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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. Dark Energy Tests.

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Weak lensing and redshift space data tests of gravity
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
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
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 i how changing gravity affects galaxies
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.

Modified gravity ii two potentials not one
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 iii how the milky way protects gr
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.

Designing spectroscopic surveys
Designing Spectroscopic Surveys asymmetric

  • 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

bulk flows asymmetric

Probes of metric potentials


Galaxy Clusters

Linear regime LSS

  • Dynamical probes (blue) measure Newtonian potential 

  • Lensing and ISW (red) measures 

  • Constraints from current data are at 20-50% level

Linear regime growth factors
Linear Regime Growth Factors asymmetric


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.


andGeffcan be scale and time dependent in modified gravity

Lensing: what we assume about gravity asymmetric


  • Deflection angle formula from Geodesic eqn


  • How the observable convergence  is related to mass fluctuations:


Poisson eqn


  • For scalar-tensor gravity theories, lensing by a given mass distribution is identical to GR.

How does lensing test gravity? asymmetric

  • 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 /

Robust Test

B galaxy galaxy lensing
B. Galaxy-galaxy lensing asymmetric

  • 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
Redshift space power spectra asymmetric


Tegmark et al 2006

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

Current tests on large scales
Current Tests on Large Scales asymmetric




Reyes et al 2010

  • SDSS data: 20% test of gravity (GR passed!) at 10-30 Mpc scale

  • Other large-scale tests combine power spectra to constrain specific models.

The future lensing and redshift space power spectra
The Future: Lensing and Redshift Space Power Spectra asymmetric


Redshift spacespectra

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.

Forecasts for g eff and
Forecasts for G asymmetriceff and 


Forecasts for g time dependent
Forecasts for asymmetricG, : time dependent

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

Mpc scales
Mpc-scales asymmetric

C. Group/Cluster Masses: Dynamical asymmetric

  • Stack velocity differences of satellite galaxies around BCG

  • Richer clusters  wider velocity histograms  higher mass

Velocity histogram within virial radius: modeling systematic errors

Main galaxies, fitting to 1 gaussian and 2 gaussians

Velocity fields around sdss galaxies
Velocity fields around SDSS galaxies errors

  • 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
Theoretical models errors

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

Three regimes
Three regimes errors

  • 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?