Pseudo-Scalar Field as a Possible Candidate for Phantom Field

We demonstrate the existence of a single pseudo-scalar (PS) field in the mathematically backed and parity preserving modifications of the standard St${\ddot u}$ckelberg formalism (SSF) in the context of the Lagrangian formulation of the (i) two (1 + 1)-dimensional (2D) massive Abelian 1-form gauge theory, (ii) three (2 + 1)-dimensional (3D) massive Abelian 2-form gauge theory, and (iii) four (3 + 1)-dimensional (4D) massive Abelian 3-form gauge theory. This PS field always turns-up with the (i) negative kinetic term, and (ii) higher order derivative terms. The latter terms are rendered into the well-defined terms due to the imposition of the on-shell condition for the PS field which is derived from the properly gauge-fixed Lagrangian densities for the above theories. These Lagrangian densities incorporate into themselves the (i) PS field with the negative kinetic term, and (ii) pure scalar field with the positive kinetic term. However, both these fields satisfy the Klein-Gordon (KG) equation of motion. The PS field (having the negative kinetic term and a well-defined mass) is one of the possible candidates for the ``phantom'' field which plays a crucial role in the cyclic, bouncing and self-accelerated cosmological models of the Universe. The ``exotic'' PS field also satisfies one of the criteria for being a possible candidate for dark matter