Modified gravitational model

Question

In an f(R) gravity model

$$ f(R)=R+\lambda{R_{0}}\left(\left(1+\frac{R^{2}}{R_{0}^{2}}\right)^{-n}-1\right). $$

What are the units of $\lambda$ and $R_{0}$?

Answer 1

By inspecting the equation, you should be able to deduce that

$R_0$ has the same dimensions as $R$ (since you are adding $1$ to $\frac{R^2}{R_0^2}$)

$\lambda$ has no dimensions (since you are adding $R$ to $\lambda R_0$ times some dimensionless term)