Testing GR with environmentdependent

Transcription

1 Testing GR with environmentdependent measures of growth Seshadri Nadathur GR Effects in LSS workshop, Sexten, July 2018

2 <latexit sha1_base64="ymc09y4iyy3whxdv6x68/yzqapa=">aaab83icbvdlssnafl2prxpfvzdubovgqiqi6lloxowlcvybbsityaqdopmemruhlh6ew7stt36p+ddo2yy09cda4zxzmxtpmelh0po+ndlg5tb2tnnx3ds/odyqhj+0tjprxpsslanuhnrwkrrvokdjo5nmnaklb4ej+7nffuhaifq94zjjquihssscubrsu/dooxhtv6pezvuarbo/ifuo0ohxvnpryvkek2ssgtp1vqydcduomortt5cbnle2ogpetvtrhjtgslh3si6sepe41fypjav198sejsamk9ame4pds+rnxf+8bo7xbtarksurk7b8km4lwztmbyer0jyhhftcmrz2v8kgvfogtigxwli2cx/17nxsuqr5xs1/uq7w74poynag53ajptxahr6gau1gmijxeiozkzsz5935wezltjfzcn/gfp4a0gcqbq==</latexit> <latexit sha1_base64="ymc09y4iyy3whxdv6x68/yzqapa=">aaab83icbvdlssnafl2prxpfvzdubovgqiqi6lloxowlcvybbsityaqdopmemruhlh6ew7stt36p+ddo2yy09cda4zxzmxtpmelh0po+ndlg5tb2tnnx3ds/odyqhj+0tjprxpsslanuhnrwkrrvokdjo5nmnaklb4ej+7nffuhaifq94zjjquihssscubrsu/dooxhtv6pezvuarbo/ifuo0ohxvnpryvkek2ssgtp1vqydcduomortt5cbnle2ogpetvtrhjtgslh3si6sepe41fypjav198sejsamk9ame4pds+rnxf+8bo7xbtarksurk7b8km4lwztmbyer0jyhhftcmrz2v8kgvfogtigxwli2cx/17nxsuqr5xs1/uq7w74poynag53ajptxahr6gau1gmijxeiozkzsz5935wezltjfzcn/gfp4a0gcqbq==</latexit> <latexit sha1_base64="ymc09y4iyy3whxdv6x68/yzqapa=">aaab83icbvdlssnafl2prxpfvzdubovgqiqi6lloxowlcvybbsityaqdopmemruhlh6ew7stt36p+ddo2yy09cda4zxzmxtpmelh0po+ndlg5tb2tnnx3ds/odyqhj+0tjprxpsslanuhnrwkrrvokdjo5nmnaklb4ej+7nffuhaifq94zjjquihssscubrsu/dooxhtv6pezvuarbo/ifuo0ohxvnpryvkek2ssgtp1vqydcduomortt5cbnle2ogpetvtrhjtgslh3si6sepe41fypjav198sejsamk9ame4pds+rnxf+8bo7xbtarksurk7b8km4lwztmbyer0jyhhftcmrz2v8kgvfogtigxwli2cx/17nxsuqr5xs1/uq7w74poynag53ajptxahr6gau1gmijxeiozkzsz5935wezltjfzcn/gfp4a0gcqbq==</latexit> <latexit sha1_base64="ymc09y4iyy3whxdv6x68/yzqapa=">aaab83icbvdlssnafl2prxpfvzdubovgqiqi6lloxowlcvybbsityaqdopmemruhlh6ew7stt36p+ddo2yy09cda4zxzmxtpmelh0po+ndlg5tb2tnnx3ds/odyqhj+0tjprxpsslanuhnrwkrrvokdjo5nmnaklb4ej+7nffuhaifq94zjjquihssscubrsu/dooxhtv6pezvuarbo/ifuo0ohxvnpryvkek2ssgtp1vqydcduomortt5cbnle2ogpetvtrhjtgslh3si6sepe41fypjav198sejsamk9ame4pds+rnxf+8bo7xbtarksurk7b8km4lwztmbyer0jyhhftcmrz2v8kgvfogtigxwli2cx/17nxsuqr5xs1/uq7w74poynag53ajptxahr6gau1gmijxeiozkzsz5935wezltjfzcn/gfp4a0gcqbq==</latexit> Motivation Explaining the observed accelerated expansion of the Universe is a major goal among the very most compelling of all outstanding problems in physical science Dark Energy Task Force report, 2006 Is it just? Vacuum energy prediction problem, coincidence problem Or could it be pointing to a failure of GR on cosmological scales?

