What do we really know about Dark Energy?

Transcription

1 What do we really know about Dark Energy? Ruth Durrer Département de Physique Théorique & Center of Astroparticle Physics (CAP) ESTEC, February 3, 2012 Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

2 Outline 1 Introduction 2 What do we really measure? 3 What do we know about dark energy? 4 Conclusions Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

3 Introduction In 98/99 Riess et al., Perlmutter et al. and Schmith et al. presented the first evidence for dark energy. They had observed SN1a s and related the inferred luminosity distance and redshift, D L (z). measured flux = F(z) = L 4πD L (z) 2 Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

4 Introduction In 98/99 Riess et al., Perlmutter et al. and Schmith et al. presented the first evidence for dark energy. They had observed SN1a s and related the inferred luminosity distance and redshift, D L (z). measured flux = F(z) = L 4πD L (z) 2 They found that the distances are too large, the SN1a too faint, to fit the distance redshift relation of a flat or open cold dark matter (CDM) model, but they are well fit by a flat ΛCDM model, i.e. a model with cold dark matter and a cosmological constant Ω Λ 0.7. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

5 Introduction In 98/99 Riess et al., Perlmutter et al. and Schmith et al. presented the first evidence for dark energy. They had observed SN1a s and related the inferred luminosity distance and redshift, D L (z). measured flux = F(z) = L 4πD L (z) 2 They found that the distances are too large, the SN1a too faint, to fit the distance redshift relation of a flat or open cold dark matter (CDM) model, but they are well fit by a flat ΛCDM model, i.e. a model with cold dark matter and a cosmological constant Ω Λ 0.7. The Hubble expansion as function of the redshift in a multi-component Friedmann universe can be written as (Friedmann equation) H 2 (z) = H0 2 Ω m(1 + z) 3 + Ω K (1 + z) 2 + Ω r(1 + z) 4 + Ω Λ + Ω m + Ω K + Ω r + Ω Λ + = 1 Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

6 Introduction This was an entirely unexpected result. It has later been confirmed with more SN1a, with observations of CMB anisotropies and polarization, LSS, weak lensing, BAO s, cluster data... Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

7 Introduction This was an entirely unexpected result. It has later been confirmed with more SN1a, with observations of CMB anisotropies and polarization, LSS, weak lensing, BAO s, cluster data... All this data is consistent with the so called concordance model, a Friedmann Lemaître (FL) universe with a nearly scale invariant spectrum of small Gaussian initial fluctuations as predicted by inflation. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

8 Introduction This was an entirely unexpected result. It has later been confirmed with more SN1a, with observations of CMB anisotropies and polarization, LSS, weak lensing, BAO s, cluster data... All this data is consistent with the so called concordance model, a Friedmann Lemaître (FL) universe with a nearly scale invariant spectrum of small Gaussian initial fluctuations as predicted by inflation. The energy content of the Universe is dominated by a cosmological constant Λ (ev) 2 such that Ω Λ = Λ/(3H 2 0) H 0 = 100h km/s/mpc, h 0.71 ± 0.06 Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

9 Introduction This was an entirely unexpected result. It has later been confirmed with more SN1a, with observations of CMB anisotropies and polarization, LSS, weak lensing, BAO s, cluster data... All this data is consistent with the so called concordance model, a Friedmann Lemaître (FL) universe with a nearly scale invariant spectrum of small Gaussian initial fluctuations as predicted by inflation. The energy content of the Universe is dominated by a cosmological constant Λ (ev) 2 such that Ω Λ = Λ/(3H 2 0) H 0 = 100h km/s/mpc, h 0.71 ± 0.06 The second component of the concordance model is pressureless matter with Ω m = ρ m/ρ c 0.13/h 2. About 83% of this matter is dark matter, i.e. an unknown non-baryonic component and only about 17% is in the form of baryons. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

10 Introduction This situation is disturbing for two main reasons: The two most abundant components of the Universe have only been inferred by their gravitational action on cosmological scales. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

11 Introduction This situation is disturbing for two main reasons: The two most abundant components of the Universe have only been inferred by their gravitational action on cosmological scales. DM: galaxies / clusters / Hubble scale. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

12 Introduction This situation is disturbing for two main reasons: The two most abundant components of the Universe have only been inferred by their gravitational action on cosmological scales. DM: galaxies / clusters / Hubble scale. DE: Hubble scale. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

13 Introduction This situation is disturbing for two main reasons: The two most abundant components of the Universe have only been inferred by their gravitational action on cosmological scales. DM: galaxies / clusters / Hubble scale. DE: Hubble scale. Including particle physics into the picture, we realize that the cosmological constant is in no way distinguishable from vacuum energy which has not only also the form Tµν vac = ρ vac g µν, but it also couples only to gravity. Hence there is no experiment that can ever distinguish between a cosmological constant Λ and a vacuum energy density. ρ vac = Λ 8πG ( ev) 4 h 2. Estimates for ρ vac are by 60 (TeV susy) respectively 120 (Planck scale) orders of magnitude too large! Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

