14
Chris Blake (Swinburne) Are VISTA/4MOST surveys interesting for cosmology?
Chris Blake (Swinburne)
Are VISTA/4MOST surveys interesting for cosmology?
Yes!
How fast are structures growing within it?
Probes of the cosmological model
How fast is the Universe expanding with time?
• Follow-up ~2x106 X-ray selected AGN from eROSITA?
4MOST BAO surveys
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From eROSITA Bulletin 4:
• The sample is very under-dense for BAO studies (issues : shot noise, reconstruction)
• Comparison : DESI is targetting 18x106 ELGs, 4x106 LRGs, 3x106 QSOs on a similar timeframe (2018-22)
• Other strong competition from Euclid and WFIRST
• Suggests that BAO studies targetting this AGN sample are likely not competitive?
• But ...
4MOST BAO surveys
4MOST lensing follow-up surveys
• Mis-match between imaging and spectroscopy
• Improvement of cosmological measurements through addition of galaxy-galaxy lensing
• [e.g. determines bias of lens sample which improves RSD measurements of lenses, especially when using multiple-tracer techniques, e.g. Cai & Bernstein (2012)]
• Spec-z survey allows definition of lens samples (e.g. groups, galaxy types) enabling a range of studies
• Understanding, calibration and risk mitigation of systematic errors (photo-z errors including outliers, intrinsic alignments, cosmic shear)
Overlaps of lensing and spec-z surveys
observer
infallinggalaxies
coherentflowsvirialized
motions
Redshift-space distortions
• RSD allow spectroscopic galaxy surveys to measure the growth rate of structure
Redshift-space distortions
• Sensitive to theories of gravity in complementary ways
• General perturbations to FRW metric:
• are metric gravitational potentials, identical in General Relativity but can differ in general theories
• Relativistic particles (e.g. light rays for lensing) collect equal contributions and are sensitive to
• Non-relativistic particles (e.g. galaxies infalling into clusters) experience the Newtonian potential
Why combination of lensing and RSD?
Applications
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 17 December 2012 (MN LATEX style file v2.2)
CFHTLenS: Testing the Laws of Gravity with Tomographic WeakLensing and Redshift Space Distortions
Fergus Simpson1!, Catherine Heymans1, David Parkinson2, Chris Blake3,Martin Kilbinger4,5,6, Jonathan Benjamin7, Thomas Erben8, Hendrik Hildebrandt7,8,Henk Hoekstra9,10, Thomas D. Kitching1, Yannick Mellier11, Lance Miller12,Ludovic Van Waerbeke7, Jean Coupon13, Liping Fu14, Joachim Harnois-Deraps15,16,Michael J. Hudson17,18, Konrad Kuijken9, Barnaby Rowe19,20, Tim Schrabback8,9,21,Elisabetta Semboloni9, Sanaz Vafaei7, Malin Velander12,9.1Scottish Universities Physics Alliance, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK.2School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia3Centre for Astrophysics & Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia4CEA Saclay, Service d’Astrophysique (SAp), Orme des Merisiers, Bat 709, F-91191 Gif-sur-Yvette, France.5Excellence Cluster Universe, Boltzmannstr. 2, D-85748 Garching, Germany.6Universitats-Sternwarte, Ludwig-Maximillians-Universitat Munchen, Scheinerstr. 1, 81679 Munchen, Germany.7Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, V6T 1Z1, BC, Canada.8Argelander Institute for Astronomy, University of Bonn, Auf dem Hugel 71, 53121 Bonn, Germany.9Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.10Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada.11Institut d’Astrophysique de Paris, Universite Pierre et Marie Curie - Paris 6, 98 bis Boulevard Arago, F-75014 Paris, France.12Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK.13Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan.14Key Lab for Astrophysics, Shanghai Normal University, 100 Guilin Road, 200234, Shanghai, China.15Canadian Institute for Theoretical Astrophysics, University of Toronto, M5S 3H8, Ontario, Canada.16Department of Physics, University of Toronto, M5S 1A7, Ontario, Canada.17Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.18Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, ON, N2L 1Y5, Canada.19Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.20California Institute of Technology, 1200 E California Boulevard, Pasadena CA 91125, USA.21Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305-4060, USA.
