If you need some money to help you carry out your research on fundamental science questions you may be able to apply for a grant. The FQXi is currently inviting proposals for grants on the “Nature of Time”. This was also the subject of their first essay contest in 2008 and it is curious that they have gone for such a narrow area for their large grants program. Initial proposal are required by June 14th 2010.
They have $2 million to give out but it is not clear where the money comes from. Previous FQXi grants were funded by the John Templeton Foundation. If the “Nature of Time” does not fit your research program you could apply directly to the JTF for a grant under one of their active funding priorities. These include “Quantum Physics and the nature of Reality”, “Foundational Questions in the Mathematical Sciences”, “Culture, Biology and Human Uniqueness”, etc. For these you have to hurry because they want proposals by April 15th.
The catch with any of these grants is that you need to be backed by an institution to be taken seriously, but it could be worth applying even of you are not affiliated to anything. In the past a few independent researchers such as Garrett Lisi have been successful.