1. Tonatiuh Matos http://www. fis. cinvestav. mx/~tmatos/ http://www. iac

2. The nD-Einstein equations with n-2 commuting Killing Vectors Rev. Mex
The nD-Einstein equations with n-2 commuting Killing Vectors Rev.Mex.Fis. 35(1989)208

3. The Ricci Tensor
z = ρ + iς

4. Ricci tensor in matrix notation

5. In vacuum
Implies:

6. Brane Cosmology
Inflation

7. 5D Gravity
Potential Space

8. The corresponding Lie Algebra
Define:
Then:

9. The ansatz
 A=  A( i)
And the Killing equation:

10. Implies

11. The main theorem Rev.Mex.Fis. 38(1992)69

12. WMAP3 Results
Milenium

13. SFDM T. Matos and F. Siddhartha Guzmán. Class. Quant. Grav
SFDM T. Matos and F. Siddhartha Guzmán. Class. Quant. Grav. 17, (2000), L9-L16.
The action:
The metric:

14. The field equations
The Laplacian:

15. The solution
Where M:
Thus:
The space-time metric:

16. The geodesics
The luminous matter contribution
The rotations curves

17. Density Profiles
T. Matos and F. Siddhartha Guzmán. Class. Quant. Grav. 17, (2000), L9-L16.

18. Density Profiles (Harko & Bhomer arXiv:0705.4158)

19. Density Profiles LSB Galaxies

20. Density Profiles LSB Galaxies

21. Density Profiles LSB Galaxies

22. The geodesics again Tonatiuh Matos, F
The geodesics again Tonatiuh Matos, F. Siddhartha Guzman and Dario Nuñez, Phys. Rev. D62(2000)061301(R);
For the metric
The rotations curves implies

23. The Cosmology T. Matos and L. Ureña, Class. Q. Grav
The Cosmology T. Matos and L. Ureña, Class. Q. Grav. 17(2000)L75
Dark Matter:  V0[cosh() –1]
Dark Energy:  , ,
Baryons, Radiation,
Neutrinos, etc.
   0.23
   0.73
b  0.04

24. The Field Equations

25. The Cosmology T. Matos and L. Ureña, Class. Q. Grav. 17(2000)L75

26. Summarizing SFDM model is insensitive to initial conditions
Behaves as CDM
Reproduces all the successes CDM above galactic scales.
Predicts a sharp cut-off in the mass power spectrum
The favored values for the two free parameters
  20 V0  (310-27 Mpl )4  m  eV

27. M  0.1 M2Planck /m If m  10-23 eV M 1012 Mo
Scalar Field Fluctuation = Halo Tonatiuh Matos and F. Siddhartha Guzman, Class.Q. Grav. 18(2001)5055 Miguel Alcubierre, F. Siddhartha Guzmán, Tonatiuh Matos, Darío Núñez, Luis A. Ureña and Petra Wiederhold.. Class.Q. Grav. 19(2002)5017
M  0.1 M2Planck /m
If m  eV
M 1012 Mo

28. Scalar Field Fluctuation = Halo

29. Scalar Field Fluctuation = Halo

30. Scalar Field Fluctuation = Halo

31. Conclusion
The scalar field is a good candidate to be the Dark Matter of the Universe