3 <latexit sha1_base64="mg1bcrxuufmqqp6uq32so8+lmlo=">aaachnicbvbnswmxem36wetx1aoxybh0unzf0itq1im3fawk3vpm09k2mgtxjcuupx/dsz/eq72jr/xfmh4ctppgmmd7mytzolrwy33/y5uanpmdmy8sfbexlldws2vr1ybjnmmas0sibymwkljcmuvw4g2qewqk8ca6pxn4n4+odu/ule2m2jdqvjzmdkytmiu/pgpjdsxvhulr096oqy80xoiddc8ltqepd2d3lmydlnaslf2kpwt9s4ixkzmxlpqlj7cvseyiskyamfxat20jb205e9grhpnbfng9tlhuqakjppepl+vrbae0ajxov8rsofpziwdptfdgblkc7zhjbyd+59uzgx82cq7szkjio4fitfcb0efmtmu1miu6jgdt3p2vsg64okwls0gdii6jypluv+r6rxl4lebyv1w9hmdsijtki+yqgbyqkjkjf6rgghkil+sv9l1nr++9ee+j0slvvlnbfsh7/ayahady</latexit> <latexit sha1_base64="mg1bcrxuufmqqp6uq32so8+lmlo=">aaachnicbvbnswmxem36wetx1aoxybh0unzf0itq1im3fawk3vpm09k2mgtxjcuupx/dsz/eq72jr/xfmh4ctppgmmd7mytzolrwy33/y5uanpmdmy8sfbexlldws2vr1ybjnmmas0sibymwkljcmuvw4g2qewqk8ca6pxn4n4+odu/ule2m2jdqvjzmdkytmiu/pgpjdsxvhulr096oqy80xoiddc8ltqepd2d3lmydlnaslf2kpwt9s4ixkzmxlpqlj7cvseyiskyamfxat20jb205e9grhpnbfng9tlhuqakjppepl+vrbae0ajxov8rsofpziwdptfdgblkc7zhjbyd+59uzgx82cq7szkjio4fitfcb0efmtmu1miu6jgdt3p2vsg64okwls0gdii6jypluv+r6rxl4lebyv1w9hmdsijtki+yqgbyqkjkjf6rgghkil+sv9l1nr++9ee+j0slvvlnbfsh7/ayahady</latexit> <latexit sha1_base64="mg1bcrxuufmqqp6uq32so8+lmlo=">aaachnicbvbnswmxem36wetx1aoxybh0unzf0itq1im3fawk3vpm09k2mgtxjcuupx/dsz/eq72jr/xfmh4ctppgmmd7mytzolrwy33/y5uanpmdmy8sfbexlldws2vr1ybjnmmas0sibymwkljcmuvw4g2qewqk8ca6pxn4n4+odu/ule2m2jdqvjzmdkytmiu/pgpjdsxvhulr096oqy80xoiddc8ltqepd2d3lmydlnaslf2kpwt9s4ixkzmxlpqlj7cvseyiskyamfxat20jb205e9grhpnbfng9tlhuqakjppepl+vrbae0ajxov8rsofpziwdptfdgblkc7zhjbyd+59uzgx82cq7szkjio4fitfcb0efmtmu1miu6jgdt3p2vsg64okwls0gdii6jypluv+r6rxl4lebyv1w9hmdsijtki+yqgbyqkjkjf6rgghkil+sv9l1nr++9ee+j0slvvlnbfsh7/ayahady</latexit> <latexit sha1_base64="mg1bcrxuufmqqp6uq32so8+lmlo=">aaachnicbvbnswmxem36wetx1aoxybh0unzf0itq1im3fawk3vpm09k2mgtxjcuupx/dsz/eq72jr/xfmh4ctppgmmd7mytzolrwy33/y5uanpmdmy8sfbexlldws2vr1ybjnmmas0sibymwkljcmuvw4g2qewqk8ca6pxn4n4+odu/ule2m2jdqvjzmdkytmiu/pgpjdsxvhulr096oqy80xoiddc8ltqepd2d3lmydlnaslf2kpwt9s4ixkzmxlpqlj7cvseyiskyamfxat20jb205e9grhpnbfng9tlhuqakjppepl+vrbae0ajxov8rsofpziwdptfdgblkc7zhjbyd+59uzgx82cq7szkjio4fitfcb0efmtmu1miu6jgdt3p2vsg64okwls0gdii6jypluv+r6rxl4lebyv1w9hmdsijtki+yqgbyqkjkjf6rgghkil+sv9l1nr++9ee+j0slvvlnbfsh7/ayahady</latexit> Modified gravity models There are many ways of modifying GR to explain the late-time acceleration (although that s not the only motivation!) These models must pass stringent solar system constraints Often achieved by a density-dependent screening mechanism: - in high density environments, theory reduces to GR - strength of gravity differs in low density regions (fifth forces) Affects growth rate of structure f = d ln D d ln a ' m(a) Can be measured using redshift space distortions (relating density and velocity fluctuations)

4 Environment-dependent growth So can we measure the growth rate specifically in low-density regions? (via RSD measurements, for example) Cross-correlation between galaxies and voids is a possible way

5 The void-galaxy correlation function vg (r) : cross-correlation between void and galaxy positions (equivalent to the galaxy density profile around a void) Real space

6 The void-galaxy correlation function vg (r) : cross-correlation between void and galaxy positions (equivalent to the galaxy density profile around a void) Real space Redshift space

7 A linear model Assumption #1: number of void-galaxy pairs conserved (1 + s (s)) d 3 s =(1+ r (r)) d 3 r Assumption #2: RSD due to galaxy motions only s = r + v ˆX ah ˆX Assumption #3: Linear dynamics, governed by void alone v(r) = 1 3 fah (r)r v rˆr ; (r) 3 r 3 Z r 0 (y)y 2 dy

8 A linear model Assumption #1 + Assumption #2 + Assumption #3 gives 1+ s (s) =(1+ r (r)) apple 1 f 3 (r) fµ 2 ( (r) (r)) 1 Expand to linear order in,

9 Deriving a linear model s (s, µ) = r (r)+ f 3 (r)(1+ r (r)) + fµ 2 [ (r) (r)] (1 + r (r)) SN & Percival 2017

10 Deriving a linear model s (s, µ) = r (r)+ f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids!

11 Deriving a linear model s (s, µ) = r (r)+ f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids!

12 Deriving a linear model s (s, s µ) = r (r)+ r f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids! Coordinate shift important at linear order! (r) = (s)+ 0 (s) f 3 s (s)µ2 +...

