Problems and Alternatives to Lambda Cold Dark Matter

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

http://www.iac.edu.mx

The LCDM Some Problems of the LCDM Some Alternatives • Space-time: FLRW • Matter: DM (p = 0), DE (p = -ρ), b (p = 0), rad (p = 1/3 ρ), ν (p = 1/3 ρ), etc. The Standard Model of Cosmology: LCDM

• Space-time: FLRW • Matter: DM (p = 0), DE (p = -ρ), b (p = 0), rad (p = 1/3 ρ), ν (p = 1/3 ρ), etc. • Inflation • BBN • CMB • Structure formation The Standard Model of Cosmology: LCDM The Standard Model of Cosmology: LCDM

4 The Standard Model of Cosmology: LCDM

CDM Paradigme

• 1.- The DM fluctuation spectrum at recombination is detemined by a small number of physical paramenters.

4 The Standard Model of Cosmology: LCDM

CDM Paradigme

• 1.- The DM fluctuation spectrum at recombination is detemined by a small number of physical paramenters. • 2.- After recombination, the amplitude of the baryonic fluctuations rapidly grows to match that of the DM fluctuations.

4 The Standard Model of Cosmology: LCDM

CDM Paradigme

• 3.- Smaller-mass fluctutions grow to nonlineartity and virialize and then are hirarchically clustered within successively larger bound systems.

4 The Standard Model of Cosmology: LCDM

CDM Paradigme

• 3.- Smaller-mass fluctutions grow to nonlineartity and virialize and then are hirarchically clustered within successively larger bound systems.

8 12 • 4.- Ordinary matter in bound systems of total mass 10 − M cools rapidly enough within the DM halos to form galaxies, while larger mass⊙ fluctutations form clusters

4 The Standard Model of Cosmology: LCDM

z=18.3 The Standard Model of Cosmology: LCDM

z=5.7 The Standard Model of Cosmology: LCDM

z=1.4 The Standard Model of Cosmology: LCDM

z=0 The Standard Model of Cosmology: LCDM The Standard Model of Cosmology: LCDM The Standard Model of Cosmology: LCDM

7 The Standard Model of Cosmology: LCDM

27 3 1 3 10− cm s− Ω h2 = × χ σv

26 3 1 σv 3 10− cm s− ∼ ×

7 The Standard Model of Cosmology: LCDM

27 3 1 3 10− cm s− Ω h2 = × χ σv

26 3 1 σv 3 10− cm s− ∼ ×

Candidates: Axions Sterile neutrinos MSSM: neutralino, gravitino, etc.

7 The Standard Model of Cosmology: LCDM

27 3 1 3 10− cm s− Ω h2 = × χ σv

26 3 1 σv 3 10− cm s− ∼ ×

Candidates: Observations: Axions 1.- Detection of products of Sterile neutrinos annihilation or decay of these particles MSSM: neutralino, 2.-Interactions with nuclei in gravitino, etc. underground detectors

7 8 Dama/Libra

8 Dama/Libra

But a light WIMP, (10-100GeV, CoGeNT collaboration) is in tension with the first XENON100 results. Aprile, E. et al. First dark matter results from the XENON100 experiment. arXiv:1005.0380.

8 • 1 km3 Antartic ice with • Fotoelectric sensors • Ready in 2011 IceCube Neutrino Telescope in Antartic

• 1 km3 Antartic ice with • Fotoelectric sensors • Ready in 2011

ANTARES –Telescopio de Neutrinos en el Mediterraneo ANTARES –Telescopio de Neutrinos en el Mediterraneo

11 γ

χχ γγ → γ rays satellites

GLAST Satellite Start 11. Juni 2008 MAGIC I, II(const), La Palma

χχ γγ Telescopio HESS, → Namibia (2004)

LHC

LHC in CERN (Genf) 2009 Direct search of WIMP’s Gianfranco Bertone, Nature,468(2010)389

Xenon 100 CDMS II

4 parameters

SuperCDMS 1TG Lux (3 T liq Xe) 7 parameters Xenon 1T Direct search of WIMP’s Gianfranco Bertone, Nature,468(2010)389

Xenon 100 CDMS II

4 parameters

SuperCDMS 1TG Lux (3 T liq Xe) 7 parameters Xenon 1T

The Standard Model of Cosmology: Problems

• Extreme fine tuning • Coincidence • Cuspy central density profiles • Missing Satellites Problem • No-fit of the early assembly of galaxies • Galaxies seems to be simpler • Voids are too empty • No-detection of DM • etc. The Standard Model of Cosmology: Problems

