Brane-world solutions, standard cosmology, and dark radiation

New exact solutions of brane-world cosmology are given. These solutions include an arbitrary constant $C$, which is determined by the geometry outside the brane and which affects the cosmological evolution in the brane-world. If C is zero, then the standard cosmology governs the brane-world as a low-energy effective cosmological theory. However, if C is not zero, then even in low-energy the brane-world cosmology gives predictions different from the standard one. The difference can be understood as ``dark radiation'', which is not real radiation but alters cosmological evolutions. Density of the dark radiation can be both positive and negative, depending on the geometry outside the brane.