13 Deriving a linear model s (s, s µ) = r (r)+ r f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids! Coordinate shift important at linear order! (r) = (s)+ 0 (s) f 3 s (s)µ Linear galaxy bias does not hold, (r) 6= b (r)

14 Improved linear model s (s, s µ) = r (r)+ r f 3 (r)(1 + r (r)) +fµ 2 [ (r) (r)] (1 + r (r)) Key features: SN & Percival 2017, are linear order inside voids! Coordinate shift important at linear order! (r) = (s)+ 0 (s) f 3 s (s)µ Linear galaxy bias does not hold, (r) 6= b (r)

15 Important improvement old model residuals new model residuals Cai et al 2016 SN & Percival 2017 Performs much better!

16 Why does a linear RSD model fit so well? SN & Percival 2017

17 Why does a linear RSD model fit so well? SN & Percival 2017

18 Why does a linear RSD model fit so well? SN & Percival 2017

19 Why doesn t this RSD model fit perfectly? Dispersion around coherent outflow is large: SN & Percival 2017

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sha1_base64="kyk7pqotfn8wuxt6jd70dknmhta=">aaacahicdzbls8nafiun9vxjk9alm8ei1e1irnflwy3lcvybbqit6aqdopmemumxpnn4q9zanbj1j4j/xmmbqhu9mhd4zr3m5qqjo1i5zpdr2tjc2t4p75p7+wehr9zxpsxjvgdsxdglrsdakjdksvnrxugneqrfasptyhq3z9tjiisn+aoajmsl0idtkgkknpktsk/sqyt8boxn02me18sfb1vd21kiovb1yhrkfvvboyzvffb6mu4jwhvmsmqu6ytky5bqfdosm71ukgtherqqrrycrur62el2hj5r0odhlptjci7o+kagiiknuaani6sg8nc2h39l3vsft15geziqwvhyozblumvwxgtsu0gwyhntebzu3wrxeamela7lhfrmehp/m9al7tq2+3bvrdeltsrgfjybgndbdaide9aatydbe3gbr2bmpbsz4814x46wjglnbpyq8fenu56vvw==</latexit> <latexit sha1_base64="kyk7pqotfn8wuxt6jd70dknmhta=">aaacahicdzbls8nafiun9vxjk9alm8ei1e1irnflwy3lcvybbqit6aqdopmemumxpnn4q9zanbj1j4j/xmmbqhu9mhd4zr3m5qqjo1i5zpdr2tjc2t4p75p7+wehr9zxpsxjvgdsxdglrsdakjdksvnrxugneqrfasptyhq3z9tjiisn+aoajmsl0idtkgkknpktsk/sqyt8boxn02me18sfb1vd21kiovb1yhrkfvvboyzvffb6mu4jwhvmsmqu6ytky5bqfdosm71ukgtherqqrrycrur62el2hj5r0odhlptjci7o+kagiiknuaani6sg8nc2h39l3vsft15geziqwvhyozblumvwxgtsu0gwyhntebzu3wrxeamela7lhfrmehp/m9al7tq2+3bvrdeltsrgfjybgndbdaide9aatydbe3gbr2bmpbsz4814x46wjglnbpyq8fenu56vvw==</latexit> Adding velocity dispersion to the model Allow for a dispersion in los velocities, v = v rˆr + v ˆX, then: 1+ s,d (, ) = Z dv 1+ s, v /ah p 2 v exp v v! s calculated as before convolved with Gaussian, with scale-dependent width v (r) SN & Percival 2017

21 <latexit sha1_base64="0vwxw9d50erqnwcu5yn0nw6dw3u=">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</latexit> <latexit sha1_base64="0vwxw9d50erqnwcu5yn0nw6dw3u=">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</latexit> <latexit sha1_base64="0vwxw9d50erqnwcu5yn0nw6dw3u=">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</latexit> <latexit sha1_base64="0vwxw9d50erqnwcu5yn0nw6dw3u=">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</latexit> Adding velocity dispersion to the model Allow for a dispersion in los velocities, v = v rˆr + v ˆX, then: 1+ s,d (, ) = Z dv 1+ s, v /ah p 2 v exp v v! Note, not 1+ s (, ) = Z (1 + r (r)) p 2 v (v v r (r)µ) 2 exp 2 2 v dv standard streaming model result does not hold for voids! SN & Percival 2017

