Testing the Copernican principle and equivalence principle on cosmological scales. Jean-Philippe UZAN

Transcription

1 16/10/2010 IPhT Testing the Copernican principle and equivalence principle on cosmological scales Jean-Philippe UZAN

2 Cosmological models Theoretical physics Principles Local law of nature Extrapolations Cosmology models Constraints Astrophysics Phenomena Gravity=GR Matter=SU(3)XSU(2)xU(1) Compatible with local physics Save the appearances Its construction relies on 4 hypothesis 1. Theory of gravity [General relativity] 2. Matter [Standard model fields + CDM + Λ] 3. Symmetry hypothesis [Copernican Principle] 4. Global structure [Topology of space is trivial] New physics with simple cosmological solution Standard physics with more involved solution In agreement with all the data. [JPU, arxiv: ]

3 13,7 Gyrs 1 Gyrs 400 m. yrs yrs 300 s 10-3 s 2.73 K 10 4 K 10 9 K K Decelerated expansion post-recombinaison universe Hot universe Known microphysics complex Supernovae LSS First stars CMB Nucleosynthesis Primordial universe (reheating/baryoegenesis/ ) Microphysics not understood s K Accelerated expansion Inflation? (Multiverse/quantum gravity/ Extra-dimensions Speculative microphysics Microphysics and structure unknown

4 Needs to test these hypothesis This model is in agreement with all existing observational data at the expense of the introduction of a dark sector: - dark matter: galaxy rotation curves, properties of the large scale structure of the universe. candidate: Weakly interacting massive particles (many candidates, e.g. from supersymmetry) or a modification of general relativity in the low acceleration regime - dark energy: acceleration of the cosmic expansion candidate: cosmological constant or more exotic models (quintessence, modification of GR in the IR etc.) This reveals the need for new degrees of freedom in our cosmological model: - physical - geometrical

5 Needs to test these hypothesis New physical degrees of freedom: - nature of the new fields - coupling with standard matter fields - new matter vs modification of general relativity [long range unscreened force is not described by GR] 0-10 Solar system Sgr A BBN - inference of the existence and properties of dark sector relies on the assumption that GR is a good description of gravity. Testing general relativity on astrophysical scales Einstein equivalence principle -20 CMB Black-hole limit New geometrical degrees of freedom: - no new physics - the propeties of spacetime on large scales have to be modified. Testing the Copernican principle -30 Dark matter a<a 0 Dark energy R<Λ SNIa

6 Copernican principle Definition & Implications

7 Isotropy: motivation Observationally, the universe seems very isotropic around our worldline. Without assumption: Isotropy of matter distribution on the lightcone è isotropy of spacetime geometry Not enough to determine the spacetime geometry. (c) L. Haddad & G. Duprat

8 Uniformity principle Two possibilities to achieve this: Spatially homogeneous & isotropic Spherically symmetric Universe has a center Copernican Principle: we do not occupy a particular spatial location in the universe (c) L. Haddad & G. Duprat

9 Geometrical implication There exists a priviledged class of observers for which the spatial sections look isotropic and homogeneous. The spatial sections are 3D constant curvature hypersurfaces. The spacetime is of the Friedmann-Lemaître type with metric Consequences: 1- The dynamics of the universe reduces to the one of the scale factor 2- It is dictated by the Friedmann equations 3- need for an equation of state

10 Implications of the Copernican principle Independently of any theory (H1, H3), the Copernican principle implies that the geometry of the universe reduces to a(t). Consequences: H2 so that Hubble diagram gives - H 0 at small z - q 0 Supernovae data (1998+) show No hypothesis on gravity at this stage. The expansion is now accelerating

11 Classifying spacetimes The solutions of Einstein equations can be classified according to their symmetries. The symmetries are characterized by the set of Killing vectors: The Killing vectors satisfy Isometry group = isotropy group + transitivity group «rotation» «translations» r n(n + 1) 2 q n(n 1) 2 s n One thus needs to specify (s, q, r)&c a bc

12 Simplest solutions In n=4 dimensions, r=q+s 10 so that s can run between 0 and 4. s=4 corresponds to static spacetimes For s<4, the possibilities are then q=3 (isotropic) q=2 is impossible [no subgroup of O(3) of dimension 2] q=1 (locally invariant under rotation) q=0 (anisotropic) Indeed, the real universe has r=0! [Peter, JPU, Cosmologie Primordiale]

13 Examples Friedmann-Lemaître Bianchi I Lemaître-Tolman-Bondi homogène-isotrope homogène-anisotrope inhomogène-loc. isotrope r =6 r =3 r =3 s =3 q =3 s =3 q =0 s =2 q =1 (centre) s =0 q =3

14 Testing the Copernican principle Homogeneity

15 This is difficult (c) L. Haddad & G. Duprat

16 Test of homogeneity Homogeneous and isotropic universe [Sandage1962, McVittie 1962] Typical order of magnitude (z~4)

17 Test of homogeneity Homogeneous and isotropic universe Inhomogeneous universe [Sandage1962, McVittie 1962] [JPU, Clarkson, Ellis, PRL (2008)] Typical order of magnitude (z~4)

18 Time drift and homogeneity Friedmann-Lemaître LTB (spherically symmetric universe) H = H H = H By combining distance measurements (D A or D L ), one can test whether H = H We have information off the past light-cone.

