Abstract
The warm dark matter (WDM) can be described by a simple and useful model called reduced relativistic gas (RRG). In this work, it is analytically constructed the scalar field actions minimally and non-minimally coupled to gravity, which are equivalent to RRG in the sense they produce the same cosmological solutions for the conformal factor of the metric. In particular, we construct the scalar theory which corresponds to the model of an ultra-relativistic ideal gas of spinless particles possessing conformal symmetry. Finally, the possibility of supplementing our scalar field model for WDM with dynamical dark energy in the form of a running cosmological constant is also considered.
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