LED growth lights would probably grow your food if you were on a space flight mission to Mars. They are more compact and more efficient than fluorescent lights, making them perfect for putting out high light intensity in a small space craft. Another advantage is LEDs don't generate much excess heat.
LEDs might also offer an alternative to fluorescents for the average home gardener for these same reasons. Plus they just look cool.
Notice they are only emitting red and blue light. That should work pretty well because that's the colors plants absorb the most from natural sunlight. Notice below how the three main pigments in leaves absorb these wavelengths of light the best.
I'm taking home my office plants for the summer break, so it's a perfect time to experiment. Looking forward to seeing how they grow!