Weak Lensing and Redshift Space Data: Tests of Gravity
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Weak Lensing and Redshift Space Data: Tests of Gravity
Bhuvnesh Jain, University of Pennsylvania
Jake VanderPlas, Joseph Clampitt, Anna Cabre, Vinu Vikram
BJ & Khoury (2010) arXiv: 1004.3294
BJ (2011) arXiv: 0223977
BJ & VanderPlas (2011) arXiv: 1106.0065
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Dark Energy Tests
• Lensing sensitive to geometry+growth: shear-shear and galaxy-shear spectra
• Redshift space power spectra measure D(z) through BAO peaks, and growth factor+bias from full 3D power spectra
• Joint constraints on Dark Energy are powerful due to complementary dependence on parameters and bias constraints.
See Gaztanaga, Bernstein, Kirk talks.
In this talk, I will focus on small-scale tests of gravity. Caveat: Much of this work is preliminary, quantitative connections to DESpec are yet to be worked out.
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Recent progress in gravity theories
• Models that produce cosmic acceleration have been proposed
• Mechanisms exist to recover GR in the solar system• General features arise in the dynamics of galaxies
and large-scale structure
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Modified Gravity Ihow changing gravity affects galaxies
• Modified gravity (MG) theories generically involve scalar fields that provide an attractive, fifth-force: a = (ΨS + ΨN)
• This can enhance effective forces on galaxies by 10-100%!
• For large-scale structure, deviations from GR are measured through power spectra of lensing or galaxy clustering (MG suppressed at high-z -> smaller deviations accumulate in the growth factor).
• For low-z galaxies or clusters with dynamical timescales ~Gyr or less, the effects can be larger.
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Modified Gravity IItwo potentials, not one
• Galaxies and Photons respond to different potentials: the mass distribution inferred from dynamics is different from lensing.
• Conformal transformation of metric -> lensing masses are true masses!
• So a fairly generic signature of modified gravity:
Dynamical mass > Lensing masses
…on a variety of scales: kpc-Gpc.
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Modified Gravity IIIhow the Milky Way protects GR
• Modified gravity theories generically involve large force enhancements.
• BUT…GR must be restored in the Milky Way - via ``natural’’ mechanisms that work for massive/dense objects. Khoury & Weltman 2004; Vainshtein 72
• So small galaxies or the outer regions of big galaxy/cluster halos may show deviations from GR.
• The best place to look for signatures of cosmic acceleration could be through the dynamics and infall of modest-sized galaxies.
– A broad class of theories requires < 10-6 for objects to feel the scalar force; dwarf galaxies have < 10-7 .
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Gravity tests in nearby galaxies
• The infall velocities of small galaxies can be enhanced due to the fifth force of the scalar field: small-scale redshift space distortions
• Enhanced forces alter the luminosities, colors and ages of stars in ``unscreened’’ galaxies.
- For realistic parameters, main sequence stars self-screen, but red giants in dwarf galaxies will be hotter. Chang & Hui 2010
• Stars may be screened due to their own Newtonian potential: so in dwarf galaxies they may move differently than dark matter and gas (which feel the fifth/scalar force).
- Stars move slower than DM/gas
- Stars separate from gas component
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Small Scale Tests: III
• Enhanced forces between dwarf galaxies can displace stellar disk from halo center.
• The neutral Hydrogen gas disk observed in 21cm would track the dark matter halo -> observable offsets between the disks, and distortions stellar disks.
BJ & VanderPlas, arXiv: 1106.0065
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Small Scale Tests: III
• Enhanced forces between dwarf galaxies displace stellar disk from halo center (and from HI disk) by up to 1kpc.
