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					    Les Houches 21/10/2009




Testing Gravity on the largest scale

                 Alain Blanchard


                October 20, 2009




            Alain Blanchard   Testing Gravity on the largest scale
              Les Houches 21/10/2009


Standard Cosmological model




   Standard Cosmological model:




                      Alain Blanchard   Testing Gravity on the largest scale
               Les Houches 21/10/2009


Standard Cosmological model




   Standard Cosmological model:

   Concordance cosmology = expansion is accelerated.




                       Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Standard Cosmological model

   Cosmological parameters




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Standard Cosmological model

   Cosmological parameters
   ...pretty well known




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Standard Cosmological model

   Cosmological parameters
   ...pretty well known
   SNIa, CMB, P(k)




                        Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


Standard Cosmological model

   Cosmological parameters
   ...pretty well known
   SNIa, CMB, P(k)




   (Ferramacho, Blanchard & Zolnirowski, 2009)

                          Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


Standard Cosmological model


   Not much progresses...




                          Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


Standard Cosmological model


   Not much progresses...




   WMAP 2003


                          Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


Standard Cosmological model


   SNIa, CMB, P(k)




                         Alain Blanchard   Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Standard Cosmological model


   SNIa, CMB, P(k)

   Cosmological parameters are derived from geometrical quantities:




                           Alain Blanchard   Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Standard Cosmological model


   SNIa, CMB, P(k)

   Cosmological parameters are derived from geometrical quantities:


                                         1+z
                                                dz
                                     0         H(z)




                           Alain Blanchard      Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Standard Cosmological model


   SNIa, CMB, P(k)

   Cosmological parameters are derived from geometrical quantities:


                                         1+z
                                                dz
                                     0         H(z)


   with the asumption of CDM.




                           Alain Blanchard      Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Growth rate of perturbations


   Equations for linear perturbations:




                           Alain Blanchard   Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Growth rate of perturbations


   Equations for linear perturbations:


                      ¨      ˙           3
                      δ + 2H δ = 4πG ρδ = ΩH 2 δ
                                         2




                           Alain Blanchard   Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Growth rate of perturbations


   Equations for linear perturbations:


                       ¨      ˙            3
                       δ + 2H δ = 4πG ρδ = ΩH 2 δ
                                           2
   is entirely determined from H(t) (or H(z) or Ω(z) ).




                           Alain Blanchard   Testing Gravity on the largest scale
                   Les Houches 21/10/2009


Growth rate of perturbations


   Equations for linear perturbations:


                       ¨      ˙            3
                       δ + 2H δ = 4πG ρδ = ΩH 2 δ
                                           2
   is entirely determined from H(t) (or H(z) or Ω(z) ).

   Solution:
                                                 +∞
                                                       1+u
                       D(t) ∝ H(z)                             du
                                             z         H 3 (z)
   Heath (1977)



                           Alain Blanchard       Testing Gravity on the largest scale
                  Les Houches 21/10/2009


But...




   if acceleration is due to some break of GR (DGP, ...)




                          Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


But...




   if acceleration is due to some break of GR (DGP, ...)

   then:

                        ¨      ˙
                        δ + 2H δ = 4πG (k, z)ρδ




                          Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


But...




   if acceleration is due to some break of GR (DGP, ...)

   then:

                        ¨      ˙
                        δ + 2H δ = 4πG (k, z)ρδ
   may be...




                          Alain Blanchard   Testing Gravity on the largest scale
              Les Houches 21/10/2009


A Measure of D(t)




   Is a test of gravity ↔ GR




                      Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


A Measure of D(t)




   Clusters abundance




                          Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


A Measure of D(t)




   Clusters abundance

                                     ρ         d ln σ
               n(M, t) = −                 δNL        F(νNL )
                                M 2 σt (M)     d ln M




                          Alain Blanchard   Testing Gravity on the largest scale
                  Les Houches 21/10/2009


A Measure of D(t)




   Clusters abundance

                                     ρ         d ln σ
               n(M, t) = −                 δNL        F(νNL )
                                M 2 σt (M)     d ln M


                                                   δNL (t)
   with : σt (M) = D(t)σ0 (M) and νNL =            σt (M)




                          Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Clusters selection




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Clusters selection




   - Optical




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Clusters selection




   - Optical

   - Lensing




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Clusters selection




   - Optical

   - Lensing

   - X-ray




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Clusters selection




   - Optical

   - Lensing

   - X-ray

   - SZ




                        Alain Blanchard   Testing Gravity on the largest scale
                Les Houches 21/10/2009


Full sky x-ray survey




                        Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


Full sky x-ray survey




   fx > 10−14 erg/s/cm2 → 3. 105 clusters




                         Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


Full sky x-ray survey




   fx > 10−14 erg/s/cm2 → 3. 105 clusters


                             δσ
                                ∼ 0.003 (5σ)
                             σ




                         Alain Blanchard   Testing Gravity on the largest scale
               Les Houches 21/10/2009


But...



    We need:




                       Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


But...



    We need:


   Accurate mass function understanding (theory)




                         Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


But...



    We need:


   Accurate mass function understanding (theory)

   A mass proxy is needed




                         Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


But...



    We need:


   Accurate mass function understanding (theory)

   A mass proxy is needed

   Accurate selection function knowledge




                         Alain Blanchard   Testing Gravity on the largest scale
             Les Houches 21/10/2009


Conclusion




                     Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


Conclusion




   Measuring D(t) is a test of GR




                         Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


Conclusion




   Measuring D(t) is a test of GR

   Several ways...vspace5mm




                         Alain Blanchard   Testing Gravity on the largest scale
                 Les Houches 21/10/2009


Conclusion




   Measuring D(t) is a test of GR

   Several ways...vspace5mm
   No designed experiment towards this target.




                         Alain Blanchard   Testing Gravity on the largest scale

				
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