22 Improved linear model with dispersion Even better residuals without dispersion with dispersion

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sha1_base64="nh7s9fkmzfc5b110dkaqkiv5oy8=">aaab8xicbvbns8naej34wetx1aoxxslus0leug9flx4rgftiy9lsn+3szw7y3ygl9gd48adi1x/jzx/jts1bwx8mpn6bywzelhkmjet+o0vlk6tr66wn8ubw9s5uzw//xstmeeotyavqr1htzgt1dtoctlnfcrjx2oqg1xo/9uivzllcmvfkwwt3byszwczkqeejpeiuw9mnqfupunv3crrivijuouczw/nq9ctjeiom4vjrwhnte+zyguy4hzc7maypjkpcp4glaiduh/n05de6tkopxvlzegzn1d8tou60hiwr7uywgeh5byl+5wwzis/cnik0m1sq2ai448hinpkf9ziixpcrjzgozm9fziavjsamvlyhepmvlxl/th5z927pqo2rio0shmir1mcdc2jadttbbwisnuev3hzjvdjvzsesdckpzg7gd5zph3fkkd0=</latexit> <latexit sha1_base64="nh7s9fkmzfc5b110dkaqkiv5oy8=">aaab8xicbvbns8naej34wetx1aoxxslus0leug9flx4rgftiy9lsn+3szw7y3ygl9gd48adi1x/jzx/jts1bwx8mpn6bywzelhkmjet+o0vlk6tr66wn8ubw9s5uzw//xstmeeotyavqr1htzgt1dtoctlnfcrjx2oqg1xo/9uivzllcmvfkwwt3byszwczkqeejpeiuw9mnqfupunv3crrivijuouczw/nq9ctjeiom4vjrwhnte+zyguy4hzc7maypjkpcp4glaiduh/n05de6tkopxvlzegzn1d8tou60hiwr7uywgeh5byl+5wwzis/cnik0m1sq2ai448hinpkf9ziixpcrjzgozm9fziavjsamvlyhepmvlxl/th5z927pqo2rio0shmir1mcdc2jadttbbwisnuev3hzjvdjvzsesdckpzg7gd5zph3fkkd0=</latexit> <latexit sha1_base64="nh7s9fkmzfc5b110dkaqkiv5oy8=">aaab8xicbvbns8naej34wetx1aoxxslus0leug9flx4rgftiy9lsn+3szw7y3ygl9gd48adi1x/jzx/jts1bwx8mpn6bywzelhkmjet+o0vlk6tr66wn8ubw9s5uzw//xstmeeotyavqr1htzgt1dtoctlnfcrjx2oqg1xo/9uivzllcmvfkwwt3byszwczkqeejpeiuw9mnqfupunv3crrivijuouczw/nq9ctjeiom4vjrwhnte+zyguy4hzc7maypjkpcp4glaiduh/n05de6tkopxvlzegzn1d8tou60hiwr7uywgeh5byl+5wwzis/cnik0m1sq2ai448hinpkf9ziixpcrjzgozm9fziavjsamvlyhepmvlxl/th5z927pqo2rio0shmir1mcdc2jadttbbwisnuev3hzjvdjvzsesdckpzg7gd5zph3fkkd0=</latexit> <latexit 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sha1_base64="9bz+qtt/fplfaztfr616rq8laoe=">aaab8xicbvbntwixeo3if+ix6tflizhbc9kljuqn6mujjq6qweq6pqsn3xbtzhrjhp/hxymar/4bb/4bc+xbwzdm8vletgbmhyngblz32ymsrk6tbxq3s1vbo7t75f2de6nstzlplvc6hrldbjfmbw6ctrpnsbwk1gph11o/9ci04urewthhquwgkkecerbsp/veh0yvxjwnufeuudv3brxmvjxuui5mr/zv7suaxkwcfcsyjucmegrea6ecturd1lce0bezsi6lkstmbnns5ak+suofr0rbkobn6u+jjmtgjopqdsyehmbrm4r/ez0uoosg4zjjguk6xxslaopc0/9xn2tgqywtivrzeyumq6ijbztsyybglb68tpx67blm3z5vgld5gkv0hi5rfxnohdxqdwoih1gk0dn6rw8ooc/ou/mxby04+cwh+gpn8wd0wja/</latexit> <latexit sha1_base64="9bz+qtt/fplfaztfr616rq8laoe=">aaab8xicbvbntwixeo3if+ix6tflizhbc9kljuqn6mujjq6qweq6pqsn3xbtzhrjhp/hxymar/4bb/4bc+xbwzdm8vletgbmhyngblz32ymsrk6tbxq3s1vbo7t75f2de6nstzlplvc6hrldbjfmbw6ctrpnsbwk1gph11o/9ci04urewthhquwgkkecerbsp/veh0yvxjwnufeuudv3brxmvjxuui5mr/zv7suaxkwcfcsyjucmegrea6ecturd1lce0bezsi6lkstmbnns5ak+suofr0rbkobn6u+jjmtgjopqdsyehmbrm4r/ez0uoosg4zjjguk6xxslaopc0/9xn2tgqywtivrzeyumq6ijbztsyybglb68tpx67blm3z5vgld5gkv0hi5rfxnohdxqdwoih1gk0dn6rw8ooc/ou/mxby04+cwh+gpn8wd0wja/</latexit> <latexit sha1_base64="9bz+qtt/fplfaztfr616rq8laoe=">aaab8xicbvbntwixeo3if+ix6tflizhbc9kljuqn6mujjq6qweq6pqsn3xbtzhrjhp/hxymar/4bb/4bc+xbwzdm8vletgbmhyngblz32ymsrk6tbxq3s1vbo7t75f2de6nstzlplvc6hrldbjfmbw6ctrpnsbwk1gph11o/9ci04urewthhquwgkkecerbsp/veh0yvxjwnufeuudv3brxmvjxuui5mr/zv7suaxkwcfcsyjucmegrea6ecturd1lce0bezsi6lkstmbnns5ak+suofr0rbkobn6u+jjmtgjopqdsyehmbrm4r/ez0uoosg4zjjguk6xxslaopc0/9xn2tgqywtivrzeyumq6ijbztsyybglb68tpx67blm3z5vgld5gkv0hi5rfxnohdxqdwoih1gk0dn6rw8ooc/ou/mxby04+cwh+gpn8wd0wja/</latexit> Multipole expansion For quantitative analyses, expand in terms of multipoles s` (s) = Z 1 0 s (s, µ)(1+2`) P`(µ)dµ Legendre polynomials To linear order, only monopole and quadrupole are non-zero s 0(s), s 2(s)

24 Multipole expansion monopole quadrupole SN & Percival 2017

25 Multipole expansion monopole quadrupole SN & Percival 2017

26 Multipole expansion monopole difference quadrupole Completely linear RSD model works well on all scales SN & Percival 2017

27 Multipole expansion monopole difference quadrupole Completely linear RSD model works well on all scales SN & Percival 2017

