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Alternatives to Dark Energy and Dark Matter and their implications Orfeu Bertolami Instituto Superior Técnico Departamento de Física (http://alfa.ist.utl.pt/~orfeu/homeorfeu.html ) International Workshop on Advances in Precision Tests and Experimental Gravitation in Space 28-30 September, Florence, Italy Evidence for Dark Energy and Dark Matter Modified Gravity Models and their observational implications
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Page 1: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Alternatives to Dark Energy and Dark Matterand their implications

Orfeu Bertolami

Instituto Superior TécnicoDepartamento de Física

(http://alfa.ist.utl.pt/~orfeu/homeorfeu.html)

International Workshop on Advances in PrecisionTests and Experimental Gravitation in Space

28-30 September, Florence, Italy

Evidence for Dark Energy and Dark Matter

Modified Gravity Models and their observational implications

Page 2: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

General Relativity( )

• GR has survived all tests so far…[C. Will, gr-qc/0510072; S. Turyshev, M. Shao, K. Nordtvedt, gr-qc/0601035][O.B., J. Páramos, S. Turyshev, gr-qc/0602016]

• Parametrized Post-Newtonian Formalism (U-gravitational potential, velocity)

• Local (solar system) tests

Mercury´s perihelion shift: [Shapiro 1990]

Lunar Laser Ranging: [Williams, Turyshev, Boggs 2004]

LBLI light deflection: [Eubanks et al. 1997]

Cassini Experiment: [Bertotti, Iess, Tortora 2003]

...,221 200 +−+−= UUg β ...)34(

21

0 ++−= ii vg γ...,)21( ++= ijij Ug δγ

iv

310312 −×<−− βγ410)5.44.4(34 −×±=−−γβ

41041 −×<−γ510)3.21.2(1 −×±=−γ

1== βγ

Page 3: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Cassini-Huygens Radiometric Experiment

B. Bertotti, L. Iess and P. Tortora, Nature 425 (2003) 374

Page 4: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

(Partially) Unconfirmed predictions:

Gravitational waves – PSR B1913+16(LIGO, …, LISA)

Lense-Thirring Effect(Gravity Probe-B)

BepiColombo Mission to Mercury (ESA/ISAS)

669

2

2 105,105.2,10 −−− ×<∆×<∆<∆ββ

γγ

JJ

γβηηη 21,102 1

5

1

1 +−−=×<∆ −

Page 5: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

10500 vacua

Turyshev et al., gr-qc/0506104

Page 6: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

• Outstanding challenges (GR + Quantum Field Theory)– Singularity Problem– Cosmological Constant Problem– Underlying particle physics theory for Inflation

• Theory provides in the context of the Big Bang model an impressivepicture of the history of the Universe– Nucleosynthesis ( , )– Cosmic Microwave Background Radiation– Large Scale Structure– Gravitational lensing– …

• Required entities (missing links):– Dark Matter– Dark Energy

Cosmological Tests of General Relativity

4<νN 001.0023.02 ±=Ω hB

Page 7: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

• Evidence:

Flatness of the rotation curve of galaxiesLarge scale structureGravitational lensingN-body simulations and comparison with observationsMerging galaxy cluster 1E 0657-56

• Cold Dark Matter (CDM) Model

Weakly interacting non-relativistic massive particle at decoupling

• Candidates:

Neutralinos (SUSY WIMPS), axions, scalar fields, self-interacting scalarparticles, etc.

Dark Matter

Page 8: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

• Evidence:Dimming of type Ia Supernovae with z > 0.35Accelerated expansion (negative deceleration parameter):

[Perlmutter et al. 1998; Riess et al. 1998, …]

• Homogeneous and isotropic expanding geometryDriven by the vacuum energy density ΩΛ and matter density ΩM

Equation of state:

• Friedmann and Raychaudhuri equations imply:

q0 < 0 suggests an invisible smooth energy distribution

• Candidates:Cosmological constant, quintessence, more complex equations of state,etc.

