Hasan Savran explains indexing in Cosmos DB:
In SQL Server you need to pick which columns you like to index, In CosmosDB you need to pick which columns not to index. It’s kind of same thing at the end. You might ask “If everything is indexed and working fine, why do you want me to poke the well running system?” When we compare SQL Server indexes to CosmosDB Indexes, one thing works exactly same. That is the index file size. CosmosDB holds the indexes in a separate file like SQL Server and if we want to index everything, index file size is going to get large. Since we need to pay for the file space in CosmosDB, you might need to pay extra for indexes that you might never use. Also, your updates, inserts and deletes might cost you more Request Units since CosmosDB needs to maintain all the indexes in the background.
There’s just enough difference to make you pay the price if you assume Cosmos DB works just like SQL Server.