Gruppe um Prof. Peter SchneiderForschungsschwerpunkt

Gravitationslinsen-Effekt und Kosmologie

Peter Schneider

Sprecher: Patrick Simon

Chris Boever (Bachelorstudent), Sabine Derdau (Sekretariat), Dr. Thomas Erben, Dominik Klaes (Doktorand), Dr. Ole Marggraf, Sandra Martin (Doktorandin), Dr. Nicolas Martinet, Dr. Reiko Nakajima, Hananeh Saghiha (Doktorandin), Dr. Tim Schrabback, Shafiee Zeinab (Doktorandin), Dr. Huan Yuan Shan, Dr. Zahra Sheikhbahaee, Prof. Dr. Peter Schneider, Dr. Patrick Simon, Dr. Malte Tewes, Sandra Unruh (Doktorandin), Jan-Luca van den Busch (Praktikant), Rongchuan Zhao (Masterstudent)

Gruppe Prof. Peter Schneider

Gruppe Prof. Peter Schneider

Illustration des Gravitationslinsen-Effekts an einem Galaxienhaufen

Abell 1689 by HST / NASA

Gruppe Prof. Peter Schneider

von Thomas Erben / Isaac Newton Group of Telescopes

Datenreduktion, Objektidentifikation,

Photometrie, Scherungsmessung

Gruppe Prof. Peter Schneider

Schrabback, T. et al., 2016, MNRAS

82 %

15 %3 %

Galaxienintergalaktisches GasDunkle Materie

Physik von Galaxienhaufen

Gruppe Prof. Peter Schneider

Gruppe Prof. Peter Schneider

Simulierte Winkelfläche am Himmel

Abstand

von S. Colombi, IAP Paris

von A. Refregier

18 Hildebrandt, Viola, Heymans, Joudaki, Kuijken & the KiDS collaboration

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Figure 6. Marginalized posterior contours (inner 68% CL, outer 95% CL) in the ⌦m-�8 plane (left) and ⌦m-S8 plane (right) from thepresent work (green), CFHTLenS (grey), pre-Planck CMB measurements (blue), and Planck 2015 (orange). Note that the horizontalextent of the confidence contours of the lensing measurements is sensitive to the choice of the prior on the scalar spectrum amplitude As.The CFHTLenS results are based on a more informative prior on As artificially shortening the contour along the degeneracy direction.

For each of the three calibration methods (DIR, CC,BOR) we estimate statistical errors from a bootstrap re-sampling of the spectroscopic calibration sample (see Sec-tion 6.2 for details of the implementation). Including thoseuncertainties will broaden the contours. As can be seen inFig. 2 these bootstrap errors are very small for the BORmethod. This is due to the fact that a lot of informationin that technique is based on the photometric P (z) and there-calibration is more stable under bootstrap re-sampling ofthe spectroscopic calibration sample than for the other twomethods. Hence to further speed up the MCMC runs we ne-glect the BOR errors in the following with no visible impacton the results. The uncertainties on the DIR method – whilelarger than the BOR errors – are also negligible comparedto the shot noise in the shear correlation function (see Ap-pendix C2). We nevertheless include these errors here (asbefore) since DIR is our primary calibration method. Thestatistical errors on the CC method are larger than for thetwo other methods, owing to the as yet small area covered bythe spectroscopic surveys that we can cross-correlate with.More importantly, we estimate that the limited availablearea also gives rise to a larger systematic uncertainty on theCC method compared to the DIR technique. All major re-quirements for the DIR technique are met in this analysiswhereas the CC method will only realise its full potentialwhen larger deep spec-z surveys become available.

The resulting confidence contours in the ⌦m-�8 planefor the four cases are shown in Fig. 7. All four cases givefully consistent results although there are some shifts inthe contours with respect to each other. However, with��2e↵ ' �10, we find that the DIR and CC methods providea better fit to the data as compared to the BPZ and BORmethods. For future cosmic shear surveys, with considerablylarger datasets, it will be essential to reduce the statisticaluncertainty in the redshift calibration in order to not com-promise the statistical power of the shear measurement. ForKiDS-450 the uncertainty for our favoured DIR calibrationscheme is still subdominant.