Dark Energy

ωρ=p 1≤ω

47.020 −≤−≡a

aaq&

&&

( ) ΛΩ−Ω+= mq 1321

0 ω

Page 9: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Supernova Legacy Survey (SNLS)

[Astier et al., astro-ph/0510447]

Page 10: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

SNLS - SDSS

13.019.002.1 +

−−=ω

)(054.0)(090.0023.1 syststat ±±−=ω

[Riess et al. 2004]

[Astier et al. 2005]

)(007.0)(021.0271.0 syststatm ±±=Ω

Page 11: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

D.N. Spergel et al., astro-ph/0603449

WMAP 3 Year Results

Page 12: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

WMAP 3 Year Results

WMAP 3 + SNLS:

ρω p=

D.N. Spergel et al., astro-ph/0603449

Page 13: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

D.N. Spergel et al., astro-ph/0603449

WMAP 3 Year Results

Page 14: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Gamma-ray bursts and Dark Matter

Effect of the increase of high red shift GRBs (90, 500, 1000) for XCDM models

[O.B., Silva, Mon. Not. R. Ast .Soc. 365 (2006) 1149]

Page 15: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Gamma-Ray Bursts Telescope

SWIFT

NASANovember 2004

Dark Matter ProbeO.B., P. Silva, MNRAS (2006)

Page 16: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

AA UniverseUniverse dominateddominated byby darkdark componentscomponents

Cosmic Concordance(ΛCDM)

ΩΛ 0.72

Ωm 0.28

Ωk 0

Page 17: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Quintessence

• V0 exp (-λφ) [Ratra, Peebles 1988; Wetterich 1988; Ferreira, Joyce 1998]

• V0 φ-α , α > 0 [Ratra, Peebles 1988]

• V0 φ-α exp ( λφ 2 ) , α > 0 [Brax, Martin 1999, 2000]

• V0 [exp ( Mp / φ ) – 1 ] [Zlatev, Wang, Steinhardt 1999]

• V0 ( cosh λ φ - 1 )p [Sahni, Wang 2000]

• V0 sinh-α ( λφ ) [Sahni, Starobinsky 2000; Urena-López, Matos 2000]

• V0 [ exp ( βφ ) + exp ( γφ ) ] [Barreiro, Copeland, Nunes 2000]

• Scalar-Tensor Theories of Gravity

[Uzan 1999; Amendola 1999; O.B., Martins 2000; Fujii 2000; ...]

• V0 exp( -λφ ) [ A + ( φ - B )2 ] [Albrecht, Skordis 2000]

• V0 exp( -λφ ) [ a + ( φ - φ0 )2 + b ( ψ - ψ0 )2+ c φ ( ψ - ψ0 )2 +d ψ ( φ - φ0 )2 ][Bento, O.B., Santos 2002]

Varying vacuum energy models[Bronstein 1933; O.B. 1986; Ratra, Peebles 1988; Wetterich 1988; …]

Page 18: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Dark Energy and Dark Matter

“Quintessential Inflation”[Peebles, Vilenkin 1999; Dimopoulos, Valle 2002; O.B., Duvvuri 2006, …]

Dark Energy – Dark Matter interaction[Amendola 2000]

Dark Energy – Dark Matter Unification[Kamenschik, Moschella, Pasquier 2001]

[Bilic, Tupper, Viollier 2002; Bento, O.B., Sen 2002]

Λ

Inflation Dynamics

DM

DE

Page 19: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Generalized Chaplygin gasmodel

Generalized Chaplygin gas

: Chaplygin gas

Dust : stiff matter De Sitter

• Unified model for Dark Energy and Dark Matter

Generalized d-brane

: d-brane

[Bento, O.B., Sen 2002]

Page 20: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Dark Energy - Dark Matter Unification:Generalized Chaplygin Gas Model

– CMBR Constraints [Bento, O. B., Sen 2003, 2004; Amendola et al. 2004]

– SNe Ia [O. B., Sen, Sen, Silva 2004; Bento, O.B., Santos, Sen 2005]

– Gravitational Lensing [Silva, O. B. 2003]

– Structure Formation *

[Sandvik, Tegmark, Zaldarriaga, Waga 2004; Bento, O. B., Sen 2004; Bilic, Tupper, Viollier 2005; …]

– Gamma-ray bursts [O. B., Silva 2006]

– Cosmic topology [Bento, O. B., Rebouças, Silva 2006]

– Inflation [O.B., Duvvuri 2006]

Background tests:

,6.0≤α 85.065.0 ≤≤ sA αρ +≡ 10Ch

sAA

Structure formation: 2.0≤α

Page 21: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Density constrast δ(aeq) for different valuesof α, as compared with ΛCDM.