19 How sensitive can such a test be? Take a LTB (spherically symmetric universe) with same lightcone structure as a FL We assume that i.e. same D L (z) & same matter profile BUT NO cosmological constant H H [Dunsby,Goheer,Osano,JPU, ]

20 Other methods Interaction of CMB photon with hot gas of galaxy clusters CMB photons are scattered into our line of sight. Gives information on the inside of our past lightcone

21 Other methods SZ effect Temperature of scattered CMB photons: - It induces spectral distortions: - Thermal SZ (due to thermal motion of electrons) reflects the monopole seen by the cluster - If the blackbody T from different direction are different, then huge distortion. - Motion of the cluster induces kinetic SZ that reflects the CMB dipole - Applied to a class of LTB model. Impressive constraints (even if do not rule out all the models) [Goodman, astro-ph/ ; Caldwell & Stebbins, arxiv: ; Zhang & Stebbins, arxiv: ] SZ effect Polarisation of scattered CMB photons: - Cluster bulk tranverse velocity & CMB monopole, quadrupole and octopole induce modifications in CMB polarisation through scattering off cluster gas. In principle, gives access to monopole-octopole of the CMB as seen by the cluster.

22 Testing the Copernican principle Isotropy

23 Testing local isotropy The simplest universe with local homogeneity and no local isotropy is Bianchi I. 3 scale factors We define the shear tensor by It is symmetric & traceless The Einstein equations now take the form H 2 = H = 3 ( +3P ) 2 3 Almost the same form as the standard FL equations: - shear acts as a massless scalar field - if the anisotropic stress vanishes the the anisotropy decays ( i j) +2H j i = i j i j = Ki j S 2 2 = K2 S 4

24 Motivations to test for isotropy At early time: -the isotropisation of the universe is efficient only if inflation lasts long enough. At late time: What is the dynamical effect of an early anisotropy? Can it be constrained observationally? Thiago Pereira, Cyril Pitrou, J.-P. U., JCAP 09 (2007) 006 Cyril Pitrou, Thiago Pereira, J.-P. U., JCAP 04 (2008) any model of dark energy involving vector fields and some models of modification of GR have a non-vanishing anisotropic stress tensor; - it has also been shown that in the approach in which the acceleration is explained by backreaction effect, the Hubble flow becomes anisotropic at late time [Marozzi, JPU, arxiv: ] How can we constrain a late time anisotropy?

25 Isotropisation during inflation Thiago Pereira, Cyril Pitrou, J.-P. U., JCAP 09 (2007) 006 Cyril Pitrou, Thiago Pereira, J.-P. U., JCAP 04 (2008) 004 The standard canonical variables can be generalised to Bianchi spacetimes. If large number of e-fold we see the isotropisation both at the background and perturbation level. Initial conditions: no unambiguous procedure - there always exist non-wkb modes - A primordial shear strongly affects the inflationary picture. If number of e-fold small, inflation loses its predictivity on large scales - initial «classical» perturbations - also true in standard inflation (SR attractor not reached) Initial power spectrum anisotropic Α Π Log k k ref

26 Late time Let us consider a bundle of null geodesics, x µ (v,s). [Pitrou, JPU, Pereira arxiv: ] u µ n µ 2 n µ 1 µ source observateur x µ [n 0,v] u µ The deformation of the geodesic bunble can be obtained from the geodesic deviation equation k µ

27 Weak-lensing B-modes Sachs equation Initial condition

28 Ceci n est pas une équation I skip the details but it involves decomposing products of spherical (spinned) harmonics, hence the C-coefficients. - Hierarchy similar to CMB Boltzmann hierarchy - does not depend on the choice of any background spacetime [but needs h lm etc..] - never been derived and generalized the particular FL case - non-vanishing Weyl implies E/B modes due to coupling to convergence

29 What to expect with Euclid (i) Visible imaging (ii) NIR photometry (iii) NIR spectroscopy. 15,000 square degrees 100 million redshifts, 2 billion images Median z~1 I will provide: - P(k,z) on 15,000 square degrees, 70,000,000 galaxy redshift with 0.5<z<2. - weak lensing on 15,000 square degrees, 40 galaxy images per square arcmin with 0.5<z<3. The error bars on the B-modes should be divided by (10-40) compared to CFHTLS. Linear regime typically for scales larger than 1 deg. And Euclid will probe scales up to ~40 deg. It will probe large scales for which astrophysical effects leading to B-modes are expected to be negligible.

