1. The Cosmological Distance Ladder - to redshift 1000 Michael Rowan-Robinson Imperial College

2. Feb 8th 2008RAS Presidential Address First steps on the distance ladder Aristotle (384-322 BC) - estimated the size of the earth - estimated the size of the earth (+ Eratosthenes, Poseidonius, 10%) Hipparcos (2 nd C BC) - estimated distance of the moon - estimated distance of the moon (59 R E, cf modern value 60.3) Aristotle, by Raphael

3. Feb 8th 2008RAS Presidential Address The Copernican revolution Copernicus (1473-1543) - gave the correct relative distances of the sun and planets (to 5%) - gave the correct relative distances of the sun and planets (to 5%) - absolute value not - absolute value not determined accurately till the 19 th century

4. Feb 8th 2008RAS Presidential Address The first steps outside the solar system Bessel 1838 - discovered parallax of nearby star 61 Cyg, its change in - discovered parallax of nearby star 61 Cyg, its change in apparent direction on the sky due to the earth’s orbit round the sun (the final proof of the Copernican system)

5. Feb 8th 2008RAS Presidential Address The key modern distance indicator – Cepheid variable stars Delta Cephei is the prototype of the Cepheid variable stars, massive stars which pulsate and vary their light output

6. Feb 8th 2008RAS Presidential Address Henrietta Leavitt’s breakthrough In 1912, Henrietta Leavitt, working at the Harvard Observatory, discovered from her studies of Cepheids in the Small Magellanic Cloud that the period of Cepheid variability was related to their lumininosity

7. Feb 8th 2008RAS Presidential Address The distances of the galaxies In 1924 Edwin Hubble used Leavitt’s discovery to estimate the distance of the Andromeda Nebula. It clearly lay far outside The Milky Way system The Milky Way system.

8. Feb 8th 2008RAS Presidential Address The expansion of the universe Three years later, in 1927, he announced, based on distances to 18 galaxies, that the more distant a galaxy, the faster it is moving away from us velocity/distance = constant, H o (the Hubble law) This is just what would be expected in an expanding universe. The Russian mathematician Alexandr Friedmann had shown (1922, 1924) that expanding universe models are what would be expected according to Einstein’s General Theory of Relativity, if the universe is (a)homogeneous (everyone sees the same picture) and (b)isotropic (the same in every direction).

9. Feb 8th 2008RAS Presidential Address The history of the Hubble constant Hubble’s estimate of the H o, the Hubble constant, was 500 km/s/Mpc, which gave an age for the universe of only 2 billion years. This was soon shown to be shorter than the age of the earth. From 1927 to 2001 the value of the Hubble constant was a matter of fierce controversy. Sandage 1958 >

10. Feb 8th 2008RAS Presidential Address The cosmological distance ladder This was my 1985 summary of the summary of the cosmological cosmological distance ladder distance ladder

11. Feb 8th 2008RAS Presidential Address The cosmological distance ladder In my monograph ‘The Cosmological Distance Ladder’ (Freeman 1985), I set out to understand the competing estimates of H o (50 - Sandage and Tammann, 100 - de Vaucouleurs), and to reconcile the systematic differences in distance estimates from different methods. With an objective weighting scheme based on quoted errors, and with higher weight for purely geometrical distance methods, I concluded that there were systematic errors in the supernova method (too high distances) and in the Tully-Fisher and HII region methods (too low) and that best overall value for H 0 was H o = 67 +_ 12 km/s/Mpc

12. Feb 8th 2008RAS Presidential Address Implications of the Hubble constant H o is (velocity/distance) so has the dimensions of (1/time). 1/H o is the expansion age of the universe (how old the Universe would be if no forces acting) = 15.3 billion yrs For simplest model universe with only gravity acting, age of universe would be 10.2 billion years (gravity slows expansion)

13. Feb 8th 2008RAS Presidential Address The age of the universe We can use the colours and brightnesses of the stars in globular clusters to estimate the age of our Galaxy ~ 12 billion years ~ 12 billion years Long-lived radioactive isotopes give a similar answer Allowing time for our Galaxy to form, the age of the universe is ~ 13 billion years ~ 13 billion years Already a problem for  = 0 ?