• Cuspy central density profiles • Missing Satellites Problem • No-fit of the early assembly of galaxies • Galaxies seems to be simpler • Voids are too empty • No-detection of DM • etc. 1 Galaxy´s density ρ ∼ xα

Observed 0 < α < 1

Theory 1 δ ρ ρ = 0 0 NFW x (1 + x)2 1 ρ NFW ∼ x

17 Galaxy’s Density 1 Galaxy´s density ρ ∼ xα

Observed 0 < α < 1

Theory 1 δ ρ ρ = 0 0 NFW x (1 + x)2 1 ρ NFW ∼ x

17 W. J. G. de Blok, Stacy S. McGaugh, Albert Bosma, and Vera C. Rubin. ApJ Letters 552(2001)L24

18 Galaxy’s Center: Observations W. J. G. de Blok, Stacy S. McGaugh, Albert Bosma, and Vera C. Rubin. ApJ Letters 552(2001)L24

18 Galaxy’s Center: Observations

Joshua D. Simon, Alberto D. Bolatto, Adam Leroy, and Leo Blitz, astro-ph/0310193

19 Galaxy’s Center: Observations

NFW

20 Galaxy’s Center: Simulations Galaxy’s Center: Simulations

F. Gobernato, et. al., NATURE, Vol 463, 14 January 2010 Galaxy’s Center: Simulations

F. Gobernato, et. al., NATURE, Vol 463, 14 January 2010 General results from several samples including THINGS, HI survey of uniform and high quality data, imply that Tri-axiality and non-circular motions cannot explain the CDM/NFW cusp/core discrepancy

ej: J. van Eymeren, C. Trachternach, B. S. Koribalski and R.- J. Dettmar: A&A arXiv:0906.4654 Galaxy’s Center: Simulations

ej: J. van Eymeren, C. Trachternach, B. S. Koribalski and R.- J. Dettmar: A&A arXiv:0906.4654

No evidence for internal features or star formation that could be the result of tidal processes or star formation induced by the cluster environment. ej: Samantha J. Penny, Christopher J. Conselice, Sven De Rijcke and Enrico V. Held: Mon. Not. R. Astron. Soc. 393, 1054–1062 (2009), etc. 23 Stellar Mass Predictions

Till Sawala, Qi Guo, Cecilia Scannapieco, Adrian Jenkins and Simon White. Mon. Not. R. Astron. To appear.

23 Stellar Mass Predictions

Till Sawala, Qi Guo, Cecilia Scannapieco, Adrian Jenkins and Simon White. Mon. Not. R. Astron. To appear.

The dwarf galaxies formed in hydrodynamical simulations are almost two orders of magnitude more luminous than expected for haloes of this mass.

23 24 Velocity predictions

Jesús Zavala, et. al. The Astrophysical Journal, 700:1779–1793, 2009 August 1

24 Velocity predictions

Jesús Zavala, et. al. The Astrophysical Journal, 700:1779–1793, 2009 August 1

The simulation with CDM predicts a steep rise in the VF toward lower velocities; for Vmax = 35 km/s, it forecasts ∼10 times more sources than the ones observed. If confirmed by the complete ALFALFA survey, these results indicate a potential problem for the CDM paradigm

Missing Satellites Problem Missing Satellites Problem Missing Satellites Problem

26 Missing Satellites Problem

Galaxies appear simpler than expected

M. J. Dysney, et. al. Vol 455(2008)1082

R R 90 ∝ 50 L R3 g ∝ 50 M R2 HI ∝ 50 M L d ∝ g Σ = L /R2 L1/3 R g 50 ∝ g ∝ 50 Whereas

3 Lg/R50 3 Md/R50

are independent of the size of the galaxy Galaxies appear simpler than expected

M. J. Dysney, et. al. Vol 455(2008)1082

Such a degree of organization appears to be at odds with hierarchical galaxy formation, a central tenet of the cold dark matter model in cosmology. 28 Voids are too empty P. J. E. Peebles & A. Nusser, Nature 465(2010)565

28 Voids are too empty P. J. E. Peebles & A. Nusser, Nature 465(2010)565

It is not clear why objects that might have been assembled in such very different ways, from different ancestral objects, should have had evolutionary tracks that converged to show small dispersions around simple power law forms for their size–luminosity relations.

Nair, P. B., van den Bergh, S. & Abraham, R. G. The environmental dependence of the luminosity-size relation for galaxies. Astrophys. J. 715, 606–622 (2010).