17 December 2012
ABSTRACTDark energy may be the first sign of new fundamental physics in the Universe, taking either aphysical form or revealing a correction to Einsteinian gravity. Weak gravitational lensing andgalaxy peculiar velocities provide complementary probes of General Relativity, and in com-bination allow us to test modified theories of gravity in a unique way. We perform such ananalysis by combining measurements of cosmic shear tomography from the Canada-FranceHawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the Wig-gleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey (6dFGS), producing thestrongest existing joint constraints on the metric potentials that describe general theories ofgravity. For scale-independent modifications to the metric potentials which evolve linearlywith the effective dark energy density, we find present-day cosmological deviations in theNewtonian potential and curvature potential from the prediction of General Relativity to be!"/" =0 .05± 0.25 and !#/# = !0.05± 0.3 respectively (68 per cent CL).
Key words: cosmology: observations - gravitational lensing
c! 0000 RAS
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12 F. Simpson et al.
Figure 11. Here we explore fractional deviations in the two gravitationalpotentials, the Newtonian potential ! and the curvature potential ", fromthe GR value at z = 0.5. The prescription for this is given by equation (21).The contours represent the same combinations of data as those in the lefthand panel of Figure 5.
8 THEORETICAL MODELS
Below we briefly review some of the theoretical models whichcould generate a departure from µ0 = !0 = 0, and interpret theimplications of our results. There is such a plethora of modifiedgravity models, that no single choice of parameterisation can ade-quately encompass all of them. This is a situation reminiscent of thedark energy equation of state, w(z), except here we are faced withuncertainty not only in the functional form of the time-dependence,but also in its scale-dependence. So how can we relate a given(µ,!) constraint to a specific model? The observed parameters µ0
and !0 may be interpreted as a weighted integral over the true func-tional form µ(k, z), such that
µ0 =
!!!(k, z)µ(k, z)
"!
"!(z)dk dz . (22)
If we perform a scale- and time-dependent principal componentanalysis (see for example Zhao et al. 2009), then the weight func-tion !(k, z) may be expressed in terms of the principal componentsei(k, z) and the errors associated with their corresponding eigen-values "(#j) (Simpson & Bridle 2006), such that
!(k, z) =
"i ei(k, z)
##ei(k
!, z!)dk! dz!/"2(#i)"
j
$##ej(k!!, z!!)dk!! dz!!
%2/"2(#j)
. (23)
The analysis of redshift space distortions in Blake et al. (2012) in-cludes information from the galaxy power spectrum up to a max-imum wavenumber kmax = 0.2hMpc"1, corresponding to theregime over which the density and velocity fields are sufficientlylinear for our theoretical models to remain valid. Since the numberof Fourier modes increases towards higher k, the scale-dependentcomponent of !(k, z) peaks close to this value of kmax, and!(k, z) = 0 for k > kmax. We evaluate the redshift-dependenceof the weight function !(z) associated with the combined WiggleZand 6dFGS data of Figure 3, following the prescription of Simp-son & Bridle (2006), and this is shown to peak at z ! 0.5 as il-lustrated in Figure 12. In the following subsections we utilise theweight function !(z) presented in Figure 12 to map specific exam-
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Redshift
!
Figure 12. The redshift sensitivity of the modified gravity parameter µ0.The weight function !(z) is defined in equation (22) and evaluated withequation (23).
ples of theoretical models onto our parameter space, by evaluatingequation (22). However as stressed earlier, we do not aim to placerigorous parameter constraints on any particular family of models.
8.1 f(R)
A more general form of the Einstein-Hilbert action replaces theRicci scalar R with an arbitrary function f(R) such that
S =
!f(R)
"#g d4x , (24)
where g is the determinant of the metric tensor. This defines thebroad class of f(R) models. One of the most difficult tasks forany modified gravity model attempting to replace dark energy isto satisfy the stringent Solar System constraints, and most natu-ral choices of the function f(R) fail to do so. The subset of f(R)models which have attracted interest are those which employ theso-called chameleon mechanism, where departures from GR arestrongly suppressed in regions where R is large, only emergingwhen R is sufficiently small. Our location within the potential wellof the Sun and the Milky Way halo may be sufficient to shield usfrom this unusual gravitational behaviour.
