Inflation and de Sitter conjectures in 8-dimensional $R+\gamma R^n$ Gravity

In this work, we study two potentials, the single-field and the two-field, from the modified ($R+\gamma R^n$) gravity in D=8 dimensions. From those potentials, we calculate four observable quantities in inflation, including scalar-to-tensor ratio, spectral index, running index and scalar amplitude. Then, we compare them to the experimental data to verify the righteousness of the models. Last but not least, de Sitter conjectures are brought up with these two potentials to investigate that it is possible or not the theory lay in the Landscape of quantum gravity.