Hypothesis Scalar Field is the Dark Matter and the Dark Energy in the Cosmos, i.e. about 95% of the matter of the Universe. Scalar Field is the Dark Matter and the Dark Energy in the Cosmos, i.e. about 95% of the matter of the Universe. At the cosmological level the hypothesis: n i) Explains quite well the recent observations on type Ia supernovae. ii) Agrees with the restrictions imposed by the Cosmic Background Radiation and by the mass power spectrum. ii) Agrees with the restrictions imposed by the Cosmic Background Radiation and by the mass power spectrum. At the galactic level the hypothesis: iii) Implies that the effective energy density of the dark matter goes like 1/(r 2 +b 2 ). iii) Implies that the effective energy density of the dark matter goes like 1/(r 2 +b 2 ). vi) The resulting circular velocity profile of test particles is in good agreement with the observed one in spiral galaxies. vi) The resulting circular velocity profile of test particles is in good agreement with the observed one in spiral galaxies. The great concordance of our hypotheses with experimental results suggests that the Universe currently lies in a scalar field dominated epoch. Jets on the center of galaxies could give a signature of the existence of such particles. Jets in the Scalar Field Dark Matter Model Tonatiuh Matos (CINVESTAV- México), Dario Núñez (ICN-UNAM- México), F. Siddhartha Guzman and Luis Ureña (CINVESTAV- México)

Observations In galaxy clusters and dynamical measurements of the mass in galaxies, indicate that  M ~ 0.3, In galaxy clusters and dynamical measurements of the mass in galaxies, indicate that  M ~ 0.3, Observations in Ia supernovae indicate   ~ 0.7 Observations in Ia supernovae indicate   ~ 0.7 These observations are in very good concordance with the preferred value  0 ~ 1.  0 ~ 1. Everything seems to agree. Everything seems to agree. The matter component, say The matter component, say  M =  b +  +  ~  DM,  M =  b +  +  ~  DM, Where  DM ~ Where  DM ~ But we do not know the nature neither of the dark matter  DM nor of the dark energy  . But we do not know the nature neither of the dark matter  DM nor of the dark energy  . We do not know what is the composition of  DM +   ~ 0.95, i.e., of 95% of the whole matter in the Universe.

The Model at Cosmological Level n   Dark Matter n   Dark Energy The action S =  d 4 x  -g [R/  0 + 2(  ) 2 – V DM (  ) + 2(  ) 2 – V  (  )] The action S =  d 4 x  -g [R/  0 + 2(  ) 2 – V DM (  ) + 2(  ) 2 – V  (  )] The metric ds 2 = -dt 2 +a 2 (t)[dr 2 /(1-kr 2 )+r 2 (d  2 +sin 2  d  2 )] The metric ds 2 = -dt 2 +a 2 (t)[dr 2 /(1-kr 2 )+r 2 (d  2 +sin 2  d  2 )] n The Field Equations d 2  /dt 2 + 3H d  /dt + dV DM /d  = 0 d 2  /dt 2 + 3H d  /dt + dV  / d  = 0 d 2  /dt 2 + 3H d  /dt + dV  / d  = 0 n H 2 + k/a 2 =  0 /3 (  M +   +   ) n where   = ½ d  2 /dt + V DM (  );   = ½ d  2 /dt + V  (  ) and H = 1/a da/dt n Let be F(a) = V DM (  ) a 6 ; G(a) = V  (  ) a 6 and   = 6/a 6  F/a da ;   = 6/a 6  G/a da n Implies t - t 0 =  3  (  0 (  M +   +   )- 3k/a 2 ) -1/2 da/a  -  0 =  6  (   - F/a 6 ) 1/2 /(  0 (  M +   +   ) - 3k/a 2 ) 1/2 da/a

The History of the Universe

Magnitude-Redshift Relation m B effective = M B + 5 log D L (z;  i,   ) D L = H 0 d L ``Hubble-constant-free’’ luminosity distance. M B := M B – 5 log H ``Hubble-constant-free’’ B-band absolute magnitude at the maximum of a Ia supernovae. D L (z;  i,   ) = (1+z)/H 0 sinn (  1/(1+z) dx/  U  ) n Where U  =  i  i x (1-3  i) – x 2 (1-  0 ) + x (1-3  x)  x n For an equation of state p x =  x  x and n U  =  i  i x (1-3  i) – x 2 (1-  0 ) + 6/(  c x 2 ) (  x dx’ F/x’ + C). For the scalar field