28 Voids are too empty P. J. E. Peebles & A. Nusser, Nature 465(2010)565

In short, the general insensitivity of galaxies to their environments is not expected in standard ideas. It would help if galaxies were more rapidly assembled, as they could then evolve as more nearly isolated island universes.

Early assembly of the most massive galaxies Chris A. Collins, et. al. Nature, 458(2009)603 Early assembly of the most massive galaxies Chris A. Collins, et. al. Nature, 458(2009)603

This suggest a new picture in which brightest cluster galaxies experience an early period of rapid growth rather than prolonged hierarchical assembly. Pieter G. van Dokkum et. al. NATURE, Vol 460, 6 August 2009. The Astrophysical Journal, 677:L5–L8, 2008 April 10

30 Early Galaxies Compactness

Pieter G. van Dokkum et. al. NATURE, Vol 460, 6 August 2009. The Astrophysical Journal, 677:L5–L8, 2008 April 10

30 Early Galaxies Compactness

Pieter G. van Dokkum et. al. NATURE, Vol 460, 6 August 2009. The Astrophysical Journal, 677:L5–L8, 2008 April 10 z=2.3 Galaxies

31 1E 0657-56, "Bullet Cluster” 2006

32 Clusters Collisons Mastropietro, C., & Burkert, A. 2008, MNRAS, 389, 967 1E 0657-56, "Bullet Cluster” 2006

The morphology of X-ray maps, the height of the projected temperature jump and the displacement of the gas peaks are best simulated by 6:1 encounters with initial velocity 3000 km/s

32 Clusters Collisons Mastropietro, C., & Burkert, A. 2008, MNRAS, 389, 967 1E 0657-56, "Bullet Cluster” 2006

The morphology of X-ray maps, the height of the projected temperature jump and the displacement of the gas peaks are best simulated by 6:1 encounters with initial velocity 3000 km/s

The only way to fit the observational data using NFW profiles would be to assume a mass ratio as small as 2.7:1, which would not reproduce X-ray data.

32 Clusters Collisons

MACS J0025.4-1222 2008 33 Clusters Collisons J. Lee & E. Komatsu, ApJ, 718(2010)60

With a large-volume (27 Gpc 3 /h 3 ) cosmological N-body MICE simulation, the probability of finding 3000 km/s is between 11 9 3.3 x 10 − and 3.6 x 10 − .

MACS J0025.4-1222 2008 33 Shaun A. Thomas, Filipe B. Abdalla, and Ofer Lahav. arXiv:1012.2272

0.55

0.45

34 Large scale structure anomaly

Shaun A. Thomas, Filipe B. Abdalla, and Ofer Lahav. arXiv:1012.2272

0.55

0.45

Some Alternatives

SM Extentions GR Extentions Some Alternatives

SM Extentions GR Extentions • Self-Interacting DM • Warm DM • Super Heavy DM • Self-Annihilating DM • Decaying DM • Extra Symmetries, • Repulsive DM • Fuzzy DM • k-essence • Scalar Field DM (BEC DM), etc. Some Alternatives

SM Extentions GR Extentions • Self-Interacting DM • Scalar Field DM (BEC DM) • Warm DM • MOND -> MOND+ • Super Heavy DM • f(R) • Self-Annihilating DM • Extra Dimensions • Decaying DM • etc. • Extra Symmetries, • Repulsive DM • Fuzzy DM • k-essence • Scalar Field DM (BEC DM), etc. Some Alternatives

Rachel Kuzio de Naray, Gregory D. Martinez, James S. Bullock, Manoj Kaplinghat. ApJ161(2010) 710L

38 Self-Interacting and Warm DM

Rachel Kuzio de Naray, Gregory D. Martinez, James S. Bullock, Manoj Kaplinghat. ApJ161(2010) 710L

39 Self-Interacting and Warm DM

Rachel Kuzio de Naray, Gregory D. Martinez, James S. Bullock, Manoj Kaplinghat. ApJ161(2010) 710L

ρ¯ ED3,4 Qρ = 3 Th1,2 σ¯

39 Self-Interacting and Warm DM

Rachel Kuzio de Naray, Gregory D. Martinez, James S. Bullock, Manoj Kaplinghat. ApJ161(2010) 710L

ρ¯ ED3,4 Qρ = 3 Th1,2 σ¯

The inferred cores do not provide motivation to prefer WDM or SIDM over other dark matter models

39 Some Alternatives

1.- Does it match the appropriate relic density? 6.- Is it compatible with constraints on self-interactions? 2.- Is it cold? 7.- Is it consistent with direct DM searches? 3.- Is it neutral? 8.- Is it compatible with gamma-ray constraints? 4.- Is it consistent with BBN? 9.- Is it compatible with other astrophysical bounds?

