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A host of dark energy models and non-standard cosmologies predict an enhancedHubble rate in the early Universe: perfectly viable models, which satisfy BigBang Nucleosynthesis (BBN), cosmic microwave background and general relativitytests, may nevertheless lead to enhancements of the Hubble rate up to manyorders of magnitude. In this paper we show that strong bounds on the pre-BBNevolution of the Universe may be derived, under the assumption that dark matteris a thermal relic, by combining the dark matter relic density bound withconstraints coming from the production of cosmic-ray antiprotons by dark matterannihilation in the Galaxy. The limits we derive can be sizable and apply tothe Hubble rate around the temperature of dark matter decoupling. For darkmatter masses lighter than 100 GeV, the bound on the Hubble-rate enhancementranges from a factor of a few to a factor of 30, depending on the actualcosmological model, while for a mass of 500 GeV the bound falls in the range50-500. Uncertainties in the derivation of the bounds and situations where thebounds become looser are discussed. We finally discuss how these limits applyto some specific realizations of non-standard cosmologies: a scalar-tensorgravity model, kination models and a Randall-Sundrum D-brane model.Comment: 19 pages, 15 figures, LaTex, uses revtex

Constraining pre-big-bang nucleosynthesis expansion using cosmic antiprotons