Cosmological Constraints on Newton s Gravitational Constant for Matter and Dark Matter

Transcription

1 Cosmological Constraints on Newton s Gravitational Constant for Matter and Dark Matter Jordi Salvadó Instituto de Física Corpuscular Talk based on: JCAP 1510 (2015) no.10, 029 [arxiv: ] In collaboration with Yang Bai and Ben Stefanek Cosmology Meeting BCN 2016 Jordi Salvadó Slide 1

2 Introduction 1 Cosmological measurements of G N Very different scale than the lab experiments! Ken-ichi Umezu, K. Ichiki and M. Yahiro Phys. Rev. D 72 (2005) [astro-ph/ ] S. Galli, A. Melchiorri, G.F. Smoot and O. Zahn, Phys. Rev. D 80 (2009) [arxiv: ] 2 We (ONLY!) know DM interacts with Gravity, but is it the same Gravity? Long Range Forces A. Nusser, S.S. Gubser and P.J.E. Peebles Phys. Rev. D 71 (2005) [astro-ph/ ] R. Bean, E.E. Flanagan, I. Laszlo and M. Trodden Phys. Rev. D 78 (2008) [arxiv: ] Dark Matter Equivalence Principle (M grav = M iner ) Jordi Salvadó Slide 2

3 Introduction Cosmological linear theory Jordi Salvadó Slide 3

4 Introduction 0-order(homogeneous and isotropic),(ω i ρ i /ρ crit, ρ crit = 3H2 8πG ) Matter Ω m Ω cdm, Ω b Radiation Ω r Ω γ (fixed by T CMB ), N rel Reionization optical depth τ Hubble parameter today H 0 Ω Λ 1-order, initial conditions for δρ/ρ are determined by the primordial power spectrum from inflation, Primordial spectrum amplitude A s Spectral index(n s = 1 flat spectra) n s P (k) = A s k 1 ns k 3 C l, P gal (k) Jordi Salvadó Slide 4

5 How can we measure the gravitational constant G N? Gravitational acceleration depends only on the product of Newton s Constant G N and the central body mass M. a grav = G NM r 2 To break this degeneracy and measure G N, an additional force is required to define the central body mass. G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli and G. M. Tino, Nature 510 (2014) Jordi Salvadó Slide 5

6 How can we use cosmology to constrain G N? Almost all can be absorbed redefining τ λ G τ and k k/λ G. The baryons interact electromagnetically with the photons. δ b = θ b + 3 φ θ b = ȧ a θ b + c 2 sk 2 δ b + 4 ρ γ 3 ρ b an e σ T (θ γ θ b ) + k 2 ψ The Thomson scattering term is the only one that can not be absorbed. Varying G now yields an observable change in cosmological evolution. Jordi Salvadó Slide 6

7 CMB Temperature Power Spectrum Cosmological equations integrated and CMB spectra computed using the publicly available CLASS code. [l(l + 1)/2π] C l T T (µk) λ G = 0.25 λ G = 0.50 λ G = 1.00 λ G = 1.50 λ G = Multipole Moment l Jordi Salvadó Slide 7

8 Analysis Method Markov Chain Monte Carlo (MCMC) using the publicly available MontePython code (written to work with CLASS). P (θ i D) = L(D θ i )π(θ i ) L(D θi )dθ 1..dθ N 1 Planck 2013 & 2015 Data Release 2 3 Yr, High-l TT polarization from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT). 3 BAO data from Sloan Digital Sky Survey (SDSS) (Data Releases 7 and 9) and Six degree Field Galaxy Survey (6dFGS). 4 H 0 measurement from Wide Field Camera 3 on HST (0.01 < z < 0.1) Jordi Salvadó Slide 8

9 Planck Constraint on λ G λg % 95% Planck 2013 Data Release Hubble Parameter H0 Mpc [km s 1 1 ] Data λ G Planck Planck+Lensing+BAO Planck+Lensing+BAO+HST Planck+Lensing+BAO+BBN Planck+ACT/SPT Planck+Lensing+BAO+HST+ACT/SPT Planck+Lensing+BAO+BBN+ACT/SPT Planck Planck 2015 gives a result consistent with lab experiments at 1σ Jordi Salvadó Slide 9

