 After moving to the US , Rihanna signed a contract with Def Jam Recordings , and released her debut album Music of the Sun ( 2005 ) . The album was inspired by caribbean music , including soca , dancehall , and reggae , and incorporates dance @-@ pop and R & B. In an interview for MTV , Rihanna said that when she had arrived in the US , she had been exposed to different types of music that she had never heard before , including rock music , which she incorporated into her second studio album , A Girl like Me ( 2006 ) . 
