Dark Energy and the Copernican Principle

Transcription

1 Dark Energy and the Copernican Principle Chris Clarkson University of Cape Town with Bruce Bassett & Teresa Hui-Ching Lu [arxiv: ] and George Ellis & Jean-Phillipe Uzan [arxiv: PRL, to appear] [see also JCAP08(2007)011; arxiv:astro-ph/ ; arxiv: ]

2 Dark Energy Evidence evidence of cosmological constant from COBE + age constraints independent confirmation from SNIa all observations consistent with cosmological constant and zero curvature but we don t know what cosmological constant is... astro-ph/

3 Evolving Dark Energy? if acceleration isn t cosmological constant: dark energy - quintessence, k-essence... modified gravity - gr wrong on Hubble scales inhomogeneous universe - copernican assumption wrong evidence for acceleration between 12σ - 5σ - 1.8σ assuming FLRW... [Seikel & Schwarz] or 0σ if not...

4 Key assumptions smooth universe - averaging issues homogeneous & isotropic model cosmological & Copernican principles

5 Key assumptions smooth universe - averaging issues homogeneous & isotropic model cosmological & Copernican principles The Cosmological Principle

6 Key assumptions smooth universe - averaging issues homogeneous & isotropic model cosmological & Copernican principles The Cosmological Principle is a preponderance of evidence the same as proof beyond reasonable doubt?

7 Problems? homogeneity assumed - observations consistent with homogeneity, but: need dark energy for it to work acceleration starts same time as formation of solar-system - coincidence? we re near massive structures at least 10% of the Hubble scale (sloan great wall [>400Mpc!], Shapely supercluster, etc). how does this affect the local Hubble rate? not clear... averaging/backreaction implies between 2% - 10% [Li & Schwarz; Rasanen...] or maybe (?) >100% [Kolb, Materrese et al]

8 Problems? homogeneity assumed - observations consistent with homogeneity, but: need dark energy for it to work acceleration starts same time as formation of solar-system - coincidence? we re near massive structures at least 10% of the Hubble scale (sloan great wall [>400Mpc!], Shapely supercluster, etc). how does this affect the local Hubble rate? not clear... averaging/backreaction implies between 2% - 10% [Li & Schwarz; Rasanen...] or maybe (?) >100% [Kolb, Materrese et al]

9 Problems? homogeneity assumed - observations consistent with homogeneity, but: need dark energy for it to work acceleration starts same time as formation of solar-system - coincidence? we re near massive structures at least 10% of the Hubble scale (sloan great wall [>400Mpc!], Shapely supercluster, etc). how does this affect the local Hubble rate? not clear... averaging/backreaction implies between 2% - 10% [Li & Schwarz; Rasanen...] or maybe (?) >100% [Kolb, Materrese et al]

10 Copernican & Cosmological Principles Copernican P says we are not at special place in universe Λ introduced for misguided temporal CP... Cosmological P says universe homogeneous plus perfect (spatial) isotropy about us => FLRW homogeneous + anisotropic models ruled out (roughly) from CMB Copernican P + isotropy of CMB => conformally stationary spacetime add comoving dust => FLRW... but: assumes comoving barotropic DE [Ehlers Geren & Sachs 1968] [Clarkson et al]

11 Copernican & Cosmological Principles isotropy about us leaves one other option: we are at the center of symmetry statistically unlikely of course... should we bother to test it?

12 Copernican & Cosmological Principles isotropy about us leaves one other option: we are at the center of symmetry statistically unlikely of course... should we bother to test it? 16 February 1995 PHYSICS LETTERS B Physics Letters B 345 ( 1995) Do we live in the center of the world? Andrei Linde av1, Dmitri Linde b,2, Arthur Mezhlumian c*3 a Department of Physics, Stanford Universiq, Stanford, CA , b California Institute of Technology, Pasadena, CA USA c Department of Physics, Stanford University, Stanford, CA , Received 28 November 1994 Editor: M. Dine USA USA Abstract We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of the volume of the universe in a state with a given density p at any given moment of time r in synchronous coordinates is concentrated near the centers of deep exponentially wide spherically symmetric holes in the density distribution.

