Cosmological perturbations in the Λ CDM-like limit of a polytropic dark matter model

It has recently been proposed that both dark matter (DM) and dark energy (DE) can be treated as a single component when they are considered in the context of a polytropic DM fluid with thermodynamical content. Depending on only one free parameter, that is, the polytropic exponent, -0.103 ⌈ ≤ 0, this unified DM model reproduces the distance measurements performed with the aid of the supernovae Type Ia (SNe Ia) standard candles to high accuracy. It avoids the age problem and the coincidence problem, meaning that it allows interpreting not only when, but also why the Universe so recently transited from deceleration to acceleration. However, a critical problem still remains that the polytropic DM model is also required to solve, that is, it needs to demonstrate its compatibility with current observational data on structure formation. We begin to untie this knot here by discussing the evolution of cosmological perturbations in the ACDM-like (i.e., ⌈ = 0) limit of the polytropic DM model. The corresponding results are quite encouraging because this model reproduces every major effect known from conventional (i.e., pressureless cold dark matter - CDM) structure formation theory, such as the constancy of metric perturbations in the vicinity of recombination and the (late-time) Meszaros effect on their rest-mass density counterparts. The non-zero (polytropic) pressure, on the other hand, drives the evolution of small-scale velocity perturbations along the lines of the root-mean-square velocity law of conventional statistical physics. As a consequence, peculiar velocities in this model slightly increase instead of being redshifted away by cosmic expansion. This result might comprise a convenient probe of the polytropic DM model with - = 0. Even more importantly, however, upon consideration of scale-invariant metric perturbations, the spectrum of their rest-mass density counterparts exhibits an effective power-law dependence on the (physical) wavenumber, kph, of the form κ , with the associated scalar spectral index, n , being equal to n = 0.970. This theoretical value reproduces the corresponding observational Planck result, that is, n = 0.968 ±; 0.006.