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Weak Lensing and Redshift Space Data: Tests of GravityPowerPoint Presentation

Weak Lensing and Redshift Space Data: Tests of Gravity

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### Probes of metric potentials

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.

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

- 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

- 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 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

bulk flows asymmetric

Galaxies

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 asymmetric

Metric

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

andGeffcan be scale and time dependent in modified gravity

Lensing: what we assume about gravity asymmetric

GR

- Deflection angle formula from Geodesic eqn
Generalize

- How the observable convergence is related to mass fluctuations:

GR

Poisson eqn

Generalize

- 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 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 asymmetric

Pgv(k)

Tegmark et al 2006

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

Current Tests on Large Scales asymmetric

<gγ>

<gg>

r

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 asymmetric

Lensingspectra

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 asymmetricG, : time dependent

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

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 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 errors

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

- Spare Slides errors

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?

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