14. Feb 8th 2008RAS Presidential Address The Hubble Space Telescope Key Program Following the first HST servicing mission, which fixed the telescope aberration, a large amount of HST observing time was dedicated to measuring Cepheids in distant galaxies, to try to measure the Hubble constant accurately, and to give the different distance methods a secure and consistent calibration. The Key Program soon split into two teams, one led by Wendy Freedman, Jeremy Mould and Rob Kennicutt, the other by Allan Sandage and Gustav Tammann.

15. Feb 8th 2008RAS Presidential Address Some of the galaxies studied by HST

16. Feb 8th 2008RAS Presidential Address HST Key Project strategy Kennicutt et al 1995

17. Feb 8th 2008RAS Presidential Address The HST Key program final result (1) log V H o = 72 +- 8 km/s/Mpc (Freedman et al 2001)

18. Feb 8th 2008RAS Presidential Address Any room for doubt ? There is good consistency between the HST Key Program value of H o and the age of the universe, provided we invoke Einstein’s Cosmological Constant,  (dark energy) There is good consistency between the HST Key Program value of H o and the age of the universe, provided we invoke Einstein’s Cosmological Constant,  (dark energy) n Uncertainties in H o are (1) distance of Large Magellanic Cloud, (2) the adopted Cepheid calibration, (3) corrections for dust extinction, (4) corrections for metallicity effects, (5) corrections for local flow n Using the Freedman et al data, my own best estimates for these corrections, and the weighting scheme of CDL 1985, I concluded: H o = 63 +- 6 (Rowan-Robinson 2000, astro-ph/0012026)

19. Feb 8th 2008RAS Presidential Address Distance of LMC  o = 18.5+-0.1  o = 18.5+-0.1 (d = 50 kpc, +-10%) - a fundamental limitation of local estimates of H o perhaps Gaia will resolve this

20. Feb 8th 2008RAS Presidential Address Type Ia supernova In 1998 two teams announced that using Type Ia supernovae as standard candles implied that  > 0 (Schmidt et al 1998, Garnevich et al 1998, Riess et al 1998, Perlmutter et al 1999) In 1998 two teams announced that using Type Ia supernovae as standard candles implied that  > 0 (Schmidt et al 1998, Garnevich et al 1998, Riess et al 1998, Perlmutter et al 1999) n There were issues with (1) treatment of extinction by dust, (2) consistency of treatment of correlation of decline rate with luminosity (Liebundgut 2001, Rowan-Robinson 2002). I also raised two other issues: (3) inconsistencies with earlier supernova data, (4) inappropriate use of supernovae not observed before maximum n Joint HST Key Project and SN team found H o = 68 +- 5 (Gibson et al 1999)

21. Feb 8th 2008RAS Presidential Address supernova issues supernova issues n data is clearly excellent, but this is not a geometric distance method n new HST-ACS observations of Cepheids in galaxies with well- observed Type Ia supernovae gives H o = 73 +- 6 (Riess et al 2005) - but based on LMC, with 10% distance uncertainty n inconsistencies with earlier results can be attributed to photographic data n issue of luminosity-decline rate relation addressed by Jha et al (2007) (see also new approach by Wang et al 2005, Nobili et al 2005) n still some unresolved inconsistencies in derivation of extinction (can only be resolved by use of more photometric bands)

22. Feb 8th 2008RAS Presidential Address supernovae 2007 supernovae 2007 n Latest data from Riess et al (2007) - clear support for consensus  model (cf also Astier et al 2005, SN Legacy Survey)

23. Feb 8th 2008RAS Presidential Address consensus ? consensus ? n HST key program found H o = 72 +- 8 (Freedman et al 2001) n WMAP (year 1) found H o = 72 +- 5 (Spergel et al 2003) (year 3) H o = 73 +- 3 (Spergel et al 2007) n new HST-ACS observations of Cepheids in galaxies with well- observed Type Ia supernovae gives H o = 73 +- 6 (Riess et al 2005) so have consensus for H 0 =73,  m =0.25,   =0.75, age of universe 13.7 billion years ? so have consensus for H 0 =73,  m =0.25,   =0.75, age of universe 13.7 billion years ?