Mass Power Spectrum n  (r) := Probability to fiend 2 galaxies n P(k)= 1/V  d 3 x  (x) exp(ikx) n with n  := V/(2  ) 3  d 3 k  |  k | 2  exp(-ikx) n where n  :=  /  =   k exp(-ikx)

Angular Power Specturm n  T( ,  )/T =  lm a lm Y lm ( ,  ) n with  a* l’m’ a lm  = C l  ll’  mm’ n where C l =  | a lm | 2 

Results  The deceleration parameter  The deceleration parameter q 0 = = constant, which really implies that the Universe is accelerating.  The density of the scalar field  The density of the scalar field   = 0.95  c a  The state equation  The state equation p  /   =   = = constant. This value of   has no problems with cosmic background radiation and with the mass power spectrum of the Universe which constraint the value of  x to be less than  The Universe changed to be matter dominated  The Universe changed to be matter dominated until a/a 0  0.21, when the density of the scalar field equals the density of matter. At this time, the density of radiation is negligible. This corresponds to the redshift z=3.7.  For this model, since approximately 14 Gyr  For this model, since approximately 14 Gyr the scalar field began to dominate the expansion of the Universe and it enters in its actual acceleration phase. the scalar field began to dominate the expansion of the Universe and it enters in its actual acceleration phase.

The Model at Galactic Level n Observations Galaxies are composed by almost 90% of dark matter. Galaxies are composed by almost 90% of dark matter. Newtonian theory explains well the dynamics of the luminous sector of the galaxy. Newtonian theory explains well the dynamics of the luminous sector of the galaxy. n The action n S =  d 4 x  -g [R/  0 + 2(  ) 2 – V o e -2  ] We neglect the baryonic matter contribution to the total energy density of the halo of the galaxy. We neglect the baryonic matter contribution to the total energy density of the halo of the galaxy. The halo is axial symmetric. The halo is axial symmetric. Dragging effects are too small to affect the test particles (stars) traveling around the galaxy. The space-time is static. Dragging effects are too small to affect the test particles (stars) traveling around the galaxy. The space-time is static. The most general metric is The most general metric is ds 2 = 1/f [ e 2k (d  2 + d  2 ) + W 2 d  2 ] – f c 2 dt 2 ds 2 = 1/f [ e 2k (d  2 + d  2 ) + W 2 d  2 ] – f c 2 dt 2

The Field Equations ,  ;  - ¼ V DM ’ = 0 ,  ;  - ¼ V DM ’ = 0 R  =  0 [ 2 ,  , + ½ g  V DM (  )] R  =  0 [ 2 ,  , + ½ g  V DM (  )] n The exact solution = ln(M) + ln(f 0 ) = ln(M) + ln(f 0 )  =  0 + ½ ln(M) /  0 V = 4 f 0 /(  0 M) e 2k = M,zz M  = - ½ V(  ) n In Schwarzschild -coordinates  2 = (r 2 +b 2 )sin 2 ,  = r cos  the metric reads ds 2 = r 2 dr 2 /(r 2 + b 2 ) +(r 2 + b 2 )[d  2 +sin 2  d  2 ]– f 0 2 c 2 (r 2 + b 2 ) l dt 2 ) ds 2 = r 2 dr 2 /(r 2 + b 2 ) +(r 2 + b 2 )[d  2 +sin 2  d  2 ]– f 0 2 c 2 (r 2 + b 2 ) l dt 2 ) with energy density with energy density  DM = 4/  0 f 0 /(r 2 + b 2 )  DM = 4/  0 f 0 /(r 2 + b 2 )