14 Introduction This situation is disturbing for two main reasons: The two most abundant components of the Universe have only been inferred by their gravitational action on cosmological scales. DM: galaxies / clusters / Hubble scale. DE: Hubble scale. Including particle physics into the picture, we realize that the cosmological constant is in no way distinguishable from vacuum energy which has not only also the form Tµν vac = ρ vac g µν, but it also couples only to gravity. Hence there is no experiment that can ever distinguish between a cosmological constant Λ and a vacuum energy density. ρ vac = Λ 8πG ( ev) 4 h 2. Estimates for ρ vac are by 60 (TeV susy) respectively 120 (Planck scale) orders of magnitude too large! Even though it cannot be a standard model particle, there are good DM candidates and there is hope to detect DM via non-gravitational interactions soon either at LHC or by direct DM searches. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

15 Supernovae lightcurve corrections Without correction. After correction, δm 0.2. Kim et al Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

16 Supernovae 1a Astronomical magnitudes are related to the luminosity distance by m(z 1 ) m(z 2 ) = 5 log 10 (D L (z 1 )/D L (z 2 )). Hence an error in the magnitude translates to an error in the luminosity distance via δd L (z) D L (z) = log(10) 5 δm(z) = 0.46δm(z). Or, an error of 0.2 in the magnitude corresponds to an error of nearly 10% in the luminosity distance. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

17 Supernovae 1a Astronomical magnitudes are related to the luminosity distance by m(z 1 ) m(z 2 ) = 5 log 10 (D L (z 1 )/D L (z 2 )). Hence an error in the magnitude translates to an error in the luminosity distance via δd L (z) D L (z) = log(10) 5 δm(z) = 0.46δm(z). Or, an error of 0.2 in the magnitude corresponds to an error of nearly 10% in the luminosity distance. If we assume that the geometry of the Universe is Friedmann Lemaître (FL), we can relate the luminosity distance to the energy content of the universe via the standard formula D L (z) = (1 + z)χ K R z 0 dz H(z ) where χ K (r) = 1 K sin(r K) and H(z) = H 0 p Ωm(1 + z) 3 + Ω K (1 + z) 2 + Ω r(1 + z) 4 + Ω DE (z) Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

18 Supernovae 1a The relative difference δd L /D L between the luminosity distance for the concordance model (Ω Λ,Ω m,ω K ) = (0.7, 0.3, 0) (red) or an open model (Ω Λ,Ω m,ω K ) = (0, 0, 1) (blue) and a pure CDM model, (Ω Λ,Ω m,ω K ) = (0, 1, 0). Seems to be well measurable with several supernovae distances at precision 0.1. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

19 Supernovae 1a 46 Union2 data-set µ µ -µ empty Λ-CDM Redshift Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

20 Baryon acoustic oscillations Another way to measure distances is to compare angles subtended by objects of a given size when placing them at different redshifts. For any metric theory, this angular diameter distance is simply related to the luminosity distance by D A = D L /(1 + z) 2. Baryon acoustic oscillations are the relics in the matter power spectrum of the oscillations in the baryon-photon plasma prior to decoupling. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

21 Baryon acoustic oscillations Another way to measure distances is to compare angles subtended by objects of a given size when placing them at different redshifts. For any metric theory, this angular diameter distance is simply related to the luminosity distance by D A = D L /(1 + z) 2. Baryon acoustic oscillations are the relics in the matter power spectrum of the oscillations in the baryon-photon plasma prior to decoupling. Transversal oscillations measure D A. Line of sight oscillations measure t(z) = z/h(z) = zd H /(z + 1), D H = (z + 1)/H(z). Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

22 Baryon acoustic oscillations Another way to measure distances is to compare angles subtended by objects of a given size when placing them at different redshifts. For any metric theory, this angular diameter distance is simply related to the luminosity distance by D A = D L /(1 + z) 2. Baryon acoustic oscillations are the relics in the matter power spectrum of the oscillations in the baryon-photon plasma prior to decoupling. Transversal oscillations measure D A. Line of sight oscillations measure t(z) = z/h(z) = zd H /(z + 1), D H = (z + 1)/H(z). With present data on large scale structure we have just measured the 3-dimensional power spectrum in different redshift bins. We cannot yet distinguish between transverse and longitudinal directions. This measures a (comoving) geometrical mean D V(z) = (D H (z)d A (z) 2 ) 1/3. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

23 Baryon acoustic oscillations BAO s for different redshift slices from SDSS, DR7. Percival et al. 09 Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

24 Baryon acoustic oscillations BAO s from different surveys. (Mehta et al., 2012) Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

