  Higher derivative scalar field theory in curved space-time belongs to the
GLPV theory coupled non-minimally to the Maxwell field is considered. We will
show that the theory admits two independent exact de Sitter solutions in the
FRW background, one driven by the cosmological constant and the other by the
GLPV scalar field. The dynamical system analysis of the theory shows that these
two exact solutions are stable fixed points. Also, cosmological perturbations
over these solutions shows that the cosmological constant based solution is
healthy at linear level but the GLPV based solution suffers from a gradient
instability in the scalar sector. This proves that the cosmological constant is
needed in the GLPV-Maxwell system in order to have a healthy de Sitter
solution.
