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Higher derivative scalar field theory in curved space-time belongs to theGLPV theory coupled non-minimally to the Maxwell field is considered. We willshow that the theory admits two independent exact de Sitter solutions in theFRW background, one driven by the cosmological constant and the other by theGLPV scalar field. The dynamical system analysis of the theory shows that thesetwo exact solutions are stable fixed points. Also, cosmological perturbationsover these solutions shows that the cosmological constant based solution ishealthy at linear level but the GLPV based solution suffers from a gradientinstability in the scalar sector. This proves that the cosmological constant isneeded in the GLPV-Maxwell system in order to have a healthy de Sittersolution.

Cosmology of a higher derivative scalar theory with non-minimal Maxwell coupling