28 <latexit sha1_base64="u3ai1xkby+t9nxi8x6j9nkgusgy=">aaab73icbvdlsgnbeoz1gemr6thlyba8hv0rzdhoxwme84bkcb2tstjkznadmrxckp/w4kerr/6on//gsbihtsxokkq66e6kesgn9f1vb219y3nru7bt3n3bpzgshr03tzxqyho0frfur2iy4io1llectrpnueactalx7cxvptftekwe7crhocsh4gno0tqp3tv8klfx7zxkfswfg6ysicdlyfhvlb66/zimkillbrrtcfzehhlqy6lg02i3nsxbosyh6ziquditzvn7p+tckx0yilurzclc/t2rotrmiipxkdgozli3e//zoqkdvmomqys1tnhfokeqii3j7hns55prkyaoinxc3urocdvs6yiquhcc5zdxsfoyeviv4p6qxlvj4yjakzzbbqrwdtw4gzo0gikaz3ifn+/re/hevy9f65qxz5zah3ifp9bhj84=</latexit> <latexit sha1_base64="u3ai1xkby+t9nxi8x6j9nkgusgy=">aaab73icbvdlsgnbeoz1gemr6thlyba8hv0rzdhoxwme84bkcb2tstjkznadmrxckp/w4kerr/6on//gsbihtsxokkq66e6kesgn9f1vb219y3nru7bt3n3bpzgshr03tzxqyho0frfur2iy4io1llectrpnueactalx7cxvptftekwe7crhocsh4gno0tqp3tv8klfx7zxkfswfg6ysicdlyfhvlb66/zimkillbrrtcfzehhlqy6lg02i3nsxbosyh6ziquditzvn7p+tckx0yilurzclc/t2rotrmiipxkdgozli3e//zoqkdvmomqys1tnhfokeqii3j7hns55prkyaoinxc3urocdvs6yiquhcc5zdxsfoyeviv4p6qxlvj4yjakzzbbqrwdtw4gzo0gikaz3ifn+/re/hevy9f65qxz5zah3ifp9bhj84=</latexit> <latexit sha1_base64="u3ai1xkby+t9nxi8x6j9nkgusgy=">aaab73icbvdlsgnbeoz1gemr6thlyba8hv0rzdhoxwme84bkcb2tstjkznadmrxckp/w4kerr/6on//gsbihtsxokkq66e6kesgn9f1vb219y3nru7bt3n3bpzgshr03tzxqyho0frfur2iy4io1llectrpnueactalx7cxvptftekwe7crhocsh4gno0tqp3tv8klfx7zxkfswfg6ysicdlyfhvlb66/zimkillbrrtcfzehhlqy6lg02i3nsxbosyh6ziquditzvn7p+tckx0yilurzclc/t2rotrmiipxkdgozli3e//zoqkdvmomqys1tnhfokeqii3j7hns55prkyaoinxc3urocdvs6yiquhcc5zdxsfoyeviv4p6qxlvj4yjakzzbbqrwdtw4gzo0gikaz3ifn+/re/hevy9f65qxz5zah3ifp9bhj84=</latexit> <latexit sha1_base64="u3ai1xkby+t9nxi8x6j9nkgusgy=">aaab73icbvdlsgnbeoz1gemr6thlyba8hv0rzdhoxwme84bkcb2tstjkznadmrxckp/w4kerr/6on//gsbihtsxokkq66e6kesgn9f1vb219y3nru7bt3n3bpzgshr03tzxqyho0frfur2iy4io1llectrpnueactalx7cxvptftekwe7crhocsh4gno0tqp3tv8klfx7zxkfswfg6ysicdlyfhvlb66/zimkillbrrtcfzehhlqy6lg02i3nsxbosyh6ziquditzvn7p+tckx0yilurzclc/t2rotrmiipxkdgozli3e//zoqkdvmomqys1tnhfokeqii3j7hns55prkyaoinxc3urocdvs6yiquhcc5zdxsfoyeviv4p6qxlvj4yjakzzbbqrwdtw4gzo0gikaz3ifn+/re/hevy9f65qxz5zah3ifp9bhj84=</latexit> Fitting for the growth rate Theory depends on growth rate, so can be used to fit for f Note: no explicit dependence on! 8

