Evidence for B-0 ->rho(0)rho(0) decays and implications for the Cabibbo-Kobayashi-Maskawa angle alpha

We search for the decays B-0 ->rho(0)rho(0), B-0 ->rho(0)f(0)(980), and B-0 -> f(0)(980)f(0)(980) in a sample of about 384x10(6) Upsilon(4S)-> B (B) over bar decays collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at Stanford Linear Accelerator Center. We find evidence for B-0 ->rho(0)rho(0) with 3.5 sigma significance and measure the branching fraction B=(1.07 +/- 0.33 +/- 0.19)x10(-6) and longitudinal polarization fraction f(L)=0.87 +/- 0.13 +/- 0.04, where the first uncertainty is statistical, and the second is systematic. The uncertainty on the Cabibbo-Kobayashi-Maskawa quark-mixing matrix unitarity angle alpha due to penguin contributions in B ->rho rho decays is 18 degrees at the 1 sigma level. We also set upper limits on the B-0 ->rho(0)f(0)(980) and B-0 -> f(0)(980)f(0)(980) decay rates.