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Science from Overlapping Lensing / Spec-Z Surveys

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Science from Overlapping Lensing / Spec-Z Surveys Science from overlapping lensing / spec-z surveys Chris Blake (Swinburne) Probes of the cosmological model How fast is the Universe How fast are structures expanding with time? growing within it? Redshift-space distortions • RSD allow spectroscopic galaxy surveys to measure the growth rate of structure coherent virialized flows infalling motions galaxies observer Why combination of lensing and RSD? • 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 Applications 12 F. Simpson et al. 0.9 arXiv:1212.3339Mon.0.8 Not. R. Astron. Soc. 000, 000–000 (0000) Printed 17 December 2012 (MN LATEX style file v2.2) CFHTLenS:0.7 Testing the Laws of Gravity with Tomographic Weak Lensing and Redshift Space Distortions 0.6 1! 1 2 3 13 Fergus0.5 Simpson , Catherine Heymans , David Parkinson , Chris Blake , Martinφ Kilbinger4,5,6, Jonathan Benjamin7, Thomas Erben8, Hendrik Hildebrandt7,8, Henk Hoekstra9,10, Thomas D. Kitching1, Yannick Mellier11, Lance Miller12, Ludovic0.4 Van Waerbeke7, Jean Coupon13, Liping Fu14, Joachim Harnois-Deraps´ 15,16, Michael J. Hudson17,18, Konrad Kuijken9, Barnaby Rowe19,20, Tim Schrabback8,9,21, Elisabetta0.3 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, Australia 3Centre0.2 for Astrophysics & Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia 4CEA Saclay, Service d’Astrophysique (SAp), Orme des Merisiers, Batˆ 709, F-91191 Gif-sur-Yvette, France. 5Excellence Cluster Universe, Boltzmannstr. 2, D-85748 Garching, Germany. 6Universit0.1 ats-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. 10Department0 of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada. 11Institut0 d’Astrophysique de Paris,0.5 Universite´ Pierre et Marie1 Curie - Paris 6, 981.5 bis Boulevard Arago, F-750142 Paris, France. 2.5 12Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK. 13Institute of Astronomy and Astrophysics, Academia Sinica, P.O.Redshift Box 23-141, Taipei 10617, Taiwan. 14Key Lab1 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. Figure 11. Here we explore fractional deviations in the two gravitational 17 arXiv:1003.2185 FigureDepartment 12. of PhysicsThe and Astronomy, redshift University sensitivity of Waterloo, Waterloo,of the ON, N2L modified 3G1, Canada. gravity parameter µ0. potentials, the Newtonian potential Ψ and the curvature potential Φ, from 18Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, ON, N2L 1Y5, Canada. The19Department weight of Physics function and Astronomy,φ University(z) is College defined London, Gower in Street, equation London WC1E (22) 6BT, UK.and evaluated with the GR value at z =0.5. The prescription for this is given by equation (21). 20California Institute of Technology, 1200 E California Boulevard, Pasadena CA 91125, USA. Confirmation of general relativity on large scales fromequation21Kavli Institute (23)for Particle. Astrophysics and Cosmology, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305-4060, USA. The contours represent the same combinations of data as those in the left 1 hand panelweak of Figure lensing 5. and galaxy velocities 17 December 2012 ples of theoretical models onto our parameter space, by evaluating 1 1 2-4 2 Reinabelle Reyes , Rachel Mandelbaum , Uros Seljak , Tobias Baldauf , Jamesequation E. (22). HoweverABSTRACT as stressed earlier, we do not aim to place 8 THEORETICAL MODELS Dark energy may be the first sign of new fundamental physics in the Universe, taking either a 1 2 2 arXiv:1212.3339v1 [astro-ph.CO] 13 Dec 2012 rigorous parameterphysical constraints form or revealing on any a correction particular to Einsteinian family gravity. Weak of gravitational models. lensing and Gunn , Lucas Lombriser , Robert E. Smith galaxy peculiar velocities provide complementary probes of General Relativity, and in com- Below we briefly review some of the theoretical models which bination allow us to test modified theories of gravity in a unique way. We perform such an analysis by combining measurements of cosmic shear tomography from the Canada-France could generate1Princeton a University departure Observatory, from µ0 Peyton= Σ0 Hall,=0 