I need a very firm mattress for my injured back. Will it work to put firm mattress on a solid wood platform?

I injured my back more than 20 years ago and arthritis is developing in it causing more pain. Right now I sleep in a recliner because the Serta Posturepedic Set I purchased a few years ago gives me back pain every morning. I am planning on buying a good Sealy Mattress during a current close out sale and I wonder if it will be more firm if it’s not on a box spring.
I don’t want to change the total height of the surface I sleep on very far either and definitely not make it any taller. I have nice drawers under my mattress and box springs and it is the perfect height to stand beside the bed for sexual intercourse which is great for my back in that position.
I have other convenient furniture for other positions that won’t hurt my back also.