[Bento, O. B., Sen 2002]

Page 22: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

The growth factor m(y) as a function of thescale factor a. The solid, dotted, dashed anddash-dot lines correspond to α = 0, 0.2, 0.4,0.6 respectively. It is assumed:Ωdm0 = 0.25, ΩΛ0 = 0.7, Ωb0 = 0.05 and α = 0.2

The bias b as a function of the scale factor a.The solid, dotted, dashed and dash-dot linescorrespond to α = 0, 0.2, 0.4, 0.6 respectively.It is assumed: Ωdm0 = 0.25, ΩΛ0 = 0.7,Ωb0 = 0.05 and α = 0.2

[Bento, O. B., Sen 2004]

Page 23: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Contours for parameters b and m in the Ωm – αplane. Solid lines are for b whereas dashedlines are for m. For b, contour values are 0.98,0.96, ..., 0.9 from left to right. For m, contourvalues are 0.6, 0.65, ..., 0.8 from left to right.

Joint 68% CL confidence regions forModel II using both SNe, gravitationallensing statistics and CMBR constraints.

[Bento, O. B., Sen 2004] [Silva, O. B. 2003]

Page 24: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Pioneer 10 anomalous decelerationPioneer 10/11 anomalous deceleration (20 AU – 70 AU):

[Anderson, Laing, Lau, Liu, Nieto, Turyshev 2002]

Cause:

Systematical effects ?Thermal effects ? [Scheffer 2003]Kuiper Belt gravity ? No ! [Anderson et al. 2002, Nieto 2005, O.B., Vieira 2005]Scalar field ? [O.B., Páramos 2004]Post-Newtonian model with running coupling consts. ? [Jaekel, Reynaud 2005]…

Deceleration due to dragging:Pio

PioPioMedPio m

AvOa2

.)1( ρ=

319.

2 /103241,9.5,/2.126.11 cmgkgmmAskmv MedPioPioPio−×=⇒==−= ρ

PioDMHaloDM aacmg 5324 102/106 −− ×≅⇒×≅≅ ρρDM

DE PioDEDE aacmg 11330 102/106 −− ×−≅⇒×≅ρ

210 /10)3.15.8( smaPio−×±=

Page 25: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

A Mission to Test the Pioneer Anomaly

Pioneer Science Team, gr-qc/0506139

Page 26: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Dark Matter Detection[Baudis 2005]

Page 27: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Merging Galaxy Cluster 1E 0657-56[Clowe et al., astro-ph/0608407]

“Bullet” Cluster

Page 28: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Self-Interacting Dark Matter

Higgs decay width

[Bento, O.B., Rosenfeld, Teodoro 2000][Silveira, Zee 1988]

[Bento, O.B., Rosenfeld 2001]

[Spergel, Steinhardt 2000]

Model:

Motivation: “cuspy core” problem

Page 29: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

[Bento, O.B., Rosenfeld 2001]

Page 30: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Direct Dark Energy Detection ?• Spectrum noise in Josephson junctions [Beck, Mackey 2005]

• No! Zero-energy fluctuations are not measurable …

[Jetzer, Straumann 2005]

• DE-gauge field coupling: variation of the “fine structure constant”[Olive, Pospelov 2002; Gardner 2003; …]

[O.B., Lehnert, Potting, Ribeiro 2003; Bento, O.B., Santos 2004]

Hzm

GeVch

cDEc12

34

3 10)05.069.1()4.09.3( ×±≅⇒±=≅ νρνπ

Page 31: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Variation of the electromagnetic coupling via direct Q-electromagnetic interaction

[ Bento, O.B., Santos 2004]

Page 32: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Oklo Meteorites

[Bento, O.B., Santos 2004]

Page 33: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Large Dark Energy Surveys

Supernovae Standard CandlesLuminosity Distance

Cosmic Shear Evolution of DM perts.