29 <latexit sha1_base64="umexrfggw+fpuzhlsgvj/kinjsq=">aaab7xicbvbns8naej3urxq/qh69lbbbu0le0iohghepldgpaepzbcft0k027g6eevolvnqbepunif/gbzudtj4yelw3w8y8mbvcg8/7dkpb2zu7e+v99+dw6pikcnrw1jjtdftmcqm6iduoeiitw43abqqqxqhatjh5xpidf1say+tztfmmyjpkemqznvzqronk1at5s5bn4hekcguag8pxfyhzfmnimkba93wvnufolefm4mztzxptyiz0hd1lexqjdvllotnyzzuhiasylriyvh9p5dtwehqhtjomzqzxvyx4n9flthqf5dxjm4mjwy2kmkgmjiuvyzarzezmlafmcxsrywoqkdm2g5dyudyjf/3vtdk+qflezw/evusprszluibluayf7qaot9cafjbaeiu3mdvsmtvvzseqtequm+fwb87nd4rcjyw=</latexit> <latexit sha1_base64="umexrfggw+fpuzhlsgvj/kinjsq=">aaab7xicbvbns8naej3urxq/qh69lbbbu0le0iohghepldgpaepzbcft0k027g6eevolvnqbepunif/gbzudtj4yelw3w8y8mbvcg8/7dkpb2zu7e+v99+dw6pikcnrw1jjtdftmcqm6iduoeiitw43abqqqxqhatjh5xpidf1say+tztfmmyjpkemqznvzqronk1at5s5bn4hekcguag8pxfyhzfmnimkba93wvnufolefm4mztzxptyiz0hd1lexqjdvllotnyzzuhiasylriyvh9p5dtwehqhtjomzqzxvyx4n9flthqf5dxjm4mjwy2kmkgmjiuvyzarzezmlafmcxsrywoqkdm2g5dyudyjf/3vtdk+qflezw/evusprszluibluayf7qaot9cafjbaeiu3mdvsmtvvzseqtequm+fwb87nd4rcjyw=</latexit> <latexit sha1_base64="q4lebfeglzncc80vj3pgbypezia=">aaab9hicbvbns8naej3urxq/qh69lbbbu0he0yohghepfewhtkfstpt26e4m7g4knfrpelu38erfef+n2zyhbx0w8hhvhpl5ucqznr7/7zq2nre2d8q77t7+wefr5fikqznmedogcu9uo8kacizpwzddattvfiui01y0epj7rtfvmixy2uxsggo8kcxmbbsrtv+6mgnfu+lvqr7nl4dwsvcqkhso9ypf3x5cmkglirxr3qn81iq5voyrtqdun9m0xwseb7rjqcsc6jbf3dtff1bpozhrtqrbc/x3ri6f1hmr2u6bzvcvenpxp6+tmfguzjlmm0mlws6km45mgubpoz5tlbg+sqqtxeytiayxwstyifxk4dokgtw/10nzygt8l3i6rtbui0zkcabncakb3einhqeodsda4rxeyoamnznz7nwsw0tomxmkf+b8/gazepae</latexit> <latexit sha1_base64="q4lebfeglzncc80vj3pgbypezia=">aaab9hicbvbns8naej3urxq/qh69lbbbu0he0yohghepfewhtkfstpt26e4m7g4knfrpelu38erfef+n2zyhbx0w8hhvhpl5ucqznr7/7zq2nre2d8q77t7+wefr5fikqznmedogcu9uo8kacizpwzddattvfiui01y0epj7rtfvmixy2uxsggo8kcxmbbsrtv+6mgnfu+lvqr7nl4dwsvcqkhso9ypf3x5cmkglirxr3qn81iq5voyrtqdun9m0xwseb7rjqcsc6jbf3dtff1bpozhrtqrbc/x3ri6f1hmr2u6bzvcvenpxp6+tmfguzjlmm0mlws6km45mgubpoz5tlbg+sqqtxeytiayxwstyifxk4dokgtw/10nzygt8l3i6rtbui0zkcabncakb3einhqeodsda4rxeyoamnznz7nwsw0tomxmkf+b8/gazepae</latexit> <latexit sha1_base64="q4lebfeglzncc80vj3pgbypezia=">aaab9hicbvbns8naej3urxq/qh69lbbbu0he0yohghepfewhtkfstpt26e4m7g4knfrpelu38erfef+n2zyhbx0w8hhvhpl5ucqznr7/7zq2nre2d8q77t7+wefr5fikqznmedogcu9uo8kacizpwzddattvfiui01y0epj7rtfvmixy2uxsggo8kcxmbbsrtv+6mgnfu+lvqr7nl4dwsvcqkhso9ypf3x5cmkglirxr3qn81iq5voyrtqdun9m0xwseb7rjqcsc6jbf3dtff1bpozhrtqrbc/x3ri6f1hmr2u6bzvcvenpxp6+tmfguzjlmm0mlws6km45mgubpoz5tlbg+sqqtxeytiayxwstyifxk4dokgtw/10nzygt8l3i6rtbui0zkcabncakb3einhqeodsda4rxeyoamnznz7nwsw0tomxmkf+b8/gazepae</latexit> <latexit sha1_base64="q4lebfeglzncc80vj3pgbypezia=">aaab9hicbvbns8naej3urxq/qh69lbbbu0he0yohghepfewhtkfstpt26e4m7g4knfrpelu38erfef+n2zyhbx0w8hhvhpl5ucqznr7/7zq2nre2d8q77t7+wefr5fikqznmedogcu9uo8kacizpwzddattvfiui01y0epj7rtfvmixy2uxsggo8kcxmbbsrtv+6mgnfu+lvqr7nl4dwsvcqkhso9ypf3x5cmkglirxr3qn81iq5voyrtqdun9m0xwseb7rjqcsc6jbf3dtff1bpozhrtqrbc/x3ri6f1hmr2u6bzvcvenpxp6+tmfguzjlmm0mlws6km45mgubpoz5tlbg+sqqtxeytiayxwstyifxk4dokgtw/10nzygt8l3i6rtbui0zkcabncakb3einhqeodsda4rxeyoamnznz7nwsw0tomxmkf+b8/gazepae</latexit> Fitting for the growth rate Fitting requires 3 functions as input: r (r) (r) v (r),, either from simulation OR reconstructed from data (must be?) calibrated from simulation Parameter that is fit is f (not f 8!) Under ideal conditions, we get a <3% constraint on at z 0.5 <latexit sha1_base64="umexrfggw+fpuzhlsgvj/kinjsq=">aaab7xicbvbns8naej3urxq/qh69lbbbu0le0iohghepldgpaepzbcft0k027g6eevolvnqbepunif/gbzudtj4yelw3w8y8mbvcg8/7dkpb2zu7e+v99+dw6pikcnrw1jjtdftmcqm6iduoeiitw43abqqqxqhatjh5xpidf1say+tztfmmyjpkemqznvzqronk1at5s5bn4hekcguag8pxfyhzfmnimkba93wvnufolefm4mztzxptyiz0hd1lexqjdvllotnyzzuhiasylriyvh9p5dtwehqhtjomzqzxvyx4n9flthqf5dxjm4mjwy2kmkgmjiuvyzarzezmlafmcxsrywoqkdm2g5dyudyjf/3vtdk+qflezw/evusprszluibluayf7qaot9cafjbaeiu3mdvsmtvvzseqtequm+fwb87nd4rcjyw=</latexit> f<latexit sha1_base64="umexrfggw+fpuzhlsgvj/kinjsq=">aaab7xicbvbns8naej3urxq/qh69lbbbu0le0iohghepldgpaepzbcft0k027g6eevolvnqbepunif/gbzudtj4yelw3w8y8mbvcg8/7dkpb2zu7e+v99+dw6pikcnrw1jjtdftmcqm6iduoeiitw43abqqqxqhatjh5xpidf1say+tztfmmyjpkemqznvzqronk1at5s5bn4hekcguag8pxfyhzfmnimkba93wvnufolefm4mztzxptyiz0hd1lexqjdvllotnyzzuhiasylriyvh9p5dtwehqhtjomzqzxvyx4n9flthqf5dxjm4mjwy2kmkgmjiuvyzarzezmlafmcxsrywoqkdm2g5dyudyjf/3vtdk+qflezw/evusprszluibluayf7qaot9cafjbaeiu3mdvsmtvvzseqtequm+fwb87nd4rcjyw=</latexit> using data only from low-density regions! But can ideal conditions be reproduced in real world?