24. Feb 8th 2008RAS Presidential Address History of the universe

25. Feb 8th 2008RAS Presidential Address The HST Key program final result (2) new study of Cepheid P-L new study of Cepheid P-L relation (Tammann et al 2003) relation (Tammann et al 2003) difference between P-L difference between P-L relation in Galaxy and LMC relation in Galaxy and LMC (Sandage et al 2005) new calibration using new calibration using Baade-Wesselink method (so no LMC distance error) new discussion of new discussion of extinction in supernovae extinction in supernovae H o = 62 +- 5 km/s/Mpc (Sandage et al 2007) Hubble diagram for 62 supernovae

26. Feb 8th 2008RAS Presidential Address other work on H o Feast review (2007, ‘From IRAS to Herschel/Planck’): new HST Cepheid distances (Benedict et al 2007) new HST Cepheid distances (Benedict et al 2007) revised Hipparcos parallaxes (van Leeuwen et al 2007) revised Hipparcos parallaxes (van Leeuwen et al 2007) - revise Sandage’s H o to 69.6 NGC4258 Cepheids (Macri et al 2006), consistency with maser distance NGC4258 Cepheids (Macri et al 2006), consistency with maser distance gravitational lens time delay: 68+- 10 (Oguri 2007) gravitational lens time delay: 68+- 10 (Oguri 2007) 72+-10 (Saha et al 2006) 72+-10 (Saha et al 2006) Sunyaev-Zeldovich method for clusters: Sunyaev-Zeldovich method for clusters: 66+-14 (Jones et al 2005) 66+-14 (Jones et al 2005) 76+-10 (Bonamente et al 05) 76+-10 (Bonamente et al 05)

27. Feb 8th 2008RAS Presidential Address CMB fluctuations and H o CMB fluctuations and H o n Boomerang and Maxima, for flat universe, H 0 = 75+-10 (Jaffe et al 2001) n WMAP first year results: 72 +- 5 (Spergel et al 2003) n include also SLOAN large-scale structure data: 68 +- 10 (Tegmark et al 2004) 68 +- 10 (Tegmark et al 2004) n include Sloan large-scale structure + baryonic acoustic oscillation data: 65 +- 4.5 (Eisenstein et al 2005), n WMAP 3-year results: 73 +- 3 (Spergel et al 2007) with LSS, BAO 69-72

28. Feb 8th 2008RAS Presidential Address Primordial density spectrum power-law assumption show that with power-law spectrum, but no restriction to flat models, can get wide range of fits just to WMAP3 Spergel et al (2004) show that with power-law spectrum, but no restriction to flat models, can get wide range of fits just to WMAP3 CMB data can see that priors on H o or assumption of flatness force us towards   = 0.75 consensus model can see that priors on H o or assumption of flatness force us towards   = 0.75 consensus model n however dropping assumption of power-law opens up possibilities even further (Blanchard et al 2003)

29. Feb 8th 2008RAS Presidential Address Blanchard et al (2003) model Blanchard et al (2003) showed that if we relax the assumption of a power-law primordial density spectrum (to a broken power-law) we can fit the CMB fluctuation spectrum just as well as the consensus model with a  =0,  0 =1 (Einstein de Sitter) model, provided H o = 46 can get consistency with large-scale structure data if  ~ 0.2 (mixed dark matter) can get consistency with large-scale structure data if  ~ 0.2 (mixed dark matter) however, inconsistent with supernova data and H 0 =46 is 3-  from the direct estimates however, inconsistent with supernova data and H 0 =46 is 3-  from the direct estimates Shafieloo and Souradeep (2007) deconvolve primordial density spectrum from CMB fluctuations and show Shafieloo and Souradeep (2007) deconvolve primordial density spectrum from CMB fluctuations and show  =0,  0 =1, H 0 =50, model is actually better fit than consensus model