25 CMB Our most precise cosmological measurements are the CMB observations which have determined the CMB anisotropies and polarization to high precision The CMB data is doubly precious since it is not only very accurate but also relatively simple to calculate in a perturbed FL universe. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

26 CMB Our most precise cosmological measurements are the CMB observations which have determined the CMB anisotropies and polarization to high precision The CMB data is doubly precious since it is not only very accurate but also relatively simple to calculate in a perturbed FL universe. The positions of the acoustic peaks, allow for a very precise determination of the distance to the last scattering surface. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

27 CMB If the distance to the last scattering surface is changed,, the CMB power spectrum, changes in a very simple way. A given scale L is seen under the angles θ = L/D A and θ = L/D A θ θ L D A D A Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

28 CMB The correlation functions for two CMB skies at distances D A and D A are related by C(r) = C (r ), where r = rd A /D A. In the flat sky approximation which is good for l > 20 this gives the following simple relation between the CMB power spectra C l = S 2 C Sl, S = D A D A Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

29 CMB The correlation functions for two CMB skies at distances D A and D A are related by C(r) = C (r ), where r = rd A /D A. In the flat sky approximation which is good for l > 20 this gives the following simple relation between the CMB power spectra C l = S 2 C Sl, S = D A D A Assuming that we do not know the distance D A and leaving S as a free parameter, we can fit the CMB data as well as in a ΛCDM model. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

30 CMB Apart from D A (z dec) the CMB determines ω m(z dec), ω b (z dec), and n s. We have fit the data with a scaled flat CDM model for l > l min 40 (Vonlanthen, Räsänen, RD 10) Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

31 CMB ω b ω b S l A R ω b ω c ω b ω c ω c ω c ω c S n s l A ω m ω c R n s ω b n s n s S l A Vonlanthen, Räsänen, RD n s R log[10 10 A s ] ω m S ω b ω m S ω m 0.15 ω m 0.15 ω m n l s A R Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

32 Large scale structure The power spectrum from SLOAN DR7 Reid et al What about relativistic corrections? Especially in what concerns the matter radiation equality scale hω m Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

33 Large scale structure Parameter constraints from SLOAN DR7 Reid et al Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

34 What do we know about dark energy? As we have seen: all our data which infers the existence of dark energy does so from measurements of the distance redshift relation, D A (z). Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

35 What do we know about dark energy? As we have seen: all our data which infers the existence of dark energy does so from measurements of the distance redshift relation, D A (z). Out to redshift z 1.5 this distance is about 40% larger than what we would expect in a flat matter dominated FL Universe and about 15% larger than what we would expect in an open FL Universe. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

36 What do we know about dark energy? As we have seen: all our data which infers the existence of dark energy does so from measurements of the distance redshift relation, D A (z). Out to redshift z 1.5 this distance is about 40% larger than what we would expect in a flat matter dominated FL Universe and about 15% larger than what we would expect in an open FL Universe. This is all. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

37 What do we know about dark energy? As we have seen: all our data which infers the existence of dark energy does so from measurements of the distance redshift relation, D A (z). Out to redshift z 1.5 this distance is about 40% larger than what we would expect in a flat matter dominated FL Universe and about 15% larger than what we would expect in an open FL Universe. This is all. Only once we insist that this distance should be computed using the FL formula do we conclude that there must be dark energy. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

38 What do we know about dark energy? As we have seen: all our data which infers the existence of dark energy does so from measurements of the distance redshift relation, D A (z). Out to redshift z 1.5 this distance is about 40% larger than what we would expect in a flat matter dominated FL Universe and about 15% larger than what we would expect in an open FL Universe. This is all. Only once we insist that this distance should be computed using the FL formula do we conclude that there must be dark energy. But is this so? On small scales matter is clustered and the photons which end up in our telescope go preferentially through empty or at least under-dense space. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

39 What do we know about dark energy? As we have seen: all our data which infers the existence of dark energy does so from measurements of the distance redshift relation, D A (z). Out to redshift z 1.5 this distance is about 40% larger than what we would expect in a flat matter dominated FL Universe and about 15% larger than what we would expect in an open FL Universe. This is all. Only once we insist that this distance should be computed using the FL formula do we conclude that there must be dark energy. But is this so? On small scales matter is clustered and the photons which end up in our telescope go preferentially through empty or at least under-dense space. Dyer & Roeder, 72 have argued that therefore the distance formula should be corrected to the one of an open universe. But as we have seen, this is not sufficient and actually Weinberg, 76 has shown that the shear term which is present if matter is clustered in the case of simple Schwarzschild clumps exactly corrects for the missing Ricci term and reproduces the FL universe formula. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

40 A clumpy Universe In a generic, clumpy spacetime the Sachs equation yields d 2 D A dv 2 = 1 2 ( σ 2 + R µνk µ k ν )D A Hence the presence of shear always leads to deceleration, like matter density. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