The Geodesics The motion equation of a test particle (a star) can be derived from the Lagrangian L = 1/f [ e 2k ((d  /d  ) 2 + (d  /d  ) 2 ) + W 2 (d  /d  ) 2 ] – f c 2 (dt/d  ) 2 For a circular trajectory  =  = 0. Using our exact solution the equation of motion reduces to B L 2 /R 2 – c 2 A 2 /R 2 = -c 2 where R=  ds at equator. From these equations B L 2 = v 2 R 2 /( f 0 2 R 2 -v 2 / c 2 ) ~ v 2 / f 0 2 where v 2 = g ab v a v b and v a = ( , ,  ) since v 2 << c 2. i.e. v DM = f 0 B L = f 0 Rv L For the luminous matter of the galaxy  L =  0 e (-r/rD) The corresponding velocity of test particles v 2 L = v 2 0 (I 0 K 0 – I 1 K 1 ) where I n and K n are modified Bessel functions valued at rD/2. v 0 is a parameter

JETS from Scalar Field Dark Matter n The Dark Matter interacts very weakly, or not at all, with the baryonic one, so in order to determine what composes the 90% of the energy and matter in our Universe, we have to use indirect observations. n On the other hand, whatever is the composition of the matter energy, it certainly has geometric effects on the space where it is located. Those effects are described by the Einstein's equations. The geometry, in turn, determines the dynamics of the objects in such space times. n This approach was been recently successfully used in studying the type of matter, which determines the flat rotational profile in the velocity of particles orbiting spiral galaxies. It presents interest to apply this program on the motion of jets.

n In this way, the idea is to consider the geodesic equation of particles moving along the symmetry axis within an arbitrary axis symmetric stationary space-time, described by the line element: n ds 2 =-e 2  (dt +  d  ) 2 + e -2  [e 2  (d  2 + dz 2 ) +  2 d  2 ], n and, using the observational data from the jets motion, to constraint the geometry to be consistent which such observations, by means of applying those data to constraint the geodesic motion along the symmetry axis. In order to do so, we know that, due to the symmetries of the space time, the energy, E, and the axial angular momentum, L z, are conserved quantities for any geodesical motion, thus for any particle with time like four velocity, v j v j = -1, we obtain that in general n v  2 + v z 2 +V=0 n with the potential V given by n V = 1/g  [g tt +2g t   + g   2 + (dt/d  ) -2 ], n n It is clear that the program described above will be noticeable in regions close to the central object, that is, close to the origin of the jets.

n Here n dt/d  = e 2  /  2 [(  2 e -4  -  2 )E -  L], n d  /d  =  = e 2  /  2 (  E + L) n g tt = - e 2  n g t  = -  e 2  n g tt =  2 e -2  -  2 e 2  n Thus, using the observational data on the motion of the particles within the jets, we can study the constraint that those observations impose on the metric coefficients which, in turn, will impose constraint on the type of matter determining such a motion by means of the Einstein's equations.

If these results will be phenomenologically justified in the future, then they imply  Scalar Fields represent 95% of the matter of the Universe. Scalar fields are the most important part of matter in Nature; they determine the structure of the Universe. After the Big Bang, they inflated the Universe; soon after they gave mass to the particles; later they concentrate maybe due to scalar field condensation, producing density fluctuations on the baryonic matter and forming stars, galaxies and galaxy clusters.  Scalar Fields represent 95% of the matter of the Universe. Scalar fields are the most important part of matter in Nature; they determine the structure of the Universe. After the Big Bang, they inflated the Universe; soon after they gave mass to the particles; later they concentrate maybe due to scalar field condensation, producing density fluctuations on the baryonic matter and forming stars, galaxies and galaxy clusters.  The question why Nature uses only the spin 1 and spin 2 fundamental interactions over the simplest spin 0 interaction becomes clear here. These results tell us that, in fact, nature has preferred the spin 0 interaction over the other two, scalar field interactions determine the cosmos structure.  The question why Nature uses only the spin 1 and spin 2 fundamental interactions over the simplest spin 0 interaction becomes clear here. These results tell us that, in fact, nature has preferred the spin 0 interaction over the other two, scalar field interactions determine the cosmos structure.  These results give also a limit for the validity of the Einstein's equations. They are valid at a local level; planets, stars, star-systems, but they are not valid at galactic or cosmological level, a scalar field interaction must be added to the original equations.  These results give also a limit for the validity of the Einstein's equations. They are valid at a local level; planets, stars, star-systems, but they are not valid at galactic or cosmological level, a scalar field interaction must be added to the original equations.  Observations of Jets in galaxies will be crucial for determining the nature of dark matter.  Observations of Jets in galaxies will be crucial for determining the nature of dark matter.