30 A major practical problem In real data, we only have redshift-space galaxy positions these galaxies define the location of voids we only have redshift-space voids

31 <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> Problems with redshift-space voids 1. void numbers are not conserved 2. velocity outflow no longer symmetrical 3. void positions themselves show RSD s = r + v ˆX ah + void motion term

32 <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> Problems with redshift-space voids 3. void positions themselves show RSD s = r + v ˆX ah + void motion term

33 <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> <latexit sha1_base64="ijdvgvp961dzsbnkqlthktmq6q8=">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</latexit> Problems with redshift-space voids 3. void positions themselves show RSD s = r + v ˆX ah + void motion term e.g. void-finding galaxy field in redshift space A non-linear transformation of a tracer density field after RSD mapping must have RSD itself, and also a velocity bias Seljak 2012, =) void motion term will be very non-trivial/ impossible to model

34 A major practical problem Assumption #1: number of void-galaxy pairs conserved (1 + s (s)) d 3 s =(1+ r (r)) d 3 r Assumption #2: RSD due to galaxy motions only s = r + v ˆX ah ˆX Assumption #3: Linear dynamics, governed by void alone v(r) = 1 3 fah (r)r v rˆr ; (r) 3 r 3 Z r 0 (y)y 2 dy The key model assumptions do not hold!

35 Quadrupole using redshift-space voids can t be modelled? can t be measured? SN, Carter & Percival, 2018

36 Luckily, there is a solution

37 Luckily, there is a solution we can reconstruct the real-space galaxy field

38 Reconstruction idea Given redshift-space galaxy positions, estimate velocity fields Thus estimate the (linear, Kaiser) RSD Shift galaxy positions back to (pseudo) real space Now perform void-finding get real-space voids! Cross-correlate these voids with redshift-space galaxies

39 <latexit sha1_base64="mt0gk6kewkqwaplm+jwkmevon68=">aaaccxicbvc7tsmwfhxkq5rxglglryxeqpugjbgykshawb59se0uoa7twrwtyhaqqigdmx/csjfeykcg/gynzqatr7j0fm69uvcep2zuksv6niorq2vrg9xn2tb2zu6eux/qlveimongiewi7ynjga1jr1hfsd8wbhgfkz4/uc793hmrkkbho5rgxovofnkayqs05jn1u4cjnfad1gllmnnft/d0/uem88yg1bqkwgvil6qbsrq988szrjjhjfsyiskhthurn0vcucxivnmsswkej2hebpqgibpppsurgtzwyhagkdavvlbqf3ekies55b6uzheui14u/ucnehvcuikn40srem8hbqmdkoj5inbibcgkttvbwfc9k8rjjbbworca1kjpjozfu5dj96xpw0377rzruiozqyi6oainwayxoavuqrt0aabp4bw8gznxysymd+njxloxyp5d8afg5w/8e5j7</latexit> <latexit sha1_base64="mt0gk6kewkqwaplm+jwkmevon68=">aaaccxicbvc7tsmwfhxkq5rxglglryxeqpugjbgykshawb59se0uoa7twrwtyhaqqigdmx/csjfeykcg/gynzqatr7j0fm69uvcep2zuksv6niorq2vrg9xn2tb2zu6eux/qlveimongiewi7ynjga1jr1hfsd8wbhgfkz4/uc793hmrkkbho5rgxovofnkayqs05jn1u4cjnfad1gllmnnft/d0/uem88yg1bqkwgvil6qbsrq988szrjjhjfsyiskhthurn0vcucxivnmsswkej2hebpqgibpppsurgtzwyhagkdavvlbqf3ekies55b6uzheui14u/ucnehvcuikn40srem8hbqmdkoj5inbibcgkttvbwfc9k8rjjbbworca1kjpjozfu5dj96xpw0377rzruiozqyi6oainwayxoavuqrt0aabp4bw8gznxysymd+njxloxyp5d8afg5w/8e5j7</latexit> <latexit sha1_base64="mt0gk6kewkqwaplm+jwkmevon68=">aaaccxicbvc7tsmwfhxkq5rxglglryxeqpugjbgykshawb59se0uoa7twrwtyhaqqigdmx/csjfeykcg/gynzqatr7j0fm69uvcep2zuksv6niorq2vrg9xn2tb2zu6eux/qlveimongiewi7ynjga1jr1hfsd8wbhgfkz4/uc793hmrkkbho5rgxovofnkayqs05jn1u4cjnfad1gllmnnft/d0/uem88yg1bqkwgvil6qbsrq988szrjjhjfsyiskhthurn0vcucxivnmsswkej2hebpqgibpppsurgtzwyhagkdavvlbqf3ekies55b6uzheui14u/ucnehvcuikn40srem8hbqmdkoj5inbibcgkttvbwfc9k8rjjbbworca1kjpjozfu5dj96xpw0377rzruiozqyi6oainwayxoavuqrt0aabp4bw8gznxysymd+njxloxyp5d8afg5w/8e5j7</latexit> <latexit sha1_base64="mt0gk6kewkqwaplm+jwkmevon68=">aaaccxicbvc7tsmwfhxkq5rxglglryxeqpugjbgykshawb59se0uoa7twrwtyhaqqigdmx/csjfeykcg/gynzqatr7j0fm69uvcep2zuksv6niorq2vrg9xn2tb2zu6eux/qlveimongiewi7ynjga1jr1hfsd8wbhgfkz4/uc793hmrkkbho5rgxovofnkayqs05jn1u4cjnfad1gllmnnft/d0/uem88yg1bqkwgvil6qbsrq988szrjjhjfsyiskhthurn0vcucxivnmsswkej2hebpqgibpppsurgtzwyhagkdavvlbqf3ekies55b6uzheui14u/ucnehvcuikn40srem8hbqmdkoj5inbibcgkttvbwfc9k8rjjbbworca1kjpjozfu5dj96xpw0377rzruiozqyi6oainwayxoavuqrt0aabp4bw8gznxysymd+njxloxyp5d8afg5w/8e5j7</latexit> Practical reconstruction SN, Carter & Percival, 2018 Eulerian posn. as Lagrangian posn. + displacement x(q,t)=q + (q,t) The displacement depends on the redshift-space galaxy density via redshift-space version of Zeldovich approximation r + f b r ( ˆr )ˆr = g b This equation can be solved by an iterative FFT-based method Burden et al (2015) The RSD component of displacement is RSD = f( ˆr )ˆr Shift the galaxy positions by distribution RSD obtain pseudo real-space galaxy

