HypothesisHypothesis

Scalar Field is the Dark Matter and the Dark Energy in the Cosmos, Scalar Field is the Dark Matter and the Dark Energy in the Cosmos, i.e.i.e. about 95% of the about 95% of the matter of the Universe. matter of the Universe.

At the cosmological levelAt the cosmological level

the hypothesis:the hypothesis: i) Explains quite well the recent observations on type Ia supernovae. 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 ii) Agrees with the restrictions imposed by the Cosmic Background Radiation and by the mass power spectrum.mass power spectrum.

At the galactic levelAt the galactic level

the hypothesis:the hypothesis: iii) Implies that the effective energy density of the dark matter goes like 1/(riii) Implies that the effective energy density of the dark matter goes like 1/(r 22+b+b22).).

vi) The resulting circular velocity profile of test particles is in good agreement with the vi) The resulting circular velocity profile of test particles is in good agreement with the observed one in spiral galaxies.observed one in spiral galaxies.

  

The great concordance of our hypotheses with experimental results suggests that 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 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.galaxies could give a signature of the existence of such particles.

Jets in the Jets in the Scalar Field Dark Matter ModelScalar Field Dark Matter Model

Tonatiuh Matos (CINVESTAV- México), Dario Núñez (ICN-UNAM- México),Tonatiuh Matos (CINVESTAV- México), Dario Núñez (ICN-UNAM- México), F. Siddhartha Guzman and Luis Ureña (CINVESTAV- México)F. Siddhartha Guzman and Luis Ureña (CINVESTAV- México)

www.fis.cinvestav.mx/~siddh/PHIwww.fis.cinvestav.mx/~siddh/PHI

ObservationsObservations In galaxy clusters and dynamical measurements of the mass in galaxies, indicate In galaxy clusters and dynamical measurements of the mass in galaxies, indicate

that that MM ~ 0.3, ~ 0.3,

   Observations in Ia supernovae indicate Observations in Ia supernovae indicate ~ 0.7 ~ 0.7

  These observations are in very good concordance with the preferred valueThese observations are in very good concordance with the preferred value

00 ~ 1. ~ 1.

   Everything seems to agree. Everything seems to agree.    The matter component, say The matter component, say

MM = = bb + + + + ~ 0.05 + ~ 0.05 + DMDM,,

   Where Where DMDM ~ 0.25. ~ 0.25.

But we do not know the nature neither of the dark matter But we do not know the nature neither of the dark matter DMDM nor of the dark nor of the dark energy energy ..

We do not know what is the composition of We do not know what is the composition of

DMDM + + ~ 0.95,~ 0.95,

i.ei.e., of 95% of the whole matter in the Universe.., of 95% of the whole matter in the Universe.

The Model at Cosmological LevelThe Model at Cosmological Level Dark MatterDark Matter Dark EnergyDark Energy

   The action S = The action S = d d44xx-g [R/-g [R/00 + 2( + 2())22 – V – VDMDM(() + 2() + 2())22 – V – V(()])]  

The metric The metric dsds22 = -dt = -dt22+a+a22(t)[dr(t)[dr22/(1-kr/(1-kr22)+r)+r22(d(d22+sin+sin22dd22)])]

The Field EquationsThe Field Equations

  

dd22/dt/dt22 + 3H d + 3H d/dt + dV/dt + dVDM DM /d/d = 0 = 0

dd22/dt/dt22 + 3H d + 3H d/dt + dV/dt + dV // dd = 0 = 0

  

HH22 + k/a + k/a22 = = 00/3 (/3 (MM + + + + ))

  

where where = ½ d = ½ d22/dt + V/dt + VDMDM ( (); ); = ½ d = ½ d22/dt + V/dt + V ( () and H = 1/a da/dt) and H = 1/a da/dt

Let be F(a) = VLet be F(a) = VDMDM ( () a) a66 ; G(a) = V ; G(a) = V ( () a) a66 and and = 6/a = 6/a66 F/a da ; F/a da ; = 6/a = 6/a66 G/a da G/a da

