Cosmological evolution in $f(T,B)$ gravity

For the fourth-order teleparallel $f\left(T,B\right)$ theory of gravity, we investigate the cosmological evolution for the universe in the case of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space. We focus on the case for which $f\left(T,B\right)$ is separable, that is, $f\left(T,B\right) _{,TB}=0$ and $f\left(T,B\right)$ is a nonlinear function on the scalars $T$ and $B$. For this fourth-order theory we use a Lagrange multiplier to introduce a scalar field function which attributes the higher-order derivatives. In order to perform the analysis of the dynamics we use dimensionless variables which allow the Hubble function to change sign. The stationary points of the dynamical system are investigated both in the finite and infinite regimes. The physical properties of the asymptotic solutions and their stability characteristics are discussed.