Predictions from the logotropic model: the universal surface density of dark matter halos and the present proportion of dark matter and dark energy

TL;DR

The logotropic model offers a unified dark fluid explanation for dark matter and dark energy, predicting a universal halo surface density and a specific ratio of dark energy to dark matter that aligns well with observations.

Contribution

It introduces the logotropic model as an alternative to ΛCDM, predicting universal halo surface density and dark energy-dark matter ratio without free parameters.

Findings

Universal dark matter halo surface density matches observations.

Predicted dark energy to dark matter ratio is close to observed values.

Model's predictions align with current cosmological measurements.

Abstract

The logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130 (2015)] may be an interesting alternative to the $\Lambda$CDM model. It is able to account for the present accelerating expansion of the universe while solving at the same time the core-cusp problem of the CDM model. In the logotropic model, there is a single dark fluid. Its rest-mass plays the role of dark matter and its internal energy plays the role of dark energy. We highlight two remarkable predictions of the logotropic model. It yields cored dark matter halos with a universal surface density equal to $\Sigma_0^{\rm th}=0.01955 c\sqrt{\Lambda}/G=133\, M_{\odot}/{\rm pc}^2$ without free parameter in very good agreement with the observational value $\Sigma_0^{\rm obs}=141_{-52}^{+83}\, M_{\odot}/{\rm pc}^2$. It also predicts the present ratio of dark energy and dark matter to be the pure number $\Omega_{\rm de,0}^{\rm th}/\Omega_{\rm dm,0}^{\rm th}=e=2.71828...$ in very good agreement with the observations giving $\Omega_{\rm de,0}^{\rm obs}/\Omega_{\rm dm,0}^{\rm obs}=2.669\pm 0.08$. Using the measured present proportion of baryonic matter $\Omega_{\rm b,0}^{\rm obs}=0.0486\pm 0.0010$, we find that the values of the present proportion of dark matter and dark energy are $\Omega_{\rm dm,0}^{\rm th}=\frac{1}{1+e}(1-\Omega_{\rm b,0})=0.2559$ and $\Omega_{\rm de,0}^{\rm th}=\frac{e}{1+e}(1-\Omega_{\rm b,0})=0.6955$ in very good agreement with the observational values $\Omega_{\rm dm,0}^{\rm obs}=0.2589\pm 0.0057$ and $\Omega_{\rm de,0}^{\rm obs}=0.6911\pm 0.0062$ within the error bars. These theoretical predictions are obtained by advocating a mysterious strong cosmic coincidence (dubbed "dark magic") implying that our epoch plays a particular role in the history of the universe.