For a particular subset of f(R) models which are capable ofsatisfying Solar System tests, the departure from GR may be char-acterised as (Zhao et al. 2012)
µ(k, a) =1
3 + 3(aM/k)2, (25)
where the scalaron mass M(a) = 1/&
3 d2f/dR2. For any givenredshift and wavenumber, the value of µ lies in the range 0 !µ < 1
3 . This generically enhances growth, so we expect thisfamily of models to lie vertically above the point (0, 0) in Fig-ure 5. We parameterise M = M0a
"! and take as an exampleM0 = 0.02hMpc"1 and " = 3, corresponding to the type ofmodel explored in Zhao et al. (2012). In f(R) models the lensingpotential for a given mass distribution is unchanged from the caseof GR, and so !f(R)
0 = 0. Our measure of µ is dominated by the
c! 0000 RAS, MNRAS 000, 000–000
13
Figure 2 | Comparison of observational constraints with predictions from
GR and viable modified gravity theories. Estimates of EG(R) are shown with
1! error bars (s.d.) including the statistical error on the measurement19 of !
(filled circles). The grey shaded region indicates the 1! envelope of the mean
EG over scales R = 10 – 50h-1 Mpc, where the systematic effects are least
important (see Supplementary Information). The horizontal line shows the mean
prediction of the GR+"CDM model, EG = !m,0/ f , for the effective redshift of the
measurement, z = 0.32. On the right side of the panel, labelled vertical bars
show the predicted ranges from three different gravity theories: (i) GR+"CDM
(EG= 0.408 ± 0.029(1! ) ), (ii) a class of cosmologically-interesting models
in f (R) theory with Compton wavelength parameters27B0= 0.001! 0.1
(EG= 0.328 ! 0.365 ), and (iii) a TeVeS model9 designed to match existing
cosmological data and to produce a significant enhancement of the growth
factor (EG= 0.22 , shown with a nominal error bar of 10 per cent for clarity).
1
Confirmation of general relativity on large scales from
weak lensing and galaxy velocities1
Reinabelle Reyes1, Rachel Mandelbaum
1, Uros Seljak
2-4, Tobias Baldauf
2, James E.
Gunn1, Lucas Lombriser
2, Robert E. Smith
2
1Princeton University Observatory, Peyton Hall, Princeton, NJ 08544 USA
2Institute for Theoretical Physics, University of Zurich, Zurich, 8057, Switzerland
3Physics and Astronomy Department and Lawrence Berkeley National Laboratory,
University of California-Berkeley, CA 94720 USA
4Institute for Early Universe, Ewha University, Seoul, S. Korea
Einstein’s general relativity (GR) is the theory of gravity underpinning our
understanding of the Universe, encapsulated in the standard cosmological model
(!CDM). To explain observations showing that the Universe is undergoing
accelerated expansion1,2
, !CDM posits the existence of a gravitationally repulsive
fluid, called dark energy (in addition to ordinary matter and dark matter).
Alternatively, the breakdown of GR on cosmological length scales could also
explain the cosmic acceleration. Indeed, modifications to GR have been proposed
as alternatives to dark energy3,4
, as well as to dark matter.5,6
These modified
gravity theories are designed to explain the observed expansion history, so the only
way to test them is to study cosmological perturbations (deviations of the matter
density from its mean value). This is a non-trivial task, compounded by our lack of
a priori knowledge of relevant astrophysical parameters.7,8
Here, we successfully
measure the probe of gravity9 EG that is robust to these uncertainties. Under
GR+!CDM, EG should approximately equal 0.4. We find EG = 0.39±0.06 at
1 Submitted version. Accepted version and supplementary material are available at:
http://www.nature.com/nature/journal/v464/n7286/full/nature08857.html.
arXiv:1212.3339
arXiv:1003.2185
• Photometric redshift errors are one of the leading systematics for weak lensing tomography
• Mean and width of redshift distributions in each photo-z bin must be known to accuracy ~ 10-3
• Method (1) : spectroscopic training set [issues : sample variance, incompleteness of training set, outliers]
• Method (2) : photo-z/spec-z cross-correlations [issues : degeneracies with galaxy bias, cosmic magnification]
• Currently unsolved problem for current and future lensing surveys (DES, LSST, Euclid)
Photometric redshift calibration
• eROSITA will provide deep survey of X-ray clusters
• Mass function of clusters is sensitive test of cosmology
• 4MOST can efficiently obtain cluster redshifts
Galaxy clusters
• VISTA/4MOST offers wide-field spectroscopic follow-up of the southern sky
• BAO surveys targetting AGN likely not competitive
• Follow-up of southern lensing surveys (DES, LSST) is most compelling cosmology science case (in my view)
• Allows cross-correlations of RSD + cosmic shear and other applications of galaxy-galaxy lensing
• Solves the photometric-redshift calibration problem
• Cluster cosmology
Summary
