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

Abstract

The logotropic model (Chavanis, 2015) may be an interesting alternative to the ΛCDM 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 Σ0th=0.01955cΛ/G=133M⊙/pc2, without free parameter, in very good agreement with the observational value Σ0obs=141−52+83M⊙/pc2. It also predicts the present ratio of dark energy and dark matter to be the Euler number Ωde,0th/Ωdm,0th=e=2.71828... in very good agreement with the observations giving Ωde,0obs/Ωdm,0obs=2.669±0.08. Using the measured present proportion of baryonic matter Ωb,0obs=0.0486±0.0010, we find that the values of the present proportions of dark matter and dark energy are Ωdm,0th=11+e(1−Ωb,0)=0.2559 and Ωde,0th=e1+e(1−Ωb,0)=0.6955 in very good agreement with the observational values Ωdm,0obs=0.2589±0.0057 and Ωde,0obs=0.6911±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. We review the three types of logotropic models introduced in our previous papers depending on whether the equation of state is expressed in terms of the energy density, the rest-mass density, or the pseudo-rest mass density of a complex scalar field. We discuss the similarities and the differences between these models. Finally, we point out some intrinsic difficulties with the logotropic model similar to those encountered by the Chaplygin gas model and discuss possible solutions.