1. On the Universe Acceleration & Zeta Function Regularization Prof. Dr. Emilio Elizalde National Higher Research Council of Spain Institut de Ciències de l’Espai (ICE/CSIC) Institut d’Estudis Espacials de Catalunya (IEEC) Campus Universitat Autònoma de Barcelona (UAB) Seminar KMI Nagoya, 16 Feb 2012

3. But... the Universe was static !! (…and very small) But... the Universe was static !! (…and very small) What is λ ? Non-physical What is λ ? Non-physical At that time: UNIVERSE = MILKY WAY (+ nebulae) At that time: UNIVERSE = MILKY WAY (+ nebulae) Ptolemy 150 DC, Almagest: mentions 5 nebulae Ptolemy 150 DC, Almagest: mentions 5 nebulae Persian, Arabic, Chinese astronomers: more nebulae Persian, Arabic, Chinese astronomers: more nebulae Edmund Halley 6 in 1715, Charles Messier 103 in 1781 Edmund Halley 6 in 1715, Charles Messier 103 in 1781 William and Caroline Herschel 3 catalogs, 1786-1802, a total of 2510 nebulae William and Caroline Herschel 3 catalogs, 1786-1802, a total of 2510 nebulae And then, Edwin Hubble, in 1922-1924, saw Andromeda nebulae (.8 Mly) was far beyond our Milky Way: nebulae were other galaxies! And then, Edwin Hubble, in 1922-1924, saw Andromeda nebulae (.8 Mly) was far beyond our Milky Way: nebulae were other galaxies! Henrietta S Leavitt (Ed Pickering’s Harvard Harem), ‘12 period-luminosity relationship of Cepheid variable stars (Eddington, He +,++ ) Hertzsprung-Russell Diagramm Henrietta S Leavitt (Ed Pickering’s Harvard Harem), ‘12 period-luminosity relationship of Cepheid variable stars (Eddington, He +,++ ) Hertzsprung-Russell Diagramm

4. Henrietta Leavitt Ed Pickering’s Harvard Harem … or Harvard Computers 1913 Mittag-Leffler NP proposal ‘26

8. Karl Schwarzschild: Black Hole solution (22 Dec 1915) Karl Schwarzschild: Black Hole solution (22 Dec 1915) Willem de Sitter: massless univer static sol (just cc,’17) Willem de Sitter: massless univer static sol (just cc,’17) Alexander Friedmann: expanding universe sol (1922) Alexander Friedmann: expanding universe sol (1922) Georges Lemaître: expanding universe (MIT 1925, AF solution); visited Vesto Slipher (Lowell Obs, Arizona, 1912 redshifts) and Edwin Hubble (Mount Wilson, Pasadena); Keeler-Slipher-Campbell, 1918 Georges Lemaître: expanding universe (MIT 1925, AF solution); visited Vesto Slipher (Lowell Obs, Arizona, 1912 redshifts) and Edwin Hubble (Mount Wilson, Pasadena); Keeler-Slipher-Campbell, 1918 Led to Big Bang theory (Fred Hoyle, BBC radio 3 rd Programme, 18:30 GMT, 28 March 1949) Led to Big Bang theory (Fred Hoyle, BBC radio 3 rd Programme, 18:30 GMT, 28 March 1949) Fred Hoyle, Thomas Gold, Hermann Bondi: SteadyState ’48, “C-field” with a negative pressure, to be consistent with energy conservation (anticipated inflation) Fred Hoyle, Thomas Gold, Hermann Bondi: SteadyState ’48, “C-field” with a negative pressure, to be consistent with energy conservation (anticipated inflation) Friedmann-Lemaître-Robertson-Walker (FLRW 1931-37) Friedmann-Lemaître-Robertson-Walker (FLRW 1931-37) Dark matter: Fritz Zwicky (1934) evidence of ‘missing mass’ in the orbital velocities of galaxies in clusters Dark matter: Fritz Zwicky (1934) evidence of ‘missing mass’ in the orbital velocities of galaxies in clusters

9. Now lots of evidence: galactic rotation curves (Vera Rubin, Kent Ford, 1975), gravitational lensing, etc Now lots of evidence: galactic rotation curves (Vera Rubin, Kent Ford, 1975), gravitational lensing, etc Arno Penzias, Robert Wilson (1964 Bell Labs, New Jersey); at Princeton (< 40 miles away) Dicke, Peebles, Wilkinson writing paper on how CMB should be Burke (MIT) told Penzias of Peebles’ work: and the Big Bang was there ! Arno Penzias, Robert Wilson (1964 Bell Labs, New Jersey); at Princeton (< 40 miles away) Dicke, Peebles, Wilkinson writing paper on how CMB should be Burke (MIT) told Penzias of Peebles’ work: and the Big Bang was there ! Alan Guth ‘80,Katsuhiko Sato ‘81,Andrei Linde: inflation Also: A Albrecht, P Steinhardt, A Starobinsky. And Ya B Zel’dovich, S Coleman (decay of false vacuum), … Alan Guth ‘80,Katsuhiko Sato ‘81,Andrei Linde: inflation Also: A Albrecht, P Steinhardt, A Starobinsky. And Ya B Zel’dovich, S Coleman (decay of false vacuum), … Quantum fluctuations + chaotic inflation  multiverse Quantum fluctuations + chaotic inflation  multiverse Hawking+Turok instanton ’98 NoBoundary (HH) vs chaotic inflation Hawking+Turok instanton ’98 NoBoundary (HH) vs chaotic inflation A Riess B Schmidt ’98, S Perlmutter ’99: acceler expan!  Dark Energy A Riess B Schmidt ’98, S Perlmutter ’99: acceler expan!  Dark Energy

22. Friedmann equation (matter,radiation,curvature) Multiply by a 2 to get When a increases, each term on rhs decreases: the universe should be decelerating (a decreases). a t Big Bang Sean Carroll, Caltech SSI 2009

23. Two groups looked for the ‘deceleration’ of the universe expansion, using type Ia supernovae as standardizable candles SN 1994d

24. Result: supernovae are dimmer than expected The universe is not decelerating It is accelerating Cannot be explained by matter+radiation (see before) Riess, Schmidt et al. ‘98 Perlmutter et al. ‘99

25. F(R) Modified Gravity Cosmic Expansion Cosmic Structure Solar-System Test Cosmological Tes ts Local Tests as demanded by obs cosmology, needs to pass Goals as a theory of modified gravity, needs to pass Explain cosmic acceleration Model (parametrize) deviations from GR Je-An Gu 顧哲安 arXiv:1009.3488

26. To summarize … Astronomical Observations Astronomical Observations –Are not enough Scientific Theories Scientific Theories –Are not enough Observations + Theory  Understanding the Universe ! Understanding the Universe !

27. Thank You Arigato