We propose a heuristic unification of dark matter and dark ener
gy in terms of a sin
gle “dark fluid” with a lo
gotropic equation of state
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si1.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=d6bae1c67c463a2fee746908ffa2e09e" title="Click to view the MathML source">P=Aln(ρ/ρP), where
ρ is the rest-mass density,
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si2.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=c23014b8ba06f16b83c5b8d77f295aa3">g class="imgLazyJSB inlineImage" height="16" width="144" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si2.gif"> is the Planck density, and
A is the lo
gotropic temperature. The ener
gy density
ϵ is the sum of a rest-mass ener
gy term
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si3.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=392d259dfbbf126ad944f4948424fb28" title="Click to view the MathML source">ρc2∝a−3 mimickin
g dark matter and an internal ener
gy term
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si4.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=802f07233221c69e99bdf6999723cb8a" title="Click to view the MathML source">u(ρ)=−P(ρ)−A=3Alna+C mimickin
g dark ener
gy (
a is the scale factor). The lo
gotropic temperature is approximately
given by
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si5.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=ca80c7bea1c6825e4c505dc44c9ea515" title="Click to view the MathML source">A≃ρΛc2/ln(ρP/ρΛ)≃ρΛc2/[123ln(10)], where
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si6.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=e6ddfc8ca7e7bd9ffa9fbc1e46589eda">g class="imgLazyJSB inlineImage" height="16" width="154" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si6.gif"> is the cosmolo
gical density and 123 is the famous number appearin
g in the ratio
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si7.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=5337850b9f67bc425c5f28ac5fde3cd8" title="Click to view the MathML source">ρP/ρΛ∼10123 between the Planck density and the cosmolo
gical density. More precisely, we obtain
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si238.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=93d6e79a077d5792740e61f565af11a1">g class="imgLazyJSB inlineImage" height="16" width="164" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si238.gif"> that we interpret as a fundamental constant. At the cosmolo
gical scale, our model fulfills the same observational constraints as the ΛCDM model (they will differ in about 25 Gyrs when the lo
gotropic universe becomes phantom). However, the lo
gotropic dark fluid has a nonzero speed of sound and a nonzero Jeans len
gth which, at the be
ginnin
g of the matter era, is about
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si9.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=120f90774c69760a6d8ff216890adc72">g class="imgLazyJSB inlineImage" height="14" width="79" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si9.gif">, in a
greement with the minimum size of the dark matter halos observed in the universe. The existence of a nonzero Jeans len
gth may solve the missin
g satellite problem. At the
galactic scale, the lo
gotropic pressure balances the
gravitational attraction, providin
g halo cores instead of cusps. This may solve the cusp problem. The lo
gotropic equation of state
generates a universal rotation curve that a
grees with the empirical Burkert profile of dark matter halos up to the halo radius. In addition, it implies that all the dark matter halos have the same surface density
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si10.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=a00e5f11fc67b0b31d5c92afd8002664">g class="imgLazyJSB inlineImage" height="16" width="155" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si10.gif"> and that the mass of dwarf
galaxies enclosed within a sphere of fixed radius
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si11.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=5eb7aeaa26808f0e12b69a78b41a6546">g class="imgLazyJSB inlineImage" height="13" width="72" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si11.gif"> has the same value
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si12.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=8a2ebf3b2387d8ab8254058700ff5ef8">g class="imgLazyJSB inlineImage" height="16" width="140" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si12.gif">, in remarkable a
greement with the observations [Donato et al.
[10], Stri
gari et al.
[13]]. It also implies the Tully–Fisher relation
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316301150&_mathId=si13.gif&_user=111111111&_pii=S0370269316301150&_rdoc=1&_issn=03702693&md5=57d5a777a78ef08a366a9738e271b3ba">g class="imgLazyJSB inlineImage" height="19" width="151" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269316301150-si13.gif">. We stress that our model has no free parameter.