We introduce an ingenious approach to explore cosmological implications of higher-derivative gravity theories. The key novelty lies in the characterization of the additional massive spin-0 modes constructed from Hubble derivatives as an effective density, with the corresponding pressure uniquely determined by energy conservation, while terms with no Hubble derivatives directly alter Friedmann equations. This classification of the Universe high-derivative contributions to Friedmann equations develops insight about their cosmological impacts and is essential for understanding the Universe’s evolution across energy scales. Various examples of higher-derivative gravity theories illustrate the power of this method in efficiently solving Friedmann equations and exploring new phenomena. Using cosmic microwave background and baryonic acoustic oscillations data, we apply this method to assess the observational feasibility of wall-bouncing universes, as predicted by scenarios with, e.g., certain third order modifications to general relativity. These models also provide an inflationary phase without the need to introduce extra scalar fields.

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• Alternative gravity theories
• Cosmology
• Inflation
• Relativistic aspects of cosmology