5.- Does it leave stellar evolution unchanged? 10.- Can it be probed experimentally? 1

I. II. III. IV. V. VI. VII. VIII. IX. X. Result DM candidate Ωh2 Cold Neutral BBN Stars Self Direct γ-rays Astro Probed SM Neutrinos – – × × × Sterile Neutrinos ! ∼ ∼ ∼ Neutralino ! ! ! Gravitino ∼ ∼ Gravitino (broken R-parity) Sneutrinoν ˜L ! ! ∼ × × Sneutrino ν˜R ! ! ! Axino SUSY Q-balls – ! 1 ∼ ∼ B UED ! ! ! First level graviton UED a × × × Axion ! Heavy photon (Little Higgs) ! ! Inert Higgs model ! – Champs – – – – × × × Wimpzillas ∼ ∼ Direct search of Particles Marco Taoso, Gianfranco Bertone, Antonio Masiero. JCAP 0803:022,2008

5.- Does it leave stellar evolution unchanged? 10.- Can it be probed experimentally? 1

I. II. III. IV. V. VI. VII. VIII. IX. X. Result DM candidate Ωh2 Cold Neutral BBN Stars Self Direct γ-rays Astro Probed SM Neutrinos – – × × × Sterile Neutrinos ! ∼ ∼ ∼ Neutralino ! ! ! Gravitino ∼ ∼ Gravitino (broken R-parity) Sneutrinoν ˜L ! ! ∼ × × Sneutrino ν˜R ! ! ! Axino SUSY Q-balls – ! 1 ∼ ∼ B UED ! ! ! First level graviton UED a × × × Axion ! Heavy photon (Little Higgs) ! ! Inert Higgs model ! – Champs – – – – × × × Wimpzillas ∼ ∼ 42 Pamela Constrains New Constraints from PAMELA anti-proton data on Annihilating and Decaying DM Ilias Cholis arXiv:1007.1160 0.001 mr = 1 TeV, BF = 28, AMS-02 expectation mr = 10 TeV, BF = 2200, AMS-02 expectation Background PAMELA Data

+ - rr A W W 1e-04 pbar/p

1e-05

1e-06 0.1 1 10 100 42 kinetic energy (GeV) Pamela Constrains

43 Pamela Constrains

Leanna Dugger, Tesla E. Jeltemaa and Stefano Profumo, JCAP12(2010)015

µ+µ< final state - dSph, without IC

27 10 Ursa Minor PAMELA Ursa Major II Bootes I Sextans Fornax 26 PAMELA 10 Draco Sculptor +FERMI Coma Berenices µ+µ< final state - M31 27 10 25 10 PAMELA PAMELA +FERMI DM lifetime [s] 26 10

24 Galactic + EG 10 Previous Constraints 25 10 Galactic + EG Previous Constraints 23 24 10 100 1000 10000 DM lifetime [s] 10 DM mass [GeV] 28 2 NFW, point-like source, D0=10 cm /s 23 28 2 10 Extended source, Mvir, D0=10 cm /s 29 2 NFW, point-like source, D0=10 cm /s 29 2 Extended source, M , D =10 cm /s 22 vir 0 43 10 1000 10000 DM mass [GeV] Pamela Constrains

Leanna Dugger, Tesla E. Jeltemaa and Stefano Profumo, JCAP12(2010)015

µ+µ< final state - dSph, without IC These results put strong constraints on the

27 possibility of ascribing to decaying dark matter 10 Ursa Minor PAMELA Ursa Major II both the increasing positron fraction reported Bootes I by PAMELA and the high-energy feature in the Sextans Fornax 26 PAMELA electron-positron spectrum measured by Fermi 10 Draco Sculptor +FERMI Coma Berenices µ+µ< final state - M31 27 10 25 10 PAMELA PAMELA +FERMI DM lifetime [s] 26 10

A. de la Macorra, C. Stephan-Otto, Phys. Rev. Lett. 87 (2001) 271301

The starting point is a dark gauge group “DG” whose particles interact with the standard model only via gravity. The gauge coupling constant becomes strong at lower energies, it will bind the elementary dark fields together at the phase transition or condensation scale Λc. Above this scale the particles are massless and at the condensation scale Λc they acquire a mass of the order of Λc. The elementary fields will form gauge invariant particles due to the strong coupling. These particles are dark “mesons” and dark “baryons”.