13 Copernican & Cosmological Principles isotropy about us leaves one other option: we are at the center of symmetry statistically unlikely of course... should we bother to test it? 16 February 1995 PHYSICS LETTERS B Physics Letters B 345 ( 1995) Do we live in the center of the world? does chaotic Andrei inflation/the Linde av1, Dmitri Linde landscape b,2, Arthur Mezhlumian mean c*3 anything is Abstract a Department of Physics, Stanford Universiq, Stanford, CA , b California Institute of Technology, Pasadena, CA USA possible in universes? c Department of Physics, Stanford University, Stanford, CA , Received 28 November 1994 Editor: M. Dine what measure would make central observer unlikely? [is being at special place worse than special time?] We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of the volume of the universe in a state with a given density p at any given moment of time r in synchronous coordinates is concentrated near the centers of deep exponentially wide spherically symmetric holes in the density distribution. must then be observationally determined USA USA

14 Spherical Symmetry within dust Lemaitre-Tolman-Bondi models - 2 free radial dof can fit distance-redshift data to any FLRW DE model Mustapha, Bassett, Hellaby, & Ellis

15 Spherical Symmetry within dust Lemaitre-Tolman-Bondi models - 2 free radial dof can fit distance-redshift data to any FLRW DE model Mustapha, Bassett, Hellaby, & Ellis Alnes, Amarzguioui, and Gron astro-ph/

16 Spherical Symmetry within dust Lemaitre-Tolman-Bondi models - 2 free radial dof can fit distance-redshift data to any FLRW DE model Mustapha, Bassett, Hellaby, & Ellis Biswas, Monsouri and Notari, astro-ph/

17 Spherical Symmetry within dust Lemaitre-Tolman-Bondi models - 2 free radial dof 46 can fit distance-redshift 44 data to any FLRW DE model m-m LCDM model Szekeres best fit model SN data set used by Davis et al Mustapha, Bassett, Hellaby, & Ellis z Ishak et al Biswas, Monsouri and Notari, astro-ph/

18 Spherical Symmetry within dust Lemaitre-Tolman-Bondi models - 2 free radial dof can fit distance-redshift data to any FLRW DE model Mustapha, Bassett, Hellaby, & Ellis given that we can always find d A [F LRW, w(z)] = d A [LT B, dust] can we distinguish between the two?

19 Model Building one way to test CP is to build up detailed alternative models 2 free functions in LTB makes modeling hard - how are these chosen? CMB & perturbation theory hard... so is structure formation unlikely to be favored in Bayesian study, even if it was better fit [unless we enforce a prior of no strange matter...] do we really need to do all this? can we test CP directly?

20 Smoking Gun Tests some signatures could be obvious - eg loops in distance-redshift curves only known direct tests use scattered CMB photons - looking inside past null cone [Goodman; Caldwell & Stebbins] if CMB very anisotropic around distant observers, SZ scattered photons have distorted spectrum but model dependent - good for void models but misses, e.g., conformally stationary spacetimes ideally we need a model-independent forensic test... is FLRW the correct metric?

21 Smoking Gun Tests some signatures could be obvious - eg loops in distance-redshift curves only known direct tests use scattered CMB photons - looking inside past null cone 0.25 d L (z) [Goodman; Caldwell & Stebbins] if CMB very anisotropic around distant observers, SZ scattered photons have distorted spectrum 0.15 but model dependent - good 0.1 for void models but misses, e.g., conformally stationary spacetimes 0.05 ideally we need a model-independent 0 forensic test... is FLRW the correct metric? z

22 Smoking Gun Tests some signatures could be obvious - eg loops in distance-redshift curves only known direct tests use scattered CMB photons - looking inside past null cone [Goodman; Caldwell & Stebbins] if CMB very anisotropic around distant observers, SZ scattered photons have distorted spectrum but model dependent - good for void models but misses, e.g., conformally stationary spacetimes ideally we need a model-independent forensic test... is FLRW the correct metric?