ImpliesImplies

t - tt - t00 = = 3 3 ( (00((MM + + + + )- 3k/a)- 3k/a22))-1/2-1/2 da/a da/a

  

- - 00 = = 6 6 ( ( - F/a - F/a66)) 1/2 1/2 /( /(00 ( (MM + + + + ) - 3k/a) - 3k/a22))1/21/2 da/a da/a

The History of the UniverseThe History of the Universe

Magnitude-Redshift RelationMagnitude-Redshift Relation

mmBBeffective effective = = MMBB + 5 log D + 5 log DLL(z;(z;ii,,))

   DDLL = H = H00ddL L ``Hubble-constant-free’’ luminosity distance. ``Hubble-constant-free’’ luminosity distance.

  

MMBB := M := MBB – 5 log H – 5 log H00 + 25 + 25

``Hubble-constant-free’’ B-band absolute magnitude at the ``Hubble-constant-free’’ B-band absolute magnitude at the maximum of a Ia supernovae. maximum of a Ia supernovae.

  

DDLL(z;(z;ii,,) = (1+z)/H) = (1+z)/H00 sinnsinn ( ( 1/(1+z)1/(1+z) dx/ dx/UU ) )

   Where Where

UU = = ii ii x x(1-3(1-3i)i) – x – x22(1-(1-00) + x) + x(1-3(1-3x)x) xx

   For an equation of state For an equation of state ppxx = = xx xx

  

andand

   UU = = ii ii x x

(1-3(1-3i)i) – x – x22(1-(1-00) + 6/() + 6/(ccxx22) () (xx dx’ F/x’ + dx’ F/x’ +

C).C).

For the scalar fieldFor the scalar field

Mass Power SpectrumMass Power Spectrum

(r) := (r) := Probability to fiend 2 Probability to fiend 2 galaxiesgalaxies

P(k)= 1/VP(k)= 1/Vdd33x x (x) exp(i(x) exp(ikk••xx)) with with := V/(2:= V/(2))33 dd33k k ||kk||22 exp(- exp(-

iikk••xx)) where where := := //= = kk exp(-i exp(-ikk••xx))

Angular Power SpecturmAngular Power Specturm

T(T(,,)/T = )/T = lmlmaalmlmYYlmlm((,,))

with with a* a*l’m’ l’m’ aalm lm = = CCllll’ll’mm’mm’

where Cwhere Cl l = = | | aalm lm ||22

ResultsResults                     The deceleration parameter The deceleration parameter

qq00 = -0.45 = constant = -0.45 = constant,,

which really implies that the Universe is accelerating.which really implies that the Universe is accelerating.                     The density of the scalar field The density of the scalar field

= 0.95= 0.95ccaa-1.09-1.09

                     The state equationThe state equation

pp // == = -0.636 = constant. = -0.636 = constant.

  

This value of This value of has no problems with cosmic background radiation and with the has no problems with cosmic background radiation and with the mass power spectrum of the Universe which constraint the value of mass power spectrum of the Universe which constraint the value of xx to be less to be less than than -0.60-0.60

                     The Universe changed to be matter dominated The Universe changed to be matter dominated

until until a/aa/a00 0.21 0.21, when the density of the scalar field equals the density of , 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 matter. At this time, the density of radiation is negligible. This corresponds to the redshift redshift z=3.7z=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 the scalar field began to dominate the expansion of the Universe and it enters in its actual acceleration phase.its actual acceleration phase.  

The Model at Galactic LevelThe Model at Galactic Level

ObservationsObservations   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.   The action The action   

S = S = d d44xx-g [R/-g [R/00 + 2( + 2())22 – V – Vooee-2-2 ] ]

We neglect the baryonic matter contribution to the total energy density of the halo We neglect the baryonic matter contribution to the total energy density of the halo of the galaxy. 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 Dragging effects are too small to affect the test particles (stars) traveling around the galaxy. The space-time is static. the galaxy. The space-time is static.

