Signatures of MG on non- linear scales Fabian Schmidt MPA Garching Lorentz Center Workshop, 7/15/14
Tests of gravity Smooth Dark Energy (DE): unique prediction for growth factor given w(a) Use evolution of perturbations to distinguish modified gravity (MG) from smooth DE Very broadly, classify gravity tests into Generic vs targeted Parametrized/consistency tests vs modelspecific constraints
Generic vs Targeted Generic tests: use popular cosmological observables, and marginalize over non-gravity nuisance parameters: Galaxy 2-pt function Redshift-space distortions Cluster abundance & density profiles Shear power spectrum... Targeted tests: constructed to specifically look for modifications of gravity (-> later)
Tests as function of scale g-isw Post-Newt. proj. effects Fig. 1. Tests of gravity at di erent length scales (adapted from Jain & Khoury 2010). Red lines shows observations that probe the sum of metric potentials via weak and strong gravitational lensing (SL) or the ISW e ect. Blue lines show dynamical measurements that rely on the motions of stars or galaxies or other non-relativistic tracers. This partial list of observables illustrates the wide range of scales that can provide interesting tests. In addition, properties of the tracer and its environment are also important. Jain & Khoury
Tests as function of scale g-isw Post-Newt. proj. effects Fig. 1. Tests of gravity at di erent length scales (adapted from Jain & Khoury 2010). Red lines shows observations that probe the sum of metric potentials via weak and strong gravitational lensing (SL) or the ISW e ect. Blue lines show dynamical measurements that rely on the motions of stars or galaxies or other non-relativistic tracers. This partial list of observables illustrates the wide range of scales that can provide interesting tests. In addition, properties of the tracer and its environment are also important. Jain & Khoury
Generic vs Targeted Generic tests: Relatively easy to do (for a theorist) Can use all information in data How do we know any discrepancies are due to gravity? (and not due to neutrinos, non-gaussianity,...) Targeted tests: Robust to (ideally) any non-gravity effects Do not use all information in data Still in an early stage
Parametrized vs Modelspecific Parametrized tests: consistency tests of ΛCDM (or smooth DE) paradigm D(z) = m (z) ; PC analysis of D(z) given H(z) Model-specific constraints: Constrain f(r), DGP, galileon, symmetron,... model parameters EFT / Horndeski approach: model-encompassing
Parametrized vs Modelspecific Parametrized tests: consistency tests of ΛCDM (or smooth DE) paradigm D(z) = m (z) ; PC analysis of D(z) given H(z) Model-specific constraints: Constrain f(r), DGP, galileon, symmetron,... model parameters EFT / Horndeski approach: model-encompassing
Downsides Parametrized tests: consistency tests of ΛCDM No consistent model away from ΛCDM (especially on nonlinear scales) What to allow in standard paradigm - w(a)? Neutrinos? Primordial non-gaussianity? Model-specific constraints: Only constrain specific models EFT / Horndeski approach: How to go beyond linear perturbations? Too general for observational purposes?
Parameter space of MG in LSS context Relation b/w dynamics and lensing Both of these to be seen as function of scale and redshift Relation b/w lensing and matter m ds 2 = (1 + 2 )dt 2 +(1+2 )a 2 (t)dx 2
Parameter space of MG in LSS context Relation b/w dynamics and lensing GR Both of these to be seen as function of scale and redshift Relation b/w lensing and matter m ds 2 = (1 + 2 )dt 2 +(1+2 )a 2 (t)dx 2
Parameter space of MG in LSS context Scalar-tensor Relation b/w dynamics and lensing GR Both of these to be seen as function of scale and redshift Relation b/w lensing and matter m ds 2 = (1 + 2 )dt 2 +(1+2 )a 2 (t)dx 2
Generic tests Matter power spectrum Measurable through cosmic shear (weak lensing) Vainshtein and chameleon effects lead to qualitatively similar suppressions f(r) Full simulations Simulations without chameleon mechanism Validity of linear theory at z=0
Generic tests Matter power spectrum Measurable through cosmic shear (weak lensing) Vainshtein and chameleon effects lead to qualitatively similar suppressions r c =500 Mpc r c =3000 Mpc ndgp
Generic tests (2) Halo mass function Measurable through cluster counts (X-ray, SZ, optical) Constraints on f R0 <~ 10-4 Shaded region: semianalytical spherical collapse approach Noticeable difference between Vainshtein and chameleon mechanisms
Generic tests (2) Halo mass function Measurable through cluster counts (X-ray, SZ, optical) ndgp Constraints on f R0 <~ 10-4 Shaded region: semianalytical spherical collapse approach Noticeable difference between Vainshtein and chameleon mechanisms
Targeted tests Scalar field generically leads to discrepancies between dynamics and lensing RSD vs lensing Phasespace of clusters 50-150 Mpc 5-20 Mpc Velocity dispersions within clusters and galaxies This is a targeted test of gravity cf PPN tests in the Solar System < 3 Mpc
Phasespace around Distribution of line-ofsight velocity as function of transverse separation Measured from spectroscopic galaxy sample Mass distribution can be measured from lensing (Partly) bridging gap between virialized scales and perturbative RSD massive halos σ vlos v los [km/s] 500 400 300 2000 1500 1000 500 0-500 -1000-1500 -2000 r p [Mpc/h] 2 4 6 8 10 12 14 16 18 0 1 2 3 4 5 6 7 8 r p [Mpc/h] Yan et al, arxiv:1202.4501, see also Yin & Weinberg, Jennings et al FIG. 1: Lower panel: The v los r p phase space distribution (in logarithmic scale) as measured using halo catalogs constructed from N-body simulations in ΛCDM (see also [7]); we considered primary halos ( clusters ) with masses 10 14 M /h and secondary halos ( galaxies ) in the range 3 10 13 M 10 14 M /h. Upper panel: The dispersion of the line-of-sight velocity distribution σ vlos as function of r p. The data points with error bars are computed from the simulation results in the lower panel, while the solid curve is our analytical model prediction. The error bars are scaled to mimic the measurement accuracies for a spectroscopic survey of 2000 sq. degrees over 0.2 <z<0.4. -10-15 -20-25 -30 ln[p(v vlos,r p )]
Phasespace around Stacking many halos: spherically symmetric system massive halos Yan et al, arxiv:1202.4501, see also Yin & Weinberg, Jennings et al Example: f(r) effect on second moment (variance) of this distribution vlos p Error bars for HSC / PFS survey Error bars for HSC (lensing) and PFS (spectroscopic) survey FIG. 2: Upper panel: Ratio of the velocity dispersion σ v along the line of sight measured around halos with M 300 > 10 14 M /h in f(r) simulationstothatmeasuredaroundhalos of the same mass in ΛCDM simulations. The error bars are estimated from the simulations, as in Fig. 1, for a spectroscopic survey of 2000 sq. degrees. Lower panel: Ratio of the enclosed projected mass profiles of the same halos in f(r) and ΛCDM simulations. This is approximately what stacked lensing would measure. The shaed region indicates the range of statistical uncertainties for an imaging survey of the same area (see text).
Phasespace around massive halos Halo model prediction for f(r) effects works quite well Yan et al, 1305.5548 Similar for Vainshteintype models (DGP+DE) Modeling the base ΛCDM model is main challenge (Hubble flow) Data exist!
Conclusions Probing gravity: we want to cover the entire accessible range of scales & redshifts Generic tests (P(k), mass function, ) are well developed EUCLID working groups, mod gravity code comparison project, Targeted tests (dynamics vs lensing) warrant more (observational and modeling) work The fact that we can do these tests with LSS is non-trivial and worth emphasizing!