40 Practical reconstruction Code to do all of this is available at REal-space VOid Locations from survey Reconstruction (sorry!) Python-based integrated reconstruction and void-finding applicable to survey data (especially BOSS) as well as simulations

41 Reconstruction works SN, Carter & Percival, 2018

42 Reconstruction works Multipoles of correlation function can be both modelled and measured SN, Carter & Percival, 2018

43 Fitting for the growth rate Reconstruction requires knowledge of growth rate! (and bias) SN, Carter & Percival, 2018

44 Avoiding circularity Choose parameters f,b Solve for RSD Reconstruct pseudo real-space galaxy field Find voids, measure r If not finished, new parameters Calculate theory for given ; 2 get for fit to data If finished, construct likelihood f Cross-correlate with redshift-space galaxies; measure multipoles SN, Carter & Percival, 2018

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sha1_base64="b1utvhz/pt4xlmqg/a2l4ms5auw=">aaab9xicbvbnswmxej3ur7p+vt16crbbu9kvwr4lxjxwsk3sliwbztvqjlskwaus/rve7u28+npef2pa7kfbhww83pthzl6ucm6s73+j0sbm1vzoedfb2z84pkocn7rnkmnkwjqrix6miggck9ay3ar2mgpgzcryjxrfzv3om9ogj+rbtliwsjjupoauwcc9xt3dh5l06/1k1a/5c+b1ehskcgwa/cpxb5dqtdjlqsdgdam/twfotovusknxywxlcr2ties6qohkjswxb0/xhvmgoe60k2xxqv09krnpzergrlmsozkr3lz8z+tmnq6hovdpzpmiy0vxjrbn8px7pocaussmjhcqubsv0xhrhfqxkycdpjdespr3omlf1qk/ftxfvxunipmynme5xeian9cao2hccyhieiu3mkexnepv6gpzwklfzcn8afr8av0fkoq=</latexit> <latexit sha1_base64="b1utvhz/pt4xlmqg/a2l4ms5auw=">aaab9xicbvbnswmxej3ur7p+vt16crbbu9kvwr4lxjxwsk3sliwbztvqjlskwaus/rve7u28+npef2pa7kfbhww83pthzl6ucm6s73+j0sbm1vzoedfb2z84pkocn7rnkmnkwjqrix6miggck9ay3ar2mgpgzcryjxrfzv3om9ogj+rbtliwsjjupoauwcc9xt3dh5l06/1k1a/5c+b1ehskcgwa/cpxb5dqtdjlqsdgdam/twfotovusknxywxlcr2ties6qohkjswxb0/xhvmgoe60k2xxqv09krnpzergrlmsozkr3lz8z+tmnq6hovdpzpmiy0vxjrbn8px7pocaussmjhcqubsv0xhrhfqxkycdpjdespr3omlf1qk/ftxfvxunipmynme5xeian9cao2hccyhieiu3mkexnepv6gpzwklfzcn8afr8av0fkoq=</latexit> Future directions What is implicit dependence on (via (r) calibration)? 8 Preliminary: seem to be sensitive to combination f not f <latexit sha1_base64="u7s+c9jq5lnm8bcfe3bu9njxpp4=">aaab/xicbvbns8naej3urxo/gvxozbeinkiigj0wvhisyd+gjwgz3brld5owuxfkkp4qr/ymxv0p4r9x2+agrq8ghu/nmdmvyjht2vo+rcrw9s7uxnxfpjg8oq45j6cdleas0dzjesp7evaus4s2ndoc9jjjsyg47uatu4xffazsstr51nombgkpehyzgrwrqqcwdxqbcrw2ngrpbcxcp+653hjok/glquojvuh8dyypyqvnnofyqb7vztoosnsmcdqzb7migsytpkj9qxmsqaqk5eezdgmuiyptasrrakn+niiwugoqitmpsb6rdw8h/uf1cx03goilwa5pqlal4pwjnajfcmjijcwatw3brdjzkyjjldhrjisbgdgmcx/9703suxz9z/ufburnzpljfc7haq7ah1towj20oa0ecnifn5hbl9bcerc+vq0vq5w5gz+wpn8awdotpq==</latexit> 8 Including uncertainty in cosmology (via AP distortions) s,obs (s) = s,model ( s,? s? ) m w(z) (joint AP fit can itself constrain and to high precision) Application to BOSS and eboss data (in progress) Application to Euclid and DESI data will give best constraints