45 Extra Symmetries

A. de la Macorra, C. Stephan-Otto, Phys. Rev. Lett. 87 (2001) 271301

Ej: The model with SU(3) gauge group has 6 chiral + antichiral fields with 97.5 degrees of freedom, a condensation scale Λc = 42 eV and an 4+n n inverse power potential with V = Λ c φ − , n = 2/3. This model gives a warm DM with a free streaming scale λfs < 0.6 Mpc and an equation of state parameter for the DE wDEo=−0.9 with Ωm = 0.27, ΩDEo = 0.73.

45 Extra Symmetries

46 Extra Symmetries

Cosmological Scalar Fields Uniﬁcation. Perez-Lorenzana, et. al. Phys. Rev. D77, (2008), 063507

Invariant under SU(1, 1)

46 Extra Symmetries

Cosmological Scalar Fields Uniﬁcation. Perez-Lorenzana, et. al. Phys. Rev. D77, (2008), 063507

Invariant under SU(1, 1)

1 µ µ = [∂ φ∂ φ + ∂ φ∗∂ φ∗] L 2 µ µ

46 Extra Symmetries

Cosmological Scalar Fields Uniﬁcation. Perez-Lorenzana, et. al. Phys. Rev. D77, (2008), 063507

Invariant under SU(1, 1)

1 µ µ = [∂ φ∂ φ + ∂ φ∗∂ φ∗] L 2 µ µ φ ΦE = φ∗ 1 2 T 1 2 U(Φ)= M Φ σ Φ + Φ†Φ m Φ†σ Φ + V 4 3 − 2 1 0 46 Extra Symmetries

47 Extra Symmetries

1 5 0,5

0 0 l k f -0,5 4 2 0 -2 -1 -4 y0 k y 47 Some Alternatives

49 Repulsive, Fuzzy and Scalar Field DM

49 Ideas

Matos-Guzman 2000

P. J. E. Peebles 2000 Ideas

Matos-Guzman 2000

P. J. E. Peebles 2000

Ureña-Lopez-et. al. 2000

Ureña-Lopez-Liddle 2007

Cervantes-Rodriguez 2001

Perez-Lorenzana-et. al. 2007

Bose-Einstein Condensates

☐☐☐☐

= 0

The Cosmology The Cosmology

Φ2 as Dark Matter. T. Matos, A. Vázquez & J.A. Magaña. MNRAS, 389, (2009) 13957. The Cosmology

Φ2 as Dark Matter. T. Matos, A. Vázquez & J.A. Magaña. MNRAS, 389, (2009) 13957. Linear regime of perturbations Linear regime of perturbations 1 δΦ¨ +3HδΦ˙ 2δΦ + V, δΦ +2V, φ =0 − a2 ∇ ΦΦ Φ Linear regime of perturbations 1 δΦ¨ +3HδΦ˙ +( 2 m2)δΦ +2V, φ =0 −a2 ∇ − Φ Linear regime of perturbations 1 δΦ¨ +3HδΦ˙ +( k2 m2)δΦ +2V, φ =0 k k a2 − k Φ Linear regime of perturbations 1 δΦ¨ +3HδΦ˙ +( k2 m2)δΦ +2V, φ =0 k k a2 − k Φ Linear regime of perturbations 1 δΦ¨ +3HδΦ˙ +( k2 m2)δΦ +2V, φ =0 k k a2 − k Φ Galactic Collapse of Scalar Field Dark Matter. M.Alcubierre, F. S. Guzmán, T. Matos, D. Núñez, L. A. Ureña and P. Wiederhold. CQG 19(2002)5017. arXiv:gr-qc /0110102. Scalar Field Fluctuation = Halo

Galactic Collapse of Scalar Field Dark Matter. M.Alcubierre, F. S. Guzmán, T. Matos, D. Núñez, L. A. Ureña and P. Wiederhold. CQG 19(2002)5017. arXiv:gr-qc /0110102.