23 Measuring Curvature in FLRW in FLRW we can combine Hubble rate and distance data to find curvature d L (z) = ( Ωk z Ω k = [H(z)D (z)] 2 1 c(1 + z) sin H [H 0 D(z)] 2 0 Ωk 0 [ ) dz H 0 H(z ) d L = (1 + z)d = (1 + z) 2 d A ] independent of all other cosmological parameters, including dark energy model, and theory of gravity can be used at single redshift what else can we learn from this? [see Clarkson Cortes & Bassett JCAP08(2007)011; arxiv:astro-ph/ ]

24 Measuring Curvature in FLRW in FLRW we can combine Hubble rate and distance data to find curvature Ω k = [H(z)D (z)] 2 1 [H 0 D(z)] 2 [ d L = (1 + z)d = (1 + z) 2 d A ] independent of all other cosmological parameters, including dark energy model, and theory of gravity can be used at single redshift what else can we learn from this? [see Clarkson Cortes & Bassett JCAP08(2007)011; arxiv:astro-ph/ ]

25 Measuring Curvature in FLRW in FLRW we can combine Hubble rate and distance data to find curvature Ω k = [H(z)D (z)] 2 1 [H 0 D(z)] 2 [ d L = (1 + z)d = (1 + z) 2 d A ] independent of all other cosmological parameters, including dark energy model, and theory of gravity can be used at single redshift what else can we learn from this? [see Clarkson Cortes & Bassett JCAP08(2007)011; arxiv:astro-ph/ ]

26 Consistency Test in FLRW since Ω k independent of z we can differentiate to get consistency relation C (z) = 1 + H 2 ( DD D 2) + HH DD = 0 depends only on FLRW geometry: independent of curvature, dark energy, theory of gravity consistency test for homogeneity and isotropy should expect C (z) 10 5 in FLRW

27 Testing the Copernican Assumption Copernican assumption hard to test... but in non-flrw even at center of symmetry C (z) 0 two free functions in LTB (even for dust) - H(z) & D(z) FLRW has just H(z) - or w(z) [ignoring inflaton] FLRW unlikely to be wrong, but since we re a bit confused... can also be used to find correct FLRW scale - cf averaging problem

28 Testing the Copernican Assumption Errors may be estimated from a series expansion deceleration parameter measured from distance measurements deceleration parameter measured from Hubble measurements simplest to measure H(z) from BAO [already a 2-sigma discrepancy...?] [Percival et al] time drift of redshifts over many years gives [in FLRW] [Uzan Clarkson & Ellis] or relative ages of passively evolving galaxies (eg, LRGs) gives [Jimemez & Loeb] can t use inverted distance data as it assumes FLRW

29 Testing the Copernican Assumption Errors may be estimated from a series expansion deceleration parameter measured from distance measurements deceleration parameter measured from Hubble measurements simplest to measure H(z) from BAO [already a 2-sigma discrepancy...?] [Percival et al] time drift of redshifts over many years gives [in FLRW] [Uzan Clarkson & Ellis] or relative ages of passively evolving galaxies (eg, LRGs) gives [Jimemez & Loeb] can t use inverted distance data as it assumes FLRW

30 It s only as difficult as dark energy... measuring w(z) from Hubble uses requires H (z) w(z) = 1 3 Ω k H 2 0 (1 + z) 2 + 2(1 + z)hh 3H 2 H 2 0 (1 + z)2 [Ω m (1 + z) + Ω k ] H 2 [see Clarkson Cortes & Bassett JCAP08(2007)011; arxiv:astro-ph/ ] and from distances requires second derivatives D (z) D L = (H 0 /c)d L w(z) = 2 { (1 + z) 3 [(1 + z)d L D [Ω k DL 2 + (1 + z) 2 ]D L 1 } L] 2 (Ω kd L 2 + 1)[(1 + z)d L D L ] / { (1 + z)[ωm (1 + z) + Ω k ]D L 2 2[Ω m (1 + z) + Ω k ]D L D L + Ω m DL 2 (1 + z) } simplest to begin with

31 Conclusions maybe dark energy is telling us something even stranger than we thought? Copernican assumption must be tested observationally we have presented a new model independent method to test the Copernican assumption much easier (& cheaper!) than fully understanding inhomogeneous cosmologies... should be only as difficult as w(z): can be implemented for free