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• Rotation curves of stars are displaced from HI gas, and are asymmetric
• Related effects may be seen in velocity dispersions of dwarf ellipticals/spheroidals – to be studied
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Designing Spectroscopic Surveys
• Ultra low-z component with three goals: – Map the gravitational field of the universe out to 100s of Mpc
– Obtain redshifts and velocity dispersions of field dwarf ellipsoids/spheroidals
– Obtain infall patterns around galaxy groups
• Medium z component: obtain lensing and dynamics of hosts with redshifts z~0.1-0.5
– Sample a sufficient number of galaxy groups (0.1-few Mpc) more densely with spectroscopy
– See Bernstein talk for advantage of estimating halo masses
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Probes of metric potentials
Dynamical probes (blue) measure Newtonian potential
Lensing and ISW (red) measures Constraints from current data are at 20-50% level
Galaxies Galaxy Clusters Linear regime LSS
bulk flows
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Linear Regime Growth Factors
Different growth factors for density and metric potentials:
– Density growth factor: D(z,k) – Lensing growth factor: D+ Geff D,
– Dynamical growth factor D = /(1+ D+
This description is valid on scales of 10s-100s Mpc.
Poisson
Metric
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ds2 = −(1+ 2ψ )dt 2 + (1− 2φ)a2(t)dx2
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∇2(ψ + φ) = 8πGeff a2ρ δ
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=φ /ψ
and Geff can be scale and time
dependent in modified gravity
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′ ′ +2H ′ δ −8πGeff
1+ηρa2δ = 0
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• Deflection angle formula from Geodesic eqn
Generalize
• How the observable convergence is related to mass fluctuations:
€
≡12 ∂1
2 + ∂22
( )(φ +ψ )2−d = Gρ dz W (z,zs)δ∫ (z)
• For scalar-tensor gravity theories, lensing by a given mass distribution is identical to GR.
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α =−2 ∇⊥φ2d
Lensing: what we assume about gravity
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α =−∇⊥(φ +ψ )2d
GR
GR
Poisson eqn
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ρ dz GeffectiveW (z,zs) δ∫ (z)Generalize
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• By itself, lensing measures the sum of metric potentials
- Lensing power spectrum can only test specific models
• Lensing tomography how D + evolves with redshift
- This is the primary test for dark energy models as well
• Relation of lensing observables to matter correlations
- Provided there is a tracer of the mass with known bias
• Cross-correlations: galaxy-lensing plus galaxy-dynamics
- Can give a model-independent measure of /
How does lensing test gravity?
Robust Test
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B. Galaxy-galaxy lensing
•Projected mass profile in three luminosity bins Mandelbaum et al 2005
•Statistical errors on lensing/dynamical comparison at 100-1000 kpc: ~20%
•Systematic errors are comparable or larger.
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Redshift space power spectra
Pgv can be combined with the lensing cross-spectrum Pg Zhang et al 2007
Pgv(k)
Tegmark et al 2006
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Current Tests on Large Scales
•SDSS data: 20% test of gravity (GR passed!) at 10-30 Mpc scale
•Other large-scale tests combine power spectra to constrain specific models.
Reyes et al 2010
<gγ>
<gg>
r
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The Future: Lensing and Redshift Space Power Spectra
Expected measurements from DES and BOSS surveys. Guzik, Jain, Takada 2009
See more recent work of Zhao et al; Gaztanaga et al; Kirk, Lahav, Bridle.
Lensing spectra
Redshift space spectra
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Forecasts for Geff and
g
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Forecasts for G, : time dependent
Results are sensitive to fiducial model and to time dependence of parameters!
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Mpc-scales
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•Stack velocity differences of satellite galaxies around BCG•Richer clusters wider velocity histograms higher mass
C. Group/Cluster Masses: Dynamical
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Velocity histogram within virial radius: modeling systematic errorsMain galaxies, fitting to 1 gaussian and 2 gaussians
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1-d velocity disperion -> 3-d mass profiles
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Velocity fields around SDSS galaxies
Anna Cabre et al, in prep.:
• Measure velocity dispersion and infall as a function of radius and host luminosity
• Go out to 10 virial radius
• Compare to halo model
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Theoretical models
Halo model and N-body predictions: Preliminary: Tsz-Yan Lam, M. Takada, F. Schmidt
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• Spare Slides
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Three regimes
• Linear regime: >100 Mpc, z>0.5
• Intermediate z, Mpc scales
• Local universe, dwarf galaxies: within 100s Mpc
• Can some fraction of fibers be used for the latter two regimes?