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In this paper, we compare the scalar field dynamics in axion-like and powerlaw potentials for both positive and negative values of the exponents. We findthat, for positive exponents, both the potentials exhibit similar scalar fielddynamics and it can be difficult to distinguish them at least at the backgroundlevel. Even though the potentials are oscillatory in nature for positiveexponents scaling solutions can be achieved for larger values of the exponentfor which the dynamics can be different during early times. Because of thepresence of this scaling nature there is a turnaround in the values of thescalar field equation of state as we increase the values of the exponent inboth the potentials. This indicates the deviation from the oscillatorybehaviour for the larger values of the exponent. For negative values of theexponent, the dynamics of the scalar field is distinguishable and axion-likepotential can give rise to cosmologically viable tracker solutions unlike thepower law potentials. So, while for positive exponents we may not distinguishthe two potentials for negative exponents the dynamics of the scalar field isdistinguishable.

A comparison between axion-like and power law potentials in cosmological background