2 • M ≈ 0.1 M Planck/mΦ

-22 • If mΦ ≈ 10 eV

• M ≈1012 Mo

Weak Field Limit A. Bernal, et. al. Flat Central Density Proﬁles from Scalar Field Dark Matter Halo. Rev. Mex. A.A. 44, (2008), 149-160 T. Harko & C. G. Bhömer JCAP 0706:025,(2007) arXiv:0705.4158 Density Profiles

T. Harko & C. G. Bhömer JCAP 0706:025,(2007) arXiv:0705.4158 Density Profiles LSB Galaxies Density Profiles LSB Galaxies Hydrodinamical version of the Linear regime of perturbations Hydrodinamical version of the Linear regime of perturbations 1 δΦ¨ +3HδΦ˙ 2δΦ + V, δΦ +2V, φ =0 − a2 ∇ ΦΦ Φ

mc2 t δΦ = ρˆ cos + S v S ≡ m∇ Hydrodinamical version of the Linear regime of perturbations

62 Hydrodinamical version of the Linear regime of perturbations

v S ≡ m∇ ∂ρˆ 1 + (ˆρv)+3Hρˆ ∂t a2 ∇ · ρˆ S¨ +3HS˙ ρˆ˙S˙ =0 − m − m ∂v 1 2 √ρˆ + v v + φ + ∂t a2 ∇ · ∇ 2m2 ∇ √ρˆ ∂v S˙ =0, − m ∂t

62 Hydrodinamical version of the Linear regime of perturbations

v S ≡ m∇ ∂ρˆ 1 + (ˆρv)+3Hρˆ =0 ∂t a2 ∇ ·

∂v 1 2 √ρˆ + v v + φ + =0, ∂t a2 ∇ · ∇ 2m2 ∇ √ρˆ

62 Hydrodinamical version of the Linear regime of perturbations

v S ≡ m∇ ∂ρˆ 1 + (ˆρv)+3Hρˆ =0 ∂t a2 ∇ ·

∂v 1 2 √ρˆ + v v + φ + =0, ∂t a2 ∇ · ∇ 2m2 ∇ √ρˆ

63 Hydrodinamical version of the Linear regime of perturbations

ρˆ =ˆρ(t) S = S(t) v S ≡ m∇ ∂ρˆ 1 + (ˆρv)+3Hρˆ =0 ∂t a2 ∇ ·

∂v 1 2 √ρˆ + v v + φ + =0, ∂t a2 ∇ · ∇ 2m2 ∇ √ρˆ

63 Hydrodinamical version of the Linear regime of perturbations

ρˆ =ˆρ(t) S = S(t) v S ≡ m∇ ∂ρˆ +3Hρˆ =0 ∂t

63 Hydrodinamical version of the Linear regime of perturbations

ρˆ =ˆρ(t) S = S(t) v S ≡ m∇ ∂ρˆ +3Hρˆ =0 ∂t

1 ρˆ ∼ a3

63 Hydrodinamical version of the Linear regime of perturbations

v S ≡ m∇

64 Hydrodinamical version of the Linear regime of perturbations

v S ≡ m∇ ∂ρˆ 1 + (ˆρv)+3Hρˆ =0 ∂t a2 ∇ ·

∂v 1 2 √ρˆ + v v + φ + =0, ∂t a2 ∇ · ∇ 2m2 ∇ √ρˆ

64 Hydrodinamical version of the Linear regime of perturbations

v S ≡ m∇ ∂ρˆ 1 + (ˆρv)=0 ∂t a2 ∇ ·

∂v 1 2 √ρˆ + v v + φ + =0, ∂t a2 ∇ · ∇ 2m2 ∇ √ρˆ

64 Hydrodinamical version of the Linear regime of perturbations

65 Hydrodinamical version of the Linear regime of perturbations

ρˆ =ˆρ + ρ (t)exp(ik x/a) 0 1 · v = v + v (t)exp(ik x/a) 0 1 · φ = φ + φ (t)exp(ik x/a) 0 1 · ∂ρ ρˆ 1 +3Hρ + i 0 k v =0, ∂t 1 a2 · 1 v2 2 ∂v1 q a + iρ1 4πG 2 k =0, ∂t ρˆ0 − k a2 φ +4πG ρ =0. 1 k2 1 2k2 v2 = q 4a2m2 65 Hydrodinamical version of the Linear regime of perturbations

66 Hydrodinamical version of the Linear regime of perturbations

v1 = λk + v2

∂ρ ρˆ 1 +3Hρ + i 0 k2λ =0 ∂t 1 a2 2 2 ∂λ vq a + i( 4πG 2 )ρ1 =0, ∂t ρˆ0 − k

66 Hydrodinamical version of the Linear regime of perturbations

v1 = λk + v2

∂ρ ρˆ 1 +3Hρ + i 0 k2λ =0 ∂t 1 a2 2 2 ∂λ vq a + i( 4πG 2 )ρ1 =0, ∂t ρˆ0 − k ρ δ = 1 ρˆ d2δ dδ k2 SFDM +2H + v2 4πGρˆ δ =0, dt2 dt q a2 − 0

