Cosmology with Higher-Derivative Gravities

TL;DR

The paper develops a systematic framework to study cosmology in higher-derivative gravity by recasting derivative contributions as an effective density $\rho_{\text{eff}}$ and deriving the corresponding pressure $p_{\text{eff}}$ from energy conservation, while terms without $\dot H$ modify the Friedmann equations directly. It analyzes several Lagrangians, including $R^2$, Weyl-squared $C^2$, $R\Box R$, $R^3$, and RGB, showing that scalar (spin-0) modes drive early-universe dynamics while spin-2 Weyl modes leave homogeneous expansion unchanged. The authors test observational feasibility with Planck 2018 and BAO data, finding general consistency with GR in the hot phase and yielding tight bounds on higher-derivative couplings for $R^3$ and RGB, while still allowing inflationary behavior without extra scalar fields. They further show that under slow-roll, higher-derivative terms can produce an inflationary era with $\mathcal N\sim60$, and discuss wall-bounce scenarios, tachyonic instabilities, and the parameter constraints required to respect the thermal history of the Universe. The results offer a clear, scalable method to explore novel cosmological phenomena in higher-derivative gravity and guide future theoretical and observational work.

Abstract

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 various 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 CMB and BAO 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.