The most general metric isThe most general metric is

dsds22 = 1/f [ e = 1/f [ e2k2k(d(d22 + d + d22) + W) + W22 d d22] – f c] – f c22dtdt22

The Field EquationsThe Field Equations

,,;; - - ¼¼VVDMDM’’ = = 00   

RR = = 00 [ 2 [ 2,,,, + + ½½ g g V VDMDM ( ()])]

The exact solution The exact solution

  

= ln(M) + ln(f= ln(M) + ln(f00))

= = 0 + 0 + ½½ln(M)ln(M)//00

V = 4 fV = 4 f00/(/(00M)M)

ee2k2k = M = M,zz,zz M M

= -= -½½ V( V())

   In Schwarzschild -coordinates In Schwarzschild -coordinates 22 = (r = (r22+b+b22)sin)sin22, , = r cos = r cos the metric readsthe metric reads

dsds22 = r = r22drdr22/(r/(r22 + b + b22) +(r) +(r22 + b + b22)[d)[d22+sin+sin22dd22]– f]– f0022cc22(r(r22 + b + b22))ll dt dt22))

with energy density with energy density DMDM = 4/ = 4/0 0 ff00/(r/(r22 + b + b22))

The GeodesicsThe Geodesics The motion equation of a test particle (a star) can be derived from the The motion equation of a test particle (a star) can be derived from the

LagrangianLagrangian  

L = 1/f [ eL = 1/f [ e2k2k((d((d/d/d))22 + (d + (d/d/d))22) + W) + W22(d(d/d/d))22] – f c] – f c22(dt/d(dt/d))22

For a circular trajectory For a circular trajectory = = = 0. = 0. Using our exact solution the equation of Using our exact solution the equation of motion reduces tomotion reduces to

  

BBLL22/R/R22 – c – c22AA22/R/R22 = -c = -c22

  where R=where R=ds at equator. From these equations ds at equator. From these equations

  

BBLL22= v= v22RR22/( f/( f00

22RR22-v-v22/ c/ c22) )

~ ~ vv22/ f/ f0022

where where vv22 = g = gababvvaavvbb and and vvaa = ( = (, , , , ))

sincesince v v22<< << cc22. . i.e.i.e.

vvDMDM = f = f00BBLL= f= f00RvRvLL    

For the luminous matter of the For the luminous matter of the galaxy galaxy

LL = = 00ee(-r/rD)(-r/rD)

   The corresponding velocity of test particles The corresponding velocity of test particles   

vv22L = L = vv

2200(I(I00KK00 – I – I11KK11))

  

where where IInn and and KKnn are modified Bessel functions valued at are modified Bessel functions valued at rD/2.rD/2. vv00 is a is a parameter parameter

JETS from Scalar Field Dark JETS from Scalar Field Dark MatterMatter

The Dark Matter interacts very weakly, or not at all, with The Dark Matter interacts very weakly, or not at all, with the baryonic one, so in order to determine what the baryonic one, so in order to determine what composes the 90% of the energy and matter in our composes the 90% of the energy and matter in our Universe, we have to use indirect observations.Universe, we have to use indirect observations.

On the other hand, whatever is the composition of the On the other hand, whatever is the composition of the matter energy, it certainly has geometric effects on the matter energy, it certainly has geometric effects on the space where it is located. Those effects are described by space where it is located. Those effects are described by the Einstein's equations. The geometry, in turn, the Einstein's equations. The geometry, in turn, determines the dynamics of the objects in such space determines the dynamics of the objects in such space times.times.

This approach was been recently successfully used in This approach was been recently successfully used in studying the type of matter, which determines the flat studying the type of matter, which determines the flat rotational profile in the velocity of particles orbiting rotational profile in the velocity of particles orbiting spiral galaxies. It presents interest to apply this program spiral galaxies. It presents interest to apply this program on the motion of jets. on the motion of jets.