In summary, we find that the four possible choices for

the photometric redshift calibration technique yield consis-tent cosmological parameters.

6.4 Impact of analytical and numerical covariancematrices

For our primary analysis we choose to adopt the analyticalestimate of the covariance matrix described in Section 5.3,as it yields the most reliable estimate of large-scale samplevariance (including super-sample contributions), is free fromnoise, and is broadly consistent with the N -body covariance(see Section 5.4). In this section we compare the cosmo-logical parameter constraints obtained with the analyticalcovariance matrix to the alternative numerical estimate asdescribed in Section 5.2. For this test, we set all astrophysi-cal and data-related systematics to zero: this applies to theintrinsic alignment amplitude, the baryon feedback ampli-tude, the errors on the shear calibration, and the errors onthe redshift distributions. Fixing these parameters allows usto focus on the e↵ect of the di↵erent covariance matrices onthe cosmological parameters.

We correct for noise bias in the inverse of the numericalcovariance matrix estimate using the method proposed bySellentin & Heavens (2016). As we have a significant num-ber of N-body simulations, however, we note that the con-straints derived using our numerical covariance matrix areunchanged if we use the less precise but alternative Hartlapet al. (2007) bias correction scheme.

We find consistency between the results for the di↵erentcovariance matrices given the statistical errors of KiDS-450.There are however small shifts in the central values of thebest-fit parameters; most notably the S8 constraints for theanalytical and numerical covariances which di↵er by ⇠ 1�.We attribute these shifts to super-sample-covariance termsthat are correctly included only in the analytical estimate(which is also the reason why we adopt it as our preferredcovariance). The SSC reduces the significance of the largeangular ⇠± measurements (see Fig. 4) where our measuredsignal is rather low in comparison to the best-fit model (see

MNRAS 000, 1–48 (2016)

Hildebrandt, H. & KiDS Consortium, 2016, MNRAS

14 Tim Schrabback et al.: Evidence for the accelerated expansion of the Universe from 3D weak lensing with COSMOS

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Fig. 12. Constraints onΩm, ΩΛ, and σ8 from our 3D weak lensing analysis of COSMOS for a general (non-flat)ΛCDM cosmologyusing our default priors. The contours indicate the 68.3% and 95.4% credibility regions, where we have marginalized over theparameters which are not shown. The non-linear blue-scale indicates the highest density region of the posterior.

where our prior excludes negative densities ΩΛ < 0. Based onour Ωm −ΩΛ constraints, we compute the posterior PDF for thedeceleration parameter

q0 = −äa/ȧ2 = Ωm/2 − ΩΛ (22)

as shown in Fig. 13, which yields

q0 < 0 (96.0% conf.).

Relaxing our priors to h = 0.72 ± 0.08 (HST Key Project,Freedman et al. 2001), Ωbh

2 = 0.021 ± 0.001 (Big-Bang nucle-osynthesis, Iocco et al. 2009), and ns ∈ [0.7, 1.2], weakens thisconstraint only slightly to

q0 < 0 (94.3% conf., weak priors).

Employing the recent distance ladder estimateh = 0.742 ± 0.036 (Riess et al. 2009) instead of the HSTKey Project constraint, we obtain q0 < 0 at 94.8% confidence.

Our analysis provides evidence for the accelerated expansionof the Universe (q0 < 0) from weak gravitational lensing. Whilethe statistical accuracy is still relatively weak due to the limitedsize of the COSMOS field, this evidence is independent of ex-ternal constraints on Ωm and ΩΛ.

We note that the lensing data alone cannot formally excludea non-flat OCDM cosmology. However, the cosmological pa-rameters inferred for such a model would be inconsistent withvarious other cosmological probes10. We therefore perform ouranalysis in the context of the well-established ΛCDM model,where the lensing data provide additional evidence for cosmicacceleration.