Princeton,, and interpret NJ 08544 the USA Hawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the Wig- 8.1 f(R) gleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey (6dFGS), producing the implications of our results. There is such a plethora of modified strongest existing joint constraints on the metric potentials that describe general theories of 2Institute for Theoretical Physics, University of Zurich, Zurich, 8057, Switzerland gravity. For scale-independent modifications to the metric potentials which evolve linearly gravity models, that no single choice of parameterisation can ade- A more general formwith the of effective the dark Einstein-Hilbert energy density, we find present-day action cosmological replaces deviations the in the 3 Newtonian potential and curvature potential from the prediction of General Relativity to be Physics and Astronomy Department and Lawrence Berkeley National Laboratory, ∆Ψ/Ψ =0 .05 0.25 and ∆Φ/Φ = 0.05 0.3 respectively (68 per cent CL). quately encompass all of them. This is a situation reminiscent of the Ricci scalar R with an arbitrary± function −f(R±) such that Figure 2 | Comparison ofKey observational words: cosmology: observations constraints - gravitational lensing with predictions from dark energyUniversity equation of California of state,-Berkeley,w(z) ,CA except 94720 hereUSA we are faced with uncertainty4 not only in the functional form of the time-dependence, but alsoInstitute in its for scale-dependence. Early Universe, Ewha So University, how can Seoul, we S. relate KoreaGR a given and viable modified gravityS = theories.f(R)√ g d Estimates4x, of EG((24)R) are shown with ! − (µ, Σ) constraint to a specific model? The observed parameters µˆ0 [email protected] ! 19 c 0000 RAS 1! error bars! (s.d.) including the statistical error on the measurement of ! and Σˆ 0 may be interpreted as a weighted integral over the true func- where g is the determinant of the metric tensor. This defines the tional formEinstein’sµ(k, general z), such relativity that (GR) is the theory of gravity underpinning our broad class of f(R) models. One of the most difficult tasks for (filled circles).any The modified grey gravity shaded model region attempting indicates to replace the dark1! energyenvelope is of the mean understanding of the Universe, encapsulatedΩΛ in the standard cosmological model µˆ0 = φ(k, z) µ(k, z) dk dz. (22) to satisfy the stringent-1 Solar System constraints, and most natu- ΩΛ(z) E over scales R = 10 – 50h Mpc, where the systematic effects are least (!CDM). To explain!! observations showing that the UniverseG is undergoing ral choices of the function f(R) fail to do so. The subset of f(R) If we performaccelerated a expansion scale- and1,2, ! time-dependentCDM posits the existence principal of a component gravitationally repulsivemodels which have attracted interest are those which employ the analysis (see for example Zhao et al. 2009), then the weightimportant func- (see Supplementary Information). The horizontal line shows the mean fluid, called dark energy (in addition to ordinary matter and dark matter). so-called chameleon mechanism, where departures from GR are tion φ(k, z) may be expressed in terms of the principal componentsprediction ofstrongly the GR+ suppressed"CDM inmodel, regions E where= !R is/ large,f , for only the emerging effective redshift of the Alternatively, the breakdown of GR on cosmological length scales could also G m,0 ei(k, z) and the errors associated with their corresponding eigen- when R is sufficiently small. Our location within the potential well values σexplain(αj ) (Simpsonthe cosmic acceleration. & Bridle 2006), Indeed, such modifications that to GRmeasurement, have been proposedof the z = Sun 0.32. and theOn Milky the right Way haloside may of bethe sufficient panel,to labelled shield us vertical bars as alternatives to dark energy3,4, as well as to dark matter.5,6 These modifiedfrom this unusual gravitational behaviour. 2 ei(k, z) ei(k!,z!)dk! dz!/σ (αi) show the predictedFor aranges particular from subset three of f( Rdifferent) models whichgravity are theories: capable of (i) GR+"CDM φ(k,gravity z)= theoriesi are designed to explain the observed expansion. (23)history, so the only 2 2 satisfying
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