Nonlocal Gravity and Structure in the Universe

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1 Nonlocl rvity nd Structure in the Universe Sohyun Prk Penn Stte University Co-uthor: Scott Dodelson Bsed on PRD 87 (013) 04003, , PRD 90 (014) , August 5, 014 Chicgo, IL Cosmo 014

2 Current cosmic ccelertion: surprise, not explined by R Einstein eqution (enerl Reltivity) 8 T does not ccount for the observed ccelertion of the Universe, so we need New substnce : Drk Energy or New formultion: Modified rvity 8 ( T T ) 8 T Models in both cmps cn reproduce the observed expnsion history. An emerging method to distinguish these models is to study rowth of structure for fixed expnsion history We pply this technique to prticulr modified grvity model, which in conclusion fils to pss this test, but we lerned n importnt lesson regrding why it doesn t work.

3 A nonloclly modified grvity model Deser nd Woodrd, PRL 99 (007) , [ ( )] 16 1 gr 1 f R ( f ) 8 T f cn be fitted to produce the expnsion history w/o Λ or DE. (See the next slide.) Advntges, min fetures, theoreticl motivtions, 1 R is dimensionless: 33 no new mss prmeter (typiclly required to be very smll 10 ev ) is needed. R 0 during rd-dom & 1 R grows slowly (logrithmiclly) during mt-dom: the modifiction does not ffect the expnsion history until recently, exctly the type of modifiction we need for the current epoch of ccelertion! 1 R is smll in the Solr System: the model psses locl tests of grvity For more generl discussion on the issues of screening nd the stbility of the model: Deser nd Woodrd, JCAP 11 (013) 036, Theoreticl motivtion for nonlocl terms might rise from quntum theory: See for exmple, Polykov, PLB 103, 07 (1981)

4 Fit ΛCDM expnsion history w/o Λ Specilize the modified field eqn to the FRW (homogeneous, isotropic, sptilly flt) geometry nd determine f so s to mtch with the ΛCDM expnsion history, which is given s Note: once H 0 & Ω vlues re given, H(t) is fixed. Friedmnn Eq. To get exctly the sme H(t) w/o ρ Λ, need to mke Newton s constnt growing with time: Problem: Dt sys growth is bit lower thn wht s expected in the ΛCDM model. 0 ( f) 8 T H ( t) H / / m 3 4 r 8 8 H ( t) ( m r) 3 3 H 8 8 ( t) ( t) ( m r) 3 3 ef f () t eff dln dt Cn we mke perturbtions behve opposite wy so s to suppress growth of structure? enericlly f R f R 1 ( ), ( ), ny modifiction to R

5 Perturbtion Eqs. & growth of structure To see the growth of structure, perturb the metric round the FRW bckground; ds (1 ( t, x)) dt ( t)(1 ( t, x)) dx 4 evolution Eqs. for 4 perturbtions,,,, enerl Reltivity ( ) 0 k 4 H 0, k H ( H H ) 0 Nonlocl rvity ( ) ( ) f ( X ) Rf X f ( X ) R f X R k { [ ( )]} { [ ( ) ]} k [ { f ( X ) [ Rf ( X) ]} { f ( X) R f( X) R} ] 4 sme sme Blue < 0: time only, At 0 th order, only Blue mtters. Stress-energy conservtion 0 still holds in this nonlocl model Red > 0: time nd spce, At 1 st order, both blue nd red mtter. X 1 R

6 Prmeteriztion of the devitions from R We solve the system of the 4 integro-differentil eqs. for,,, (numericlly) ( ) ( ) f ( X ) Rf X f ( X ) R f X R { [ ( )]} { [ ( ) ]} k k [ { f ( X) [ Rf( X)] } { f ( X ) R f ( X) R} ] k k E[, ] 4 H 0, k H ( H H ) 0 nd the following prmeteriztions re useful for nlyzing the solutions: eff k 1 4 E[, ] 1 or (1 ) R (1 )[ ] R R relted by 1 (1 ) eff It turns out 0 0, 0, eff 1 E[, ] i.e. Red > 0 is dominnt over Blue < 0 3H t t

7 rowth Eqution Combining the 4 evolution eqns. we hve n eqn for δ: enerl Reltivity Nonlocl rvity ln( ) 3 3 m [ ] 0 5 d d d h ( ) d d H d 3 m [ ] ( 1 ) 0 5 d d d h ( ) d d ln( H ) 3 d eff 1 (1 ) 1 eff 1 (1 ) 1 Who wins? rowth gets enhnced rowth gets suppressed eff 1 or (equivlently ) 1 1 Prtilly successful: eff 1 but the effect of overwhelms it.

8 Figures for eff 1 (1 ) 1

9 Wek Lensing Fixing the redshift-distnce reltion nd the initil mplitude of fluctutions, the power spectrum of the convergence of glxies in two redshift bins is where ( ) ( ) ij 3mH g 0 i g j Cl ( / ; ) 1 ( ) d P l 0 ( ) dni gi ( ) d 1 d the weighting function in ech redshift bin dni / d the redshift distribution of source glxies in bin i ξ in three different redshift bins s mesured in CFHTLenS (blck points with error brs). Top nd bottom pnels: correltion function in the high nd low redshift bins resp. Middle pnel: the cross spectrum. Both R nd nonlocl models hve the redshift-distnce reltion corresponding to Plnck prmeters. 5.9-σ preference for R over the nonlocl model

10 Redshift Spce Distortions Redshift spce distortions probe the product of the growth rte d ln D / d ln nd () z 8 mesure of the clustering mplitude. Here the growth function D ( ) is the solution to the growth eq. with initil condition D( ). Mesurement of 8 This is directly mesured in spectroscopic surveys cpble of probing redshift spce distortions. Dt points come from BOSS, df, SDSS LR, WiggleZ. 7.8-σ preference for R over the nonlocl model

11 Estimtor of rvity E_ rvittionl lensing is sensitive to the combintion, while spectroscopic surveys re sensitive to the velocity field, which is relted to Combining the two, we hve n estimtor of grvity (Zhng, Liguori, Ben, nd Dodelson, PRL 99, (007), ) E k( ) 1 m 3H 0 E Estimtor of grvity s function of redshift in R nd the nonlocl model. The dt point is from Reyes et l. (010) E The growth rte is lrger in nonlocl grvity, but is positive; n interesting interply between the two effects. On blnce, the enhncement wins, leding to lrger vlues of E in the nonlocl model.

12 Tke Home Messge Modified grvity, imed t reproducing the expnsion history, tends to mke grvity stronger t 0 th order. rowth of structure is observed to be bit lower thn expected in the simplest ΛCDM model. In successful modified grvity model, perturbtions would weken grvity enough to overcome strengthened grvity in the bckground level.