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Quintessential inflation describes a scenario in which both inflation anddark energy (quintessence) are described by the same scalar field. Inconventional braneworld models of quintessential inflation gravitationalparticle production is used to reheat the universe. This reheating mechanism isvery inefficient and results in an excessive production of gravity waves whichviolate nucleosynthesis constraints and invalidate the model. We describe a newmethod of realizing quintessential inflation on the brane in which inflation isfollowed by `instant preheating' (Felder, Kofman & Linde 1999). The largerreheating temperature in this model results in a smaller amplitude of relicgravity waves which is consistent with nucleosynthesis bounds. The relicgravity wave background has a `blue' spectrum at high frequencies and is ageneric byproduct of successful quintessential inflation on the brane.Comment: 9 pages, 5 eps figures. Discussion and one eps figure summarizing the  GB correction to steep brane world inflation added, typos corrected and  references added; final version to appear in PR

Quintessential inflation on the brane and the relic gravity wave background