10 DM sector Long Range Force Model Use a traditional long range fifth force to model different dynamics in the dark matter sector. L 1 2 µφ µ φ 1 ( 2 m φ 2 φ 2 + χγ µ µ χ 1 + φ ) m χ χχ f For scales smaller than r s = m φ 1, the Yukawa interaction mediates a fifth force. This fifth force will be long ranged if the mediator φ is nearly massless. V (r) = G Nm D1 m D2 r [ 1 + αf e m φ r ] Attempt to constrain α f using the latest cosmological data. Jordi Salvadó Slide 10

11 DM sector Long Range Force Model 2(dΦH/dτ) τ = τ 0 αf = 0 α f = α f = α f = [l(l + 1)/2π] C l T T (µk) αf = 0, mφ/h0 = 0 αf = , mφ/h0 = 0 αf = , mφ/h0 = 0 αf = , mφ/h0 = Multipole Moment l Large effect at small multipoles Multipole Moment l Jordi Salvadó Slide 11

12 DM sector Long Range Force Model mφ/h % 95% We get a bound of O(10 4 ) for α s The bound on the α f is independent of m φ in this range α f = (M Pl/f) 2 Jordi Salvadó Slide 12

13 DM sector Weak Equivalence Principle The Weak Equivalence Principle (WEP) states that all objects in a uniform gravitational field, independent of the mass or other compositional properties, will experience the same acceleration. Modern experiments report that the difference between inertial and gravitational masses is zero at the level. Thus, violations of the WEP in the visible sector are tightly constrained. However, WEP violation in the Dark Matter sector is far less constrained. Jordi Salvadó Slide 13

14 DM sector WEP Violation We introduce WEP violation into the dark matter sector by allowing the gravitational charge of dark matter to differ from the inertial mass by a factor of λ D m grav D = λ Dm D Consequently, if we have two matter particles b 1 and b 2 and two dark matter particles D 1 and D 2, the gravitational forces in terms of the particle inertial masses are F b1,b 2 = G Nm b1 m b2 r 2, F bi,d j = λ D G N m bi m Dj r 2, F D1,D 2 = λ D 2 G Nm D1 m D2 r 2. We use the modified EQ. from red-shift z T Jordi Salvadó Slide 14

15 DM sector Effect of dark WEP breaking on the CMB TT Spectrum η D = λ D 1 Starting Redshift z T η D = 10 6 η D = 0 η D = [l(l + 1)/2π] C l T T (µk) Multipole Moment l Jordi Salvadó Slide 15

16 DM sector Allowed region for λ D as a function of z T Using just data from Planck, λ D 1 is consistent with zero at the 10 6 level or less for all z T % 95% 10 ηd = λd 1 [10 7 ] Transition Redshift zt Strong correlation with H σ 2σ % 95% Planck+Lensing+HST zt = Eotvos Parameter ηd [10 7 ] ηd = λd 1 [10 7 ] Hubble Parameter H0 Mpc [km s 1 1 ] Expansion Rate Today H0 [km s 1 Mpc 1 ] Jordi Salvadó Slide 16

17 Conclusions We used the latest cosmological data to derive a constraint on G N for all matter at the 2.7% level. We use the latest cosmological data to constrain a long range force between dark matter particles at the level of Using this method, we can constrain WEP in the dark matter sector at the 10 6 level or less for all z T Jordi Salvadó Slide 17

18 THE END Jordi Salvadó Slide 18

19 Effect of dark WEP breaking on the CMB EE Spectrum η D = λ D η D = 10 6 η D = 0 η D = [l(l + 1)/2π] C l EE (µk) Multipole Moment l Jordi Salvadó Slide 19

20 Effect of dark WEP breaking on the CMB TE Spectrum η D = λ D η D = 10 6 η D = 0 η D = [l(l + 1)/2π] C l T E (µk) Multipole Moment l Jordi Salvadó Slide 20

21 CMB EE Power Spectrum [l(l + 1)/2π] C l EE (µk) λ G = 0.25 λ G = 0.50 λ G = 1.00 λ G = 1.50 λ G = Multipole Moment l Jordi Salvadó Slide 21

22 CMB TE Power Spectrum [l(l + 1)/2π] C l T E (µk) λ G = 0.25 λ G = 0.50 λ G = 1.00 λ G = 1.50 λ G = Multipole Moment l Jordi Salvadó Slide 22

23 Ionization Fraction If λ G is increased (decreased), recombination takes place over a longer (shorter) period of time. Ionization Fraction Xe X e = n e /n H λ G = 0.25 λ G = 0.50 λ G = 1.00 λ G = 1.50 λ G = Redshift z Jordi Salvadó Slide 23