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

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.

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

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.

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 .

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

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

Small Scale Tests: III

• Enhanced forces between dwarf galaxies displace stellar disk from halo center (and from HI disk) by up to 1kpc.

• 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

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

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

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

• Deflection angle formula from Geodesic eqn

Generalize

• How the observable convergence is related to mass fluctuations:

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≡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

• 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

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.

Redshift space power spectra

Pgv can be combined with the lensing cross-spectrum Pg Zhang et al 2007

Pgv(k)

Tegmark et al 2006

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

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

Forecasts for Geff and

g

Forecasts for G, : time dependent

Results are sensitive to fiducial model and to time dependence of parameters!

Mpc-scales

•Stack velocity differences of satellite galaxies around BCG•Richer clusters wider velocity histograms higher mass

C. Group/Cluster Masses: Dynamical

Velocity histogram within virial radius: modeling systematic errorsMain galaxies, fitting to 1 gaussian and 2 gaussians

1-d velocity disperion -> 3-d mass profiles

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

Theoretical models

Halo model and N-body predictions: Preliminary: Tsz-Yan Lam, M. Takada, F. Schmidt

• Spare Slides

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?