In this way, the idea is to consider the geodesic equation of particles moving In this way, the idea is to consider the geodesic equation of particles moving along the symmetry axis within an arbitrary axis symmetric stationary along the symmetry axis within an arbitrary axis symmetric stationary space-time, described by the line element:space-time, described by the line element:

dsds22=-e=-e22 (dt + (dt + d d) ) 22+ e+ e-2-2 [e [e22 (d (d2 2 + dz+ dz22) + ) + 2 2 dd 22],],

and, using the observational data from the jets motion, to constraint the and, using the observational data from the jets motion, to constraint the geometry to be consistent which such observations, by means of applying geometry to be consistent which such observations, by means of applying those data to constraint the geodesic motion along the symmetry axis. In 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 order to do so, we know that, due to the symmetries of the space time, the energy, energy, EE, and the axial angular momentum, , and the axial angular momentum, LLzz , are conserved quantities , are conserved quantities for any geodesical motion, thus for any particle with time like four velocity, for any geodesical motion, thus for any particle with time like four velocity, vvjj v vjj= -1= -1, we obtain that in general, we obtain that in general

vv22+ v+ vzz

22+V=0+V=0

with the potential with the potential VV given by given by

V = 1/gV = 1/g [g [gtttt +2g +2gtt + g+ g 2 2 + (dt+ (dt//dd) ) -2-2],],

It is clear that the program described above will be noticeable in regions 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 jetsclose to the central object, that is, close to the origin of the jets..

HereHere

dtdt//dd = e = e22// 2 2 [( [( 2 2 ee-4-4 - - 22)E - )E - L], L],

dd //dd = = = e = e22//22(( E + L) E + L)

ggtttt = - e = - e22

ggtt = -= - e e22

ggtttt = = 2 2 ee-2-2 - - 22 e e22

Thus, using the observational data on the motion of the Thus, using the observational data on the motion of the particles within the jets, we can study the constraint that those particles within the jets, we can study the constraint that those observations impose on the metric coefficients which, in turn, will observations impose on the metric coefficients which, in turn, will impose constraint on the type of matter determining such a motion impose constraint on the type of matter determining such a motion by means of the Einstein's equations.by means of the Einstein's equations.

If these results will be If these results will be phenomenologically justified in the phenomenologically justified in the

future, then they implyfuture, then they imply       Scalar Fields represent 95% of the matter of the Universe. Scalar Scalar Fields represent 95% of the matter of the Universe. Scalar

fields are the most important part of matter in Nature; they determine fields are the most important part of matter in Nature; they determine the structure of the Universe. After the Big Bang, they inflated the the structure of the Universe. After the Big Bang, they inflated the Universe; soon after they gave mass to the particles; later they Universe; soon after they gave mass to the particles; later they concentrate maybe due to scalar field condensation, producing concentrate maybe due to scalar field condensation, producing density fluctuations on the baryonic matter and forming stars, galaxies density fluctuations on the baryonic matter and forming stars, galaxies and galaxy clusters. and galaxy clusters.

      The question why Nature uses only the spin 1 and spin 2 The question why Nature uses only the spin 1 and spin 2 fundamental interactions over the simplest spin 0 interaction becomes fundamental interactions over the simplest spin 0 interaction becomes clear here. These results tell us that, in fact, nature has preferred the clear here. These results tell us that, in fact, nature has preferred the spin 0 interaction over the other two, scalar field interactions spin 0 interaction over the other two, scalar field interactions determine the cosmos structure.determine the cosmos structure.

      These results give also a limit for the validity of the Einstein's 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, 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 but they are not valid at galactic or cosmological level, a scalar field interaction must be added to the original equations.interaction must be added to the original equations.

            Observations of Observations of Jets in galaxies will be crucial for determining Jets in galaxies will be crucial for determining the nature of dark matter.the nature of dark matter.