Constraints on decaying early modified gravity from cosmological observations

Abstract: Most of the information on our cosmos stems from either late-time observations or the imprint of early-time inhomogeneities on the cosmic microwave background. We explore to what extent early modifications of gravity, which become significant after recombination but then decay towards the present, can be constrained by current cosmological observations. For the evolution of the gravitational modification, we adopt the decaying mode of a hybrid-metric Palatini $f(\mathcal{R})$ gravity model which is designed to reproduce the standard cosmological background expansion history and due to the decay of the modification is naturally compatible with Solar-System tests. We embed the model in the effective field theory description of Horndeski scalar-tensor gravity with an early-time decoupling of the gravitational modification. Since the quasistatic approximation for the perturbations in the model breaks down at high redshifts, where modifications remain relevant, we introduce a computationally efficient correction to describe the evolution of the scalar field fluctuation in this regime. We compare the decaying early-time modification against geometric probes and recent Planck measurements and find no evidence for such effects in the observations. Current data constrains the scalar field value at $|f_{\mathcal{R}}(z=z_{\rm on})| \lesssim 10^{-2}$ for modifications introduced at redshifts $z_{\rm on}\sim(500-1000)$ with present-day value $|f_{\mathcal{R}0}|\lesssim10^{-8}$. Finally, we comment on constraints that will be achievable with future 21~cm surveys and gravitational wave experiments.