6.3.3. Flat wCDM cosmology

For a flat wCDM cosmology we plot our constraints on the (con-stant) dark energy equation of state parameterw in Fig. 14, show-

10 For a lensing-only OCDM analysis the posterior peaks atΩm ≃ 0.1, σ8 ≃ 1.4 (close to the prior boundaries). In the comparisonwith a ΛCDM analysis, the additional parameter ΩΛ causes a penaltyin the Bayesian model comparison (computed as in Kilbinger et al.2009b). This leads to an only slightly larger evidence for the non-flatΛCDMmodel compared to the OCDMmodel, with an inconclusive ev-idence ratio of 65:35. The evidence ratio becomes a “weak preference”(77:23) if we employ a (still conservative) prior σ8 < 1. Hence, withthis prior the ΛCDM model makes the data more than 3 times moreprobable than the OCDM model.

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Fig. 13. Posterior PDF for the deceleration parameter q0 as com-puted from our constraints onΩm andΩΛ for a general (non-flat)ΛCDM cosmology, using our default priors (solid curve), andusing weaker priors from the HST Key Project and Big-Bang nu-cleosynthesis (dashed curve). The line at q0 = 0 separates accel-erating (q0 < 0) and decelerating (q0 > 0) cosmologies. We findq0 < 0 at 96.0% confidence using our default priors, or 94.3%confidence for the weaker priors.

ing that the measurement is consistent with ΛCDM (w = −1).From the posterior PDF we compute

w < −0.41 (90% conf.)

for the chosen prior w ∈ [−2, 0]. The exact value of this upperlimit depends on the lower bound of the prior PDF given the non-closed credibility regions. We have chosen this prior as morenegativew would require a worrisome extrapolation for the non-linear power spectrum corrections (Sect. 6.2). For comparison,we repeat the analysis with a much wider prior w ∈ [−3.5, 0.5]leading to a stronger upper limit w < −0.78 (90% conf.). Whilethe COSMOS data are capable to exclude very large valuesw≫ −1, larger lensing data-sets will be required to obtain re-ally competitive constraints on w.

To test the consistency of the data with ΛCDM, we com-pare the Bayesian evidence for the flat ΛCDM and wCDMmodels, which we compute in the PMC analysis as detailedin Kilbinger et al. (2009b). Here we find completely inconclu-

Expansion beschleunigt

Expansion abgebremst

Schrabback, T. et al., 2010, A&A, 516, 63

Kosmologische Messungen

Materiedichte / -fluktuation

Dunkle Energie

Gruppe Prof. Peter Schneider

van Waerbeke, L. et al., 2013, MNRAS, 433, 337

Kartographie

Gruppe Prof. Peter Schneider

Massenpeak

Massensenke

Shan, H. et al., 2014, MNRAS, 442, 2534

van Uitert, E. et al., 2016, MNRAS, 459, 325

Korrelations- analysen

Galaxy-Galaxy Lensing

Galaxy Bias

Gruppe Prof. Peter Schneider

Saghiha, H., 2016, doctoral thesis

Simon, P. et al., 2013, MNRAS, 430, 2476

Galaxie 1 Galaxie 2

elliptische Galaxien

Spiralgalaxien

Modell Messung

Tests von Galaxienmodellen

Gruppe Prof. Peter Schneider

200 kpc/h

Galaxy-Galaxy-Galaxy Lensing

Gruppe Prof. Peter Schneider

•1.2m ESA-Weltraumteleskop für optische und nahinfrarote Aufnahmen

• Missionsdauer 2020 + 6 Jahre (L2)


• Konsortium mit ~1300 Wissenschaftlern

• 15.000 Quadratgrad Himmel mit 10 Mrd Galaxien; insgesamt 1 Mrd für Lensing

• ein Ziel: Erforschung der Natur der Dunklen Energie

Missions- vorbereitung

Peter Schneider

Fragen oder Interesse an einem Thema für eine Bachelorarbeit oder Masterarbeit?

E-Mail: peter@astro.uni-bonn.de

mailto:peter@astro.uni-bonn.de