A heat-expandable rubber composition includes, in a non-vulcanized state, from 50 to 100 phr of a copolymer based on styrene and butadiene; optionally from 0 to 50 phr of another diene elastomer, such as a polybutadiene or natural rubber; more than 50 phr of a reinforcing filler, such as silica and/or carbon black; between 5 and 25 phr of microparticles of sodium or potassium (hydrogen)carbonate having a median size between 1 and 50 um; and between 2 and 15 phr of a carboxylic acid have a melting point between 60° C. and 220° C., such as citric acid. The composition is useable in a tyre of a vehicle. When the (hydrogen)carbonate and the carboxylic acid are present in the composition at a total content greater than 10 phr, it is possible to significantly reduce tyre noise during running of the vehicle, without adversely affecting a curing rate of the composition.