We perform a detailed comparison between the Logotropic model [ P.H .
Chavanis , Eur .
Phys .
J .
Plus 130 , 130 ( 2015 ) ] and the \Lambda CDM model .
These two models behave similarly at large ( cosmological ) scales up to the present .
Differences will appear only in the far future , in about 25 { Gyrs } , when the Logotropic Universe becomes phantom while the \Lambda CDM Universe enters in the de Sitter era .
However , the Logotropic model differs from the \Lambda CDM model at small ( galactic ) scales , where the latter encounters serious problems .
Having a nonvanishing pressure , the Logotropic model can solve the cusp problem and the missing satellite problem of the \Lambda CDM model .
In addition , it leads to dark matter halos with a constant surface density \Sigma _ { 0 } = \rho _ { 0 } r _ { h } , and can explain its observed value \Sigma _ { 0 } = 141 M _ { \odot } / { pc } ^ { 2 } without adjustable parameter .
This makes the logotropic model rather unique among all the models attempting to unify dark matter and dark energy .
In this paper , we compare the Logotropic and \Lambda CDM models at the cosmological scale where they are very close to each other in order to determine quantitatively how much they differ .
This comparison is facilitated by the fact that these models depend on only two parameters , the Hubble constant H _ { 0 } and the present fraction of dark matter \Omega _ { m 0 } .
Using the latest observational data from Planck 2015+Lensing+BAO+JLA+HST , we find that the best fit values of H _ { 0 } and \Omega _ { m 0 } are H _ { 0 } = 68.30 { km } { s } ^ { -1 } { Mpc } ^ { -1 } and \Omega _ { m 0 } = 0.3014 for the Logotropic model , and H _ { 0 } = 68.02 { km } { s } ^ { -1 } { Mpc } ^ { -1 } and \Omega _ { m 0 } = 0.3049 for the \Lambda CDM model .
The difference between the two models is at the percent level .
As a result , the Logotropic model competes with the \Lambda CDM model at large scales and solves its problems at small scales .
It may therefore represent a viable alternative to the \Lambda CDM model .
Our study provides an explicit example of a theoretically motivated model that is almost indistinguishable from the \Lambda CDM model at the present time while having a completely different ( phantom ) evolution in the future .
We analytically derive the statefinders of the Logotropic model for all values of the logotropic constant B .
We show that the parameter s _ { 0 } is directly related to this constant since s _ { 0 } = - B / ( B + 1 ) independently of any other parameter like H _ { 0 } or \Omega _ { m 0 } .
For the predicted value of B = 3.53 \times 10 ^ { -3 } , we obtain ( q _ { 0 } ,r _ { 0 } ,s _ { 0 } ) = ( -0.5516 , 1.011 , -0.003518 ) instead of ( q _ { 0 } ,r _ { 0 } ,s _ { 0 } ) = ( -0.5427 , 1 , 0 ) for the \Lambda CDM model corresponding to B = 0 .