Tonatiuh Matos
http://www.fis.cinvestav.mx/~tmatos/
http://www.iac.edu.mx
The nD-Einstein equations
with n-2 commuting
Killing Vectors
Rev.Mex.Fis. 35(1989)208
The Ricci Tensor
• z = ρ + iς
Ricci tensor in matrix
notation
In vacuum
• Implies:
Brane Cosmology
• Inflation
5D Gravity
• Potential Space
The corresponding Lie Algebra
• Define:
• Then:
The ansatz
 A=  A( i)
• And the Killing equation:
Implies
The main theorem
Rev.Mex.Fis. 38(1992)69
WMAP3 Results
• Milenium
SFDM
T. Matos and F. Siddhartha Guzmán. Class. Quant. Grav. 17, (2000), L9-L16.
• The action:
• The metric:
The field equations
• The Laplacian:
The solution
• Where M:
• Thus:
• The space-time metric:
The geodesics
• The luminous matter contribution
• The rotations curves
Density Profiles
T. Matos and F. Siddhartha Guzmán. Class. Quant. Grav. 17, (2000), L9-L16.
Density Profiles
(Harko & Bhomer arXiv:0705.4158)
Density Profiles LSB Galaxies
Density Profiles LSB Galaxies
Density Profiles LSB Galaxies
The geodesics again
Tonatiuh Matos, F. Siddhartha Guzman and Dario Nuñez,
Phys. Rev. D62(2000)061301(R);
• For the metric
• The rotations curves implies
The Cosmology
T. Matos and L. Ureña, Class. Q. Grav. 17(2000)L75
http://www.iac.edu.mx
• Dark Matter:  V0[cosh() –1]
• Dark Energy:  , ,
• Baryons, Radiation,
• Neutrinos, etc.
•    0.23
•    0.73
• b  0.04
The Field Equations
The Cosmology
T. Matos and L. Ureña, Class. Q. Grav. 17(2000)L75
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  10-23 eV
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  10-23 eV
• M 1012 Mo
Scalar Field Fluctuation = Halo
Scalar Field Fluctuation = Halo
Scalar Field Fluctuation = Halo
• 3D
Conclusion
• The scalar field is a good
candidate to be the Dark Matter
of the Universe