Cosmic Growth, Gravitational Waves, and CMB

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1 Cosmic Growth, Gravitational Waves, and CMB Eric Linder UC Berkeley/KASI 8 th KIAS Workshop on Cosmology 5 November

2 New Connections In just the last couple of years, we have fully recognized close connections: Cosmic Growth Δ(D GW /D EM ) çè Δ growth Δ growth çè Δ CMB lensing Gravitational Waves CMB Δ gravity çè Δ CMB lensing + B-modes 2 2

3 Implications of c T = c GW GRB A: synchronicity of GW and photon arrival within 2 seconds after signal propagation for 130 My (400 x s) limits c T /c 1 < Any theory with c q T c is essentially* ruled out. Δt Light follows null geodesics. q If GW follows disformal à Δt. g µ dx µ dx =0 G µ dx µ dx =0 G µ = g µ + q Only conformal theories survive. G µ = C(,X) g µ For nonrelativists: Additive gravity is dead Multiplicative gravity is ok 3 3

4 Gravitational Wave Distances Just because c T =c doesn t mean no effect on GW propagation. ḧ +(2+ M )Hḣ + c2 T k 2 h =0, GW amplitude ot stands is proportional for a derivativeto with 1 / redistance (energy goes as inverse square) h ~ 1/D L GW So we can measure changes in gravity by comparing the GW distance to the photon luminosity distance to the same object. Horndeski α M (running of Planck mass) damps h. Nishizawa Arai & Nishizawa Belgacem Amendola Linder

5 Gravitational Wave Distances Modified gravity α [ ] M (running of Planck mass) damps h h = h GR e (1/2) R obs em = h GR " M 2?,em M 2?,obs M = d ln M 2? d ln a d ln a M (a) = h GR e (1/2) R obs em # 1/2 d ln M 2? (a) So [ ] M d L,GW (a) =d GR 2 1/2 L (a) (a =1) M 2(a) but M * also affects growth, so GW distance tied to growth! Linder e.g. in No Slip Gravity (also in nonlocal gravity) d L,GW (a) =d GR L (a) [ Gmatter (a) ] 1/2 G matter (a =1) 5 5

6 Gravitational Waves and Cosmic Growth GW distance tied to growth! If we detect, e.g., a suppression in growth, then this can be checked vs GW distances different than GR. Example: No Slip Gravity (1 free function) fits growth from redshift space distortions, better than GR. It predicts ~5% deviation in GW distances. Galaxy surveys have deep complementarity with GW and CMB surveys. 6 6

7 CMB B-modes and Gravity Effective field theory approach to modified gravity defines property functions α B, α K, α M, α T. We know* α T =0, and α K is only important on horizon scales. Even with α T =0, GW propagation affected by α M. Low l bump is primordial GW. Clear impact of (only) α M. High l bump is lensing. Matter growth suppression by α M, α B. hi_class with α i =α i,0 a 1 Denissenya & Linder

8 CMB B-modes and Gravity No Slip Gravity with α B = -2α M. B-modes modified: GW + Lensing Lensing power modified: Analytic prediction based on cosmic growth Brush, Linder, Zumalacárregui

9 Cosmic Growth and Why Now? Growth is a battle between gravitational attraction and cosmic acceleration. f = d ln D d ln a Gravity loses growth ends. Falls from 1 to 0 in 2 efolds, with today in middle. Linder & Polarski

10 Growth index transition Define growth index by f = m (a) Transitions today from past constant to future asymptote

11 f(r) gravity à GR Today is the maximal deviation of G eff in f(r). Do surveys today, not an e-fold from now! 11 11

12 Summary The tensor sector of modified gravity can be probed by interferometers, CMB, and cosmic surveys. Cosmic Growth Δ(D GW /D EM ) çè Δ growth Δ growth çè Δ CMB lensing Gravitational Waves CMB Δ gravity çè Δ CMB lensing + B-modes 12 12