How to index WHERE (start_date >= '2013-12-15')
You just need to add a B-tree index to the some_date DB field. Partial indexes work, only if you know your query parameters and want to exclude / include particular ranges (http://www.postgresql.org/docs/current/static/indexes-partial.html).

Another alternative is to use table partitioning (http://www.postgresql.org/docs/current/static/ddl-partitioning.html) for the some_date DB field per day or month, so you may exclude huge number of rows easily.