66 Hydrodinamical version of the Linear regime of perturbations

v1 = λk + v2

∂ρ ρˆ 1 +3Hρ + i 0 k2λ =0 ∂t 1 a2 2 2 ∂λ vq a + i( 4πG 2 )ρ1 =0, ∂t ρˆ0 − k ρ δ = 1 ρˆ d2δ dδ k2 SFDM +2H + v2 4πGρˆ δ =0, dt2 dt q a2 − 0

d2δ dδ k2 CDM +2H + v2 4πGρˆ δ =0, dt2 dt s a2 − 0 66 Hydrodinamical version of the Linear regime of perturbations

0.0001 b 9e-05

8e-05

7e-05

6e-05

b 5e-05

4e-05

3e-05

2e-05

1e-05

0 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 t 67 68 k-essence

S = d4x√ g (X, Φ) Φ − L 1 X = gµν Φ Φ 2 ∇µ ∇ν

SFDM Some Alternatives

71 MOND and MOND+

M. Milgrom. Acta Phys.Polon.B32:3613,2001. e-Print: astro-ph/0112069 m a = F

71 MOND and MOND+

M. Milgrom. Acta Phys.Polon.B32:3613,2001. e-Print: astro-ph/0112069 8 2 mµ(a)=F a 10− cm/s | | ∼

71 MOND and MOND+

M. Milgrom. Acta Phys.Polon.B32:3613,2001. e-Print: astro-ph/0112069 8 2 mµ(a)=F a 10− cm/s | | ∼

71 MOND and MOND+

R. H. Sanders. The Astrophysical Journal, 512:L23–L26, 1999 February 10

72 MOND and MOND+

J. D. Bekenstain. PHYSICAL REVIEW D, VOLUME 70, 083509

73 MOND and MOND+

J. D. Bekenstain. PHYSICAL REVIEW D, VOLUME 70, 083509

TeVeS

4φ µ G =8πG T˜ +(1 e− )U T˜ U + τ + Θ αβ αβ − µ(α β) αβ αβ where

2 1 µν µ 1 ν ταβ σ φ,αφ,β g φ,µφ,ν gαβ U φ,µ U(αφ,β) U φ,ν gαβ ≡ − 2 − − 2 1 2 4 2 G− σ F (kGσ )gαβ − 4

µν 1 στ µν Θαβ K g U[µ,α]U[ν,β] g g U[σ,µ]U[τ,ν] gαβ λUαUβ ≡ − 4 −

73 MOND and MOND+

R. Reyes, R. Mandelbaum, U. Seljak, T. Baldauf, J. E. Gunn, L. Lombriser & R. E. Smith. NATURE, Vol 464, 11 March 2010

1 Υgm EG = β Υgg

74 MOND and MOND+

S. Mendoza, X. Hernandez, J.C. Hidalgo & T. Bernal. arXiv: 1006.5037

75 MOND and MOND+

S. Mendoza, X. Hernandez, J.C. Hidalgo & T. Bernal. arXiv: 1006.5037 8 2 mµ(a)=F a 10− cm/s | | ∼

75 MOND and MOND+

S. Mendoza, X. Hernandez, J.C. Hidalgo & T. Bernal. arXiv: 1006.5037 ma = µ(F )

75 MOND and MOND+

S. Mendoza, X. Hernandez, J.C. Hidalgo & T. Bernal. arXiv: 1006.5037 ma = µ(F ) lm GM = ma0 f l = r m a 0

75 MOND and MOND+

S. Mendoza, X. Hernandez, J.C. Hidalgo & T. Bernal. arXiv: 1006.5037 ma = µ(F ) lm GM = ma0 f lm = r a0 300

250

200

) 2 3 s

/ 1+x + x + x 150 km f(x)=x

( 2

V 1+x + x 100

0 0 2 4 6 8 10 12 14 16 18 20 75 r(kpc) Some Alternatives

1 S = d4x√ gf(R)+ d4x (g , Ψ ) , 2κ2 − LM µν M

77 f(R)

1 S = d4x√ g [f(χ)+f (χ)(R χ)] + d4x (g , Ψ ) . 2κ2 − ,χ − LM µν M Varying this action with respect to χ, one obtains χ = R,thus

1 S = d4x√ g ϕR U(ϕ) + d4x (g , Ψ ) − 2κ2 − LM µν M χ(ϕ) ϕ f(χ(ϕ)) ϕ f,χ(χ) , U(ϕ)= − ≡ 2κ2

77 f(R)