30 Testing the Copernican principle Fluid approximation

31 Extending CP: how homogeneous is homogeneous? [Clarkson, Ellis, Maartens, Umeh, JPU, arxiv: ] R µ =0 C µ =0 R µ =0 C µ =0

32 Extending CP: how homogeneous is homogeneous? [Clarkson, Ellis, Maartens, Umeh, JPU, arxiv: ] R µ =0 C µ =0 R µ =0 C µ =0 SN: - beam is very thin: 1 z=1 corresponds to 10-7 arcsec. Typically smaller than the distance between any massive object. - beam propagates mostly in underdense regions [Zel dovich, Dyer, Roeder] - distribution of magnification - scatter of the m-z diagram allow to constrain the smoothness of the matter distribution. systematic shift + scatter On which scale are we allowed to use the fluid approximation? Different from the backreaction approach.

33 Extending CP: how homogeneous is homogeneous? Small scales (e.g. ~AU) cannot be reched by numerical simulations. Find some approximate exact solutions [Fleury, Dupuy, JPU, in preparation]

34 Extending CP: how homogeneous is homogeneous? Preliminary 74% matter in point masses 26% matter in homoheneous fluid [Fleury, Dupuy, JPU, in preparation]

35 Testing the equivalence principle JPU, Rev. Mod. Phys. 75, 403 (2003); Liv. Rev. Relat. 4, 2 (2011) JPU, [astro-ph/ , arxiv: ] R. Lehoucq, JPU, Les constantes fondamentales (Belin, 2005) G.F.R. Ellis and JPU, Am. J. Phys. 73 (2005) 240 JPU, B. Leclercq, De l importance d être une constante (Dunod, 2005) translated as The natural laws of the universe (Praxis, 2008).

36 On the basis of general relativity The equivalence principle takes much more importance in general relativity It is based on Einstein equivalence principle universality of free fall local Lorentz invariance local position invariance If this principle holds then gravity is a consequence of the geometry of spacetime This principle has been a driving idea in theories of gravity from Galileo to Einstein

37 GR in a nutshell Underlying hypothesis Equivalence principle Universality of free fall Local lorentz invariance Local position invariance Physical metric Dynamics gravitational metric Relativity

38 The equivalence principle in Newtonian physics The deviation from the universality of free fall is characterized by Second law: Definition of weight So that Consider a pendumum of length L in a gravitational field g, Then

39 Tests on the universality of free fall 2014 MicroScope

40 Equivalence principle and constants In general relativity, any test particle follow a geodesic, which does not depend on the mass or on the chemical composition Imagine some constants are space-time dependent 1- Local position invariance is violated. 2- Universality of free fall has also to be violated Mass of test body = mass of its constituants + binding energy In Newtonian terms, a free motion implies dp dt = mdv dt = 0 But, now d p dt = 0=m a + dm d v ma anomalous

41 Field theory Physical theories involve constants These parameters cannot be determined by the theory that introduces them. These arbitrary parameters have to be assumed constant: - experimental validation - no evolution equation If a constant is varying, this implies that it has to be replaced by a dynamical field This has 2 consequences: 1- the equations derived with this parameter constant will be modified one cannot just make it vary in the equations 2- the theory will provide an equation of evolution for this new parameter The field responsible for the time variation of the «constant» is also responsible for a long-range (composition-dependent) interaction i.e. at the origin of the deviation from General Relativity. [Ellis & JPU, gr-qc/ ]

42 Physical systems Atomic clocks Oklo phenomenon Quasar absorption spectra Meteorite dating CMB BBN Local obs QSO obs CMB obs

43 Observables and primary constraints A given physical system gives us an observable quantity Step 1: External parameters: temperature,...: Primary physical parameters From a physical model of our system we can deduce the sensitivities to the primary physical parameters Step 2: The primary physical parameters are usually not fundamental constants.

44 Examples - Atomic clocks [Luo, Olive, JPU, arxiv: ] - Big Bang nucleosynthesis [Coc, Nunes, Olive, JPU, Vangioni, astro-ph/ ] [Coc, Descouvemont, Olive, JPU, Vangioni, arxiv: ] - Stellar nucleosynthesis [Ekström, Coc, Descouvemont, Meynet, Olive, JPU, Vangioni, arxiv: ] - Cosmic microwave background anisotropies [Planck collaboration, JPU, in preparation]

45 Physical systems: new and future Atomic clocks Oklo phenomenon Meteorite dating Quasar absorption spectra Pop III stars [Ekström, Coc, Descouvemont, Meynet, Olive, JPU, Vangioni, 2009] 21 cm CMB BBN [Coc, Nunes, Olive, JPU, Vangioni] JPU, Liv. Rev. Relat., arxiv:

46 Conclusions Cosmological data allow us to test the hypothesis of our cosmological model Copernican principle: - various tests proposed recently to test local isotropy and homogeneity - set strong constraints on «void models» - stronger constraints on local isotropy expected from weak lensing - study of propagation of light in highly inhomogeneous universe Why does a simple solution as FL describe our universe so well? Equivalence principle: - part of the general program to test GR on astrophysical scales - constraints from various systems Great progresses. This complements other tests of the hypothesis underlying the construction of our cosmological model: - test of GR on astrophysical scales [see e.g. JPU and F. Bernardeau, 2001] - test of distance duality - test of spatial topology.