We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on higher-order
modified gravity, and in particular on: (i) 𝑓(𝐺) Gauss-Bonnet gravity, and 𝑓(𝑃) cubic gravity,
arising respectively through the use of the quadratic-curvature Gauss-Bonnet 𝐺 term, and the
cubic-curvature combination. We perform a detailed investigation of the BBN epoch and we
calculate the deviations of the freeze-out temperature 𝑇𝑓
in comparison to ΛCDM paradigm.
We then use the observational bound on |𝛿𝑇𝑓/𝑇𝑓| in order to extract constraints on the involved
parameters. We find that all models can satisfy the BBN constraints and thus they constitute
viable cosmological scenarios, since they can additionally account for the dark energy sector
and the late-time acceleration, in a quantitative manner, without spoiling the formation of light
elements during the BBN epoch. Nevertheless, the obtained constraints on the relevant model
parameters are quite strong.