Gravity is everywhere: Two new tests of gravity. Luca Amendola University of Heidelberg

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1 Gravity is everywhere: Two new tests of gravity Luca Amendola University of Heidelberg

2 Gravity in polarization maps and in supernovae

3 Gravity in polarization maps and in supernovae

4 Why testing gravity? we only directly test gravity within the solar system, at the present time, and with baryons On Space and Time, Edited by Shahn Majid

5 Why testing gravity: dark energy Isotropy Abundance Observational requirements Slow evolution Weak clustering

6 The Horndeski Lagrangian The most general 4D scalar field theory with second order equation of motion 4 dx g L i +Lmatter i ü First found by Horndeski in 1975 ü rediscovered by Deffayet et al. in 2011 ü no ghosts, no classical instabilities ü it modifies gravity! ü it includes f(r), Brans-Dicke, k-essence, Galileons, etc etc etc

7 Massive gravity Pauli-Fierz (1939) action: the only ghost-free quadratic action for a massive spin two field The three deadly sins of Pauli-Fierz theory: It does not reduce to massless gravity for m 0 (vdvz disc.) It violates diffeomorphism invariance It contains a ghost when extended to non-linear level (Boulware-Deser ghost)

8 Bigravity The first problem was partially solved by Vainshtein (1972): there exists a radius below which the linear theory cannot be applied; For the Sun, this radius is larger than the solar system! The second and third problems can be solved introducing a second metric: The only ghost-free local non-linear massive gravity theory! derham, Gabadadze, Tolley 2010 Hassan & Rosen, 2011

9 Standard rulers R 1 dz Dz ( ) = = sinh( Ω ) θ H H0 k 0 ( ) 0 Ω H z k 0 R θ H( z) = dz R

10 Background: SNIa, BAO, Then we can measure H(z) and 1 dz Dz ( ) = sinh( H0 Ωk 0 ) H Ω H() z 0 k 0 and therefore we can reconstruct the full FRW metric at () ds dt ( dx dy dz )] = Ωk H r

11 Two free functions ds = a [(1 + 2Ψ) dt (1 + 2Φ)( dx + dy + dz 2 )] At linear order we can write: Poisson equation zero anisotropic stress Ψ= πGa ρmδm Φ = Ψ

12 Two free functions ds = a [(1 + 2Ψ) dt (1 + 2Φ)( dx + dy + dz 2 )] At linear order we can write: modified Poisson equation Ψ= 4 πga Y( k, a) ρ m δ m 2 2 non-zero anisotropic stress η( ka, ) Φ = Ψ

13 Modified Gravity at the linear level standard gravity Yka (, ) = 1 η( ka, ) = 1 scalar-tensor models f(r) DGP * 2 G 2( F + F' ) Ya ( ) = 2 FG 2F + 3 F ' cav,0 2 F ' η( a) = 1+ 2 F + F' 2 2 k k * 1+ 4m m G 2 2 Ya ( ) = ar, η( a) = 1+ ar 2 2 FGcav,0 k k 1+ 3m 1+ 2m 2 2 ar ar 1 Y ( a) = 1 ; β = 1+ 2Hrc w 3β 2 η( a) = 1+ 3 β 1 Ya ( ) =... DE Bean et al Hu et al Tsujikawa 2007 Lue et al. 2004; Koyama et al massive bi-gravity See Koennig et al η( a) =... Boisseau et al Acquaviva et al Schimd et al L.A., Kunz &Sapone 2007

14 Modified Gravity at the linear level In the quasi-static limit, every Horndeski and massive bigravity model is characterized at linear scales by the two functions η( ka, ) Yka (, ) 2 1+ kh 4 = h kh kh 5 = h kh3 De Felice et al. 2011; L.A. et al.,arxiv: , 2012

15 Multifield dark energy? If DE is composed by several fields! 1+ k 2 h η(k,a) = h 4 + k 4 h $ 2 # " 1+ k 2 h 5 + k 4 h & %! 1+ k 2 h Y (k,a) = h 5 + k 4 h $ 1 # " 1+ k 2 h 3 + k 4 h & % L.A, T. Barreiro, N. Nunes 2014; V. Vardanyan, L.A, 2015

16 Reconstruction of the metric ds = a [(1 + 2 Ψ) dt (1 + 2 Φ )( dx + dy + dz )] Non-relativistic particles respond to Ψ v&= Hv Ψ Relativistic particles respond to Φ-Ψ α = perp ( Ψ Φ)dz

17 Testing the entire Horndeski Lagrangian P 2 L Ω Y(1 ) m0 +η = = P3 R f = R' f ' R = f + f E H = f = d lnδ H d ln a 0 A unique combination of model independent observables P2(1 + z) 1+ k h 4 1 = η = h2 2 2 E ' 2 E ( P ) + kh E Observables Theory L.A., Kunz, Motta, Saltas, Sawicki,

18 The importance of being eta Anisotropic stress η Φ Ψ Horndeski GW equation!! h + 3H(1+α M )! h + c 2 T k 2 h = 0 Bellini & Sawicki 2013 I. Saltas, I. Sawicki, L.A., M. Kunz

19 Eta and gravitational waves: Horndeski!! h + 3H(1+α M )! h + c 2 T k 2 h = 0 Horndeski It turns out that iff η 1 then the GW equation is modified. CMB B-polarization can be a tool to detect modified gravity!

