reasoning about distance invariance and how it determines or not a linear scale factor.