41 A clumpy Universe In a generic, clumpy spacetime the Sachs equation yields d 2 D A dv 2 = 1 2 ( σ 2 + R µνk µ k ν )D A Hence the presence of shear always leads to deceleration, like matter density. But the measured quantity is not D A (v) but D A (z) so we have to study how the redshift is affected by clumping due to the motion of observers. dz dv = u a;bk a k b Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

42 A clumpy Universe In a generic, clumpy spacetime the Sachs equation yields d 2 D A dv 2 = 1 2 ( σ 2 + R µνk µ k ν )D A Hence the presence of shear always leads to deceleration, like matter density. But the measured quantity is not D A (v) but D A (z) so we have to study how the redshift is affected by clumping due to the motion of observers. dz dv = u a;bk a k b If the expansion of matter (observers) is substantially reduced in a clumping universe this can reduce the redshift at fixed v and therefore lead to seemingly larger distance... (Wiltshire?) Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

43 A clumpy Universe In a generic, clumpy spacetime the Sachs equation yields d 2 D A dv 2 = 1 2 ( σ 2 + R µνk µ k ν )D A Hence the presence of shear always leads to deceleration, like matter density. But the measured quantity is not D A (v) but D A (z) so we have to study how the redshift is affected by clumping due to the motion of observers. dz dv = u a;bk a k b If the expansion of matter (observers) is substantially reduced in a clumping universe this can reduce the redshift at fixed v and therefore lead to seemingly larger distance... (Wiltshire?) But of course we need to study this quantitatively! Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

44 A clumpy Universe: walls Distance redshift in a universe with high density walls. (Di Dio, Vonlanthen & RD, 2011) Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

45 What can we know about dark energy? In order to decide whether dark energy is really a new component to the energy momentum tensor (or an infrared modification of GR) and not just a phantom due to the misinterpretation of distances, we have to find another observation to infer it. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

46 What can we know about dark energy? In order to decide whether dark energy is really a new component to the energy momentum tensor (or an infrared modification of GR) and not just a phantom due to the misinterpretation of distances, we have to find another observation to infer it. The growth of fluctuations γ (weak lensing,...). Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

47 What can we know about dark energy? In order to decide whether dark energy is really a new component to the energy momentum tensor (or an infrared modification of GR) and not just a phantom due to the misinterpretation of distances, we have to find another observation to infer it. The growth of fluctuations γ (weak lensing,...). Independent determination of H(z) and D A (z) (e.g. using the Alcock Paczynski test) which can then be used to check of the FL formula Z z «D A (z) = (1 + z) 1 dz χ K H(z ) 0 Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

48 What can we know about dark energy? In order to decide whether dark energy is really a new component to the energy momentum tensor (or an infrared modification of GR) and not just a phantom due to the misinterpretation of distances, we have to find another observation to infer it. The growth of fluctuations γ (weak lensing,...). Independent determination of H(z) and D A (z) (e.g. using the Alcock Paczynski test) which can then be used to check of the FL formula Z z «D A (z) = (1 + z) 1 dz χ K H(z ) 0 ISW, ISW LSS Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

49 What can we know about dark energy? In order to decide whether dark energy is really a new component to the energy momentum tensor (or an infrared modification of GR) and not just a phantom due to the misinterpretation of distances, we have to find another observation to infer it. The growth of fluctuations γ (weak lensing,...). Independent determination of H(z) and D A (z) (e.g. using the Alcock Paczynski test) which can then be used to check of the FL formula Z z «D A (z) = (1 + z) 1 dz χ K H(z ) 0 ISW, ISW LSS Peculiar velocities Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

50 What can we know about dark energy? The Alcock Paczynski test using the matter power spectrum: If the true D A (z) and H(z) differ from the ones adopted to generate the galaxy power spectrum, P(k, µ, z), the latter will depend on µ [(1 + z)d A (z)h(z)] 2. Problems: Need a fiducial cosmology to generate the power spectrum, P(k, µ). Have to subtract the much stronger redshift space distortions. Determinations of the function ȧ(z) = H(z)/(1+z) using the Alcock Paczynski test and SN distances to eliminate D A (z). (Blake et al., 2011) Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

51 Conclusions Distances always have been a big problem for observational cosmology. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

52 Conclusions Distances always have been a big problem for observational cosmology. More than 2000 years ago, an underestimation of distances already let the Greeks to reject Aristarchos heliocentric solar system due to the absence of parallaxes. Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25

53 Conclusions Distances always have been a big problem for observational cosmology. More than 2000 years ago, an underestimation of distances already let the Greeks to reject Aristarchos heliocentric solar system due to the absence of parallaxes. Might dark energy be yet another problem with distance measurements in cosmology? Ruth Durrer (Université de Genève ) Dark Energy ESTEC February / 25