20 Eta and gravitational waves: bimetric gravity Bimetric It turns out that iff η 1 then the GW equation is modified. CMB B-polarization can be a tool to detect modified gravity!

21 Crash course on CMB polarization

22 Gravitational wave speed CT varying c T 2 l(l+1)c l BB /2π [µk 2 ] fast ΛCDM, r 0.05 = 0 ΛCDM, r 0.05 = 0.2 a 1 = 0.8, r 0.05 = 0.2, c T 2 = 1.7 a 1 = 1, r 0.05 = 0.2, c T 2 = 1 a 1 = 1.5, r 0.05 = 0.2, c T 2 = 0.5 a 1 = 2, r 0.05 = 0.2, c T 2 = 0.3 slow multipole L.A., G. Ballesteros, V. Pettorino, 2014 See also Raveri, Silvestri and Zhou, 2014

23 GW speed and lensing CT lensing l(l+1)c l BB /2π [µk 2 ] ΛCDM, r 0.05 = 0 ΛCDM, r 0.05 = 0.2 a 1 = 0.8, r 0.05 = 0.2 a 1 = 1, r 0.05 = 0.2 a 1 = 1.5, r 0.05 = 0.2 a 1 = 2, r 0.05 = 0.2 slow 0.01 fast multipole L.A., G. Ballesteros, V. Pettorino, 2014

24 Constraints on GW speed 1.0 lensing 0.9 CT CT + lensing P P max Warning: BICEP data! C T 2 L.A., G. Ballesteros, V. Pettorino, 2014

25 GW speed at reionization CT The proposed satellite LiteBIRD plans to measure r at the reionization peak to 0.001! l(l+1)c l BB /2π [µk 2 ] fast ΛCDM, r 0.05 = 0 ΛCDM, r 0.05 = 0.2 a 1 = 0.8, r 0.05 = 0.2 a 1 = 1, r 0.05 = 0.2 a 1 = 1.5, r 0.05 = 0.2 a 1 = 2, r 0.05 = 0.2 slow multipole L.A., G. Ballesteros, V. Pettorino, 2014

26 Combined constraints!! h + 3H(1+α M )! h + c 2 T k 2 h = 0 V. Pettorino, L.A., 2014

27 Gravity in polarization maps and in supernovae

28 Lensing magnification UNION catalog 580 SNIa Credit: Kavli IPMU

29 Lensing magnification : no lensing on average This is true also within full nonlinear lensing because of photon flux conservation

30 Magnification distribution Low probability of strong magnification High probability of weak demagnification

31 turbogl: a fast lensing simulator! Convergence of a given halo Excess number of halos Kainulainen & Marra, , ,

32 turbogl: publicly available Mathematica code! Kainulainen & Marra, , ,

33 Compare with N-body simulations Comparing 2 nd,3 rd,4 th moments to simulations µ n (X X ) n

34 Signal from noise µ n,lens

35 Method of the Moments convolution of lensing PDF with intrinsic SN mag PDF Fundamental assumption: the SN intrinsic distribution is independent of redshift

36 Cosmology dependence! Marra, Quartin & Amendola! arxiv: !

37 Constraining perturbations within ΛCDM SNIa distribution 3% constraint on σ8 (fixing ) Ω m Quartin, Marra & Amendola, PRD 2014

38 Constraining the growth of perturbations LSST WFIRST Growth index Amendola, Castro, Marra & Quartin, arxiv

39 Simple fitting functions 3% RMS error

40 Redshift distortions + SN lensing RSD: 2dFGS 6dFGS LRG BOSS CMASS WiggleZ VIPERS Amendola, Castro, Marra & Quartin, arxiv

41 Gravity is everywhere

42 Galileo Galilei Institute Florence April-May 2016 Theoretical Cosmology in the Era of Large Surveys Giovanni Marozzi, Claudia de Rham, Sabino Matarrese, Valeria Pettorino, Martin Kunz, Ruth Durrer, L.A.

43 Constraining the growth of perturbations Amendola, Castro, Marra & Quartin, arxiv

44 Lensing variance for supernovae Amendola, Castro, Marra & Quartin, arxiv

45 Redshift distortions + SN lensing RSD: 2dFGS 6dFGS LRG BOSS CMASS WiggleZ VIPERS growth rate likelihood Amendola, Castro, Marra & Quartin, arxiv

46 Step-wise parametrization Amendola, Castro, Marra & Quartin, arxiv

Gravity Testing and Interpreting Cosmological Measurement

Gravity Testing and Interpreting Cosmological Measurement Cosmological Scale Tests of Gravity Edmund Bertschinger MIT Department of Physics and Kavli Institute for Astrophysics and Space Research January 2011 References Caldwell & Kamionkowski 0903.0866 Silvestri