PostgreSQL : Where is index kept until check point occures ?

In PostgreSQL data is first written to WAL files. When commit is done, data is written to WAL files and then return to client (synchronous commit). When checkpoint reached or WAL buffer becomes full, these WAL files are written to data files. My question is where does the database keep indexes before writing to data files. Assume checkpoint occurs in every 15 min , then in this time window all the data is in WAL files and when user request for data, database read WAL files and provide data. In this time period does WAL also keep indexes ?