30. Feb 8th 2008RAS Presidential Address galaxy baryon acoustic peak n SDSS (Eistenstein et al 2005) and 2dFGRS (Cole et al 2005) have claimed to detect baryon acoustic oscillation (BAO) peak on scale ~ 150 Mpc in the galaxy correlation function Blanchard et al (2006) admit this is fatal for their  =0 model, if confirmed Blanchard et al (2006) admit this is fatal for their  =0 model, if confirmed n BAO plus CMB first Doppler peak is the ultimate geometrical measurement of H o

31. Feb 8th 2008RAS Presidential Address angular diameter distance test courtesy: Paniez Paykari

32. Feb 8th 2008RAS Presidential Address some formulae  r ph = R(t dec )  ph (radius of particle horizon at decoupling)  ph = A 1/2 ∫ 0 1/Zdec {  0 x +  r +   x 4-3(1+w) + (1-  0 -  r -   )x 2 } -1/2 dx A = |(1-  0 -  r -   )| if k=+1,-1, A = |(1-  0 -  r -   )| if k=+1,-1, = 1 if k= 0 = 1 if k= 0 z dec ~ 1100, w =-1 z dec ~ 1100, w =-1 radius of acoustic horizon radius of acoustic horizon r acoust = r ph /{3(1+3  b /4  )}1/2 = r ph /{3(1+1.25(  b h 2 )/(  0 h 2 )}1/2 r acoust = r ph /{3(1+3  b /4  )}1/2 = r ph /{3(1+1.25(  b h 2 )/(  0 h 2 )}1/2  b h 2 ~ 0.022 (Doppler peak ratios+nucleosynthesis)  b h 2 ~ 0.022 (Doppler peak ratios+nucleosynthesis) angular radius of first Doppler peak angular radius of first Doppler peak  Doppler = r acoust /D diam (z dec )  Doppler = r acoust /D diam (z dec ) angular radius of baryon acoustic peak angular radius of baryon acoustic peak  BAO ~ 150 (  0 h 2 /0.25x0.73 2 ) -0.0853 Mpc/D diam (z)  BAO ~ 150 (  0 h 2 /0.25x0.73 2 ) -0.0853 Mpc/D diam (z) diameter distance diameter distance D diam (z) = c  0 r o (z)/(A 1/2 (1+z)) D diam (z) = c  0 r o (z)/(A 1/2 (1+z)) c  0 = 9.8 h -1 Gyr c  0 = 9.8 h -1 Gyr r o (z) = sin  (z) for k = +1, =  (z) for k = 0, = sinh  (z) for k =-1 r o (z) = sin  (z) for k = +1, =  (z) for k = 0, = sinh  (z) for k =-1  (z) = A 1/2 ∫ 1 1/(1+z) {  0 x +  r +   x 4-3(1+w) + (1-  0 -  r -   )x 2 } -1/2 dx  (z) = A 1/2 ∫ 1 1/(1+z) {  0 x +  r +   x 4-3(1+w) + (1-  0 -  r -   )x 2 } -1/2 dx

33. Feb 8th 2008RAS Presidential Address to z = 1100 n black curve: zero curvature n solid curves: first Doppler peak for H o = 73 (blue), 65 (red), 48 (green) n dotted curves: baryon acoustic peak for same 3 cases n C: consensus model n E: Einstein de Sitter

34. Feb 8th 2008RAS Presidential Address conclusions n local direct estimates of H 0 = 62-72 +- 10% CMB estimates = 65-73 +- 4% (generally assuming flat universe, power-law spectrum, negligible , w=-1) CMB estimates = 65-73 +- 4% (generally assuming flat universe, power-law spectrum, negligible , w=-1) n baryonic acoustic peak plus CMB first Doppler peak is the ultimate geometrical measurement of H o n precision measurements of H 0 (say to 1%) could tell us that we need new physics beyond Standard Model. * accurate distance to LMC (Gaia) * Baade-Wesselink methods for Cepheids and supernovae, * multi- photometry to control extinction and metallicity