1 S = d4x√ g [f(χ)+f (χ)(R χ)] + d4x (g , Ψ ) . 2κ2 − ,χ − LM µν M Varying this action with respect to χ, one obtains χ = R,thus

1 S = d4x√ g ϕR U(ϕ) + d4x (g , Ψ ) − 2κ2 − LM µν M χ(ϕ) ϕ f(χ(ϕ)) ϕ f,χ(χ) , U(ϕ)= − ≡ 2κ2 With Palatini 1 3 1 S = d4x√ g ϕR(g)+ ( ϕ)2 U(ϕ) + d4x (g , Ψ ) − 2κ2 4κ2 ϕ ∇ − LM µν M 77 f(R) Yong-Seon Song, Hiranya Peiris, and Wayne Hu. Phys.Rev.D76:063517,2007

78 f(R) Yong-Seon Song, Hiranya Peiris, and Wayne Hu. Phys.Rev.D76:063517,2007

1 f dR d ln H − B RR ≡ 1+f d ln a d ln a R B B(z = 0) 0 ≡ 78 f(R)

Dark matter as a geometric effect in f(R) gravity C. G. Böhmer, T. Harko, F. S.N. Lobo. Astroparticle Physics 29 (2008) 386–392 A Model of f(R) Gravity as an Alternative for Dark Matter in Spiral Galaxies. S. Asgari. Applied Physics Research. Vol. 2, No.1, 2010

79 f(R)

1 ω S = d4x√ g ϕR BD ( ϕ)2 U(ϕ) + d4x (g , Ψ ) − 2 − 2ϕ ∇ − LM µν M

79 f(R)

1 ω S = d4x√ g ϕR BD ( ϕ)2 U(ϕ) + d4x (g , Ψ ) − 2 − 2ϕ ∇ − LM µν M

Conformal Transformation g˜µν = Fgµν

4 1 1 µν 4 1 S = d x g˜ R˜ g˜ ∂ φ∂ φ V (φ) + d x (F − (φ)˜g , Ψ ) E − 2κ2 − 2 µ ν − LM µν M

U FR f κφ 3/2 ln F V (φ)= = − ≡ F 2 2κ2F 2 79 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104

80 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104 • Spontaneus scalarization = Chameleon

2 gµν = A g˜µν

φ V + A3 A T =0 − φ φ

80 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104 • Spontaneus scalarization = Chameleon

2 gµν = A g˜µν

φ V + A3 A T =0 − φ φ

ρ˜ = A3 ρ

Veff = V +˜ρ A

meff = V,φφ +˜ρ A,φφ

80 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104 • Spontaneus scalarization = Chameleon

2 gµν = A g˜µν

φ V + A3 A T =0 − φ φ

ρ˜ = A3 ρ

Veff = V +˜ρ A

meff = V,φφ +˜ρ A,φφ

80 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104 • Spontaneus scalarization = Chameleon

2 gµν = A g˜µν

φ V + A3 A T =0 − φ φ

ρ˜ = A3 ρ

Veff = V +˜ρ A ρ˜A meff = V,φφ +˜ρ A,φφ

V ρ˜A

80 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104 • Spontaneus scalarization = Chameleon

2 gµν = A g˜µν

φ V + A3 A T =0 − φ φ

ρ˜ = A3 ρ

Veff = V +˜ρ A Veff ρ˜A meff = V,φφ +˜ρ A,φφ

V ρ˜A

80 f(R)

T. Damour & Esposito-Farèse. PRL 70(1993)2220 J. Khoury & A. Weltman. PRL 93(2004)171104 • Spontaneus scalarization = Chameleon

2 gµν = A g˜µν

φ V + A3 A T =0 − φ φ

ρ˜ = A3 ρ

Veff = V +˜ρ A Veff ρ˜A meff = V,φφ +˜ρ A,φφ

Searching for Chameleon-like Scalar Fields S. A. Levshakov, P. Molaro, M. G. Kozlov, A. V. V ρ˜A Lapinov, C. Henkel, D. Reimers, T. Sakai & I. I. Agafonova. arXiv: 1012.0642 80 81 Extra Dimensions

81 Extra Dimensions

M. A. G-Aspeitia, et. al. Gen Relativ Gravit (2011) 43:315–329

Hidden Brane Visible Brane

Scalar Field Standard Model

Conclusion Conclusion

• We are in the threshold for a new era in Cosmology, Science and Thought