Baryon Acoustic OscillationsStandard rulerAngular diameter distance

SNAP, DUNE…

Page 34: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Dark MatterModified Newtonian Dynamics (MOND)[Milgrom 1983, Bekenstein, Milgrom 1984, ..., Bekenstein 2004]

Motivation: Flatness Rotation Curve of Galaxies

a0 ≈ 1.2 × 10 -10 m/s2 - universal acceleration

Tully-Fisher Law: as

TeVeS2 version: F-function problem

Page 35: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

MOND

Tensor-Vector-Scalar field theory, S = Sg + Ss + Sv + Sm:

Conformal transformation to the physical metric:

Page 36: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Scalar field:

Vector field:

• Timelike vector tracks the metric

consistent with eq. of motion

• Einstein eq.

MOND in Post-Newtonian regime

[Bekenstein 2004]

Page 37: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

• Parametrization of the metric

• Expansion of Einstein eq. up to order r − 4

• Solution:

• Transformation into physical, isotropic PPN metric yields

(like GR !)

Page 38: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

• Assume

• Solution:

Dynamic solution for the vector field

, γ = 1

Constraint |β - 1| < 6 × 10-4allows for k < kup

[O.B., Páramos, to appear]

(different from GR!)

Page 39: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Consistency with Cosmology

i) (Potentially) compatible

[Skordis, Mota, Ferreira, Boehm 2005]• CMBR

ii) Problem with the third peak[Slosar, Melchiorri, Silk 2005]

• Gravitational lensing – great potential for testing[Zhao, Bacon, Taylor, Horne 2005]

2102×≅Λ

MOND

CDM

PP

Page 40: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Can MOND take a bullet ?

• Doubled and tripled-centered baryonic systems

• Multi-field TeVeS gravity

[Angus, Famaey, Zhao 2006]

Newtonian (baryons + DM) (full)MOND (dashed)TeVeS (scalar field) (dot-dashed)

Page 41: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Dark EnergySelf-accelerating gravity models

[Dvali, Gabadadze, Porrati 2000; Deffayet 2001; Freese, Lewis 2002; … ]

Motivation: 5D Braneworlds

E.g. BPS-branes (Randall-Sundrum, Dilatonic): bulk scalar field

2σσφ −∂=U

φσ

σα

∂∂

≡1

PPN:

[Palma 2006]

2

341 αγ −=−

( )21

2

911 ααβ −=−

Page 42: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Self-accelerating gravity models

• “Infrared” Modifications of Gravity (rc= 3 Gpc – crossover constant):

• PPN:

• Lense-Thirring effect unchanged [Iorio 2006]

• DGP [Dvali, Gabadadze, Porrati 2000][Deffayet 2001]

• DT [Dvali, Turner 2003]

• Cardassian [Freese, Lewis 2002]

1,1 == γβ

Page 43: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Cosmological Constraints

[Bento, O.B., Rebouças, Santos 2006]

Page 44: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Cosmological Constraints

[Eisenstein et al. 2005]

• Baryon Acoustic Oscillations

LRG (SDSS):

• CMBR Shift Parameter ( )

WMP 3:

Page 45: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Scalar-Tensor Theories of Gravity

Binary Pulsars (B1913+16; J1141-6545)

[Esposito-Farese 2004]

20

0

121ααγ

+−=−

1.111 <

−−

γβ

5.4,060.0 00 −>< βα22

0

020

)1(1

αβαβ

+=−

Page 46: Alternatives to Dark Energy and Dark Matter and their implications · 2017. 6. 6. · •Evidence: Dimming of type Ia Supernovae with z > 0.35 Accelerated expansion (negative deceleration

Conclusions

• Resolving the dichotomy DE - DM X Modified Gravity will requirea concerted effort and a whole new programme of dedicatedexperiments in space:

- To observe SNe (SNe “factories”), gamma-ray bursts,gravitational lensing, cosmic shear, etc, so to characterize theproperties of DE and DM, or alternatively, to find evidence forthe inadequacy of General Relativity

- To test General Relativity and examine the implications of itscontending theories or extensions (scalar-tensor theories,braneworld models, strings)

- For the search of evidence of new forces with ranges of abouthundreds AU and for resolving the Pioneer anomaly problem


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