The present invention provides a rubber composition having adequate foamability, uses thereof, a
copolymer contained in the rubber composition, a rubber composition capable of providing a cross-linked foam, which has a low
specific gravity and an excellent shape-retaining property even when the usage of a nonconjugated
polyene is reduced, and a cross-linked rubber and a cross-linked foam, which are produced from the rubber composition. A
copolymer (A) according to the present invention is a
copolymer including structural units derived from
ethylene [A], an α-olefin [B], a nonconjugated
polyene [C-1], in which one carbon-carbon
double bond (C═C) polymerizable with a
metallocene catalyst is present in one molecule, and a nonconjugated
polyene [C-2], in which two bonds of C═C polymerizable with the
metallocene catalyst are present in one molecule, and being synthesized with the
metallocene catalyst, wherein (1) the units derived from the component [B] constitute 10 to 50 percent by mole, (2) the total of the units derived from the component [C-1] and the units derived from the component [C-2] is 1.0 to 6.0 percent by mole, (3) the
molar ratio of the units derived from the component [C-1] to the units derived from the component [C-2] is 75 / 25 to 99.5 / 0.5, (4) [ML (1+4) 100° C.] is 10 to 200, and (5) 50>
activation energy of
fluidization (kJ / mol)>35 is satisfied.