On the Universe On the Universe Acceleration & Zeta Acceleration & Zeta

Function Function RegularizationRegularization

Prof. Dr. Emilio ElizaldeProf. Dr. Emilio ElizaldeNational Higher Research Council of Spain National Higher Research Council of Spain

Institut de Ciències de l’Espai (ICE/CSIC)Institut de Ciències de l’Espai (ICE/CSIC)Institut d’Estudis Espacials de Catalunya (IEEC)Institut d’Estudis Espacials de Catalunya (IEEC)

Campus Universitat Autònoma de Barcelona (UAB)Campus Universitat Autònoma de Barcelona (UAB)

Seminar KMI Nagoya, 16 FebSeminar KMI Nagoya, 16 Feb 2012 2012

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• But... But... the Universe was static !! (…and very small)the Universe was static !! (…and very small)

• What is What is λλ ? ? Non-physicalNon-physical

• At that time: At that time: UNIVERSE = MILKY WAY (+ nebulae)UNIVERSE = MILKY WAY (+ nebulae)

• PtolemyPtolemy 150 DC, 150 DC, Almagest:Almagest: mentions mentions 55 nebulae nebulae

• Persian, Arabic, Chinese Persian, Arabic, Chinese astronomers: astronomers: moremore nebulae nebulae

• Edmund Halley Edmund Halley 66 in 1715, in 1715, Charles Messier Charles Messier 103103 in in 17811781

WilliamWilliam and and Caroline Herschel Caroline Herschel 3 catalogs, 1786-1802, 3 catalogs, 1786-1802, a total of a total of 2510 2510 nebulaenebulae

• And then, And then, Edwin Hubble, Edwin Hubble, in 1922-1924, saw in 1922-1924, saw Andromeda nebulae (.8 Mly) was Andromeda nebulae (.8 Mly) was far beyond our Milky far beyond our Milky Way: Way: nebulae were nebulae were other galaxies!other galaxies!

• Henrietta S Leavitt Henrietta S Leavitt (Ed Pickering’s Harvard Harem), (Ed Pickering’s Harvard Harem), ‘12 ‘12 period-luminosity relationshipperiod-luminosity relationship of Cepheid of Cepheid variable stars (Eddington , Hevariable stars (Eddington , He+,+++,++) ) Hertzsprung-Hertzsprung-RussellRussell Diagramm Diagramm

Henrietta Leavitt

Ed Pickering’s Harvard Harem

… or Harvard Computers

1913

Mittag-LefflerNP proposal ‘26

• Karl Schwarzschild: Karl Schwarzschild: Black Hole solution (22 Dec 1915)Black Hole solution (22 Dec 1915)

• Willem de Sitter: Willem de Sitter: massless univer static sol (just cc,’17)massless univer static sol (just cc,’17)

• Alexander Friedmann: Alexander Friedmann: expanding universe sol (1922)expanding universe sol (1922)

• Georges Lemaître: Georges Lemaître: expanding universe (MIT 1925, AF expanding universe (MIT 1925, AF solution); visited solution); visited Vesto Slipher Vesto Slipher (Lowell Obs, Arizona, (Lowell Obs, Arizona, 1912 redshifts) and 1912 redshifts) and Edwin Edwin Hubble Hubble (Mount Wilson, (Mount Wilson, Pasadena); Pasadena); Keeler-Slipher-Campbell,Keeler-Slipher-Campbell, 1918 1918

• Led to Led to Big Bang theory Big Bang theory (Fred Hoyle,(Fred Hoyle, BBC radio 3 BBC radio 3rdrd Programme, 18:30 GMT, 28 March 1949)Programme, 18:30 GMT, 28 March 1949)

• Fred Hoyle, Thomas Gold, Hermann Bondi:Fred Hoyle, Thomas Gold, Hermann Bondi: SteadyState SteadyState ’48, “C-field” with a negative pressure, to be ’48, “C-field” with a negative pressure, to be consistent with energy conservation consistent with energy conservation (anticipated (anticipated inflation)inflation)

• Friedmann-Lemaître-Robertson-WalkerFriedmann-Lemaître-Robertson-Walker (FLRW 1931- (FLRW 1931-37)37)

• Dark matter: Dark matter: Fritz Zwicky Fritz Zwicky (1934) evidence of (1934) evidence of ‘missing ‘missing mass’mass’ in the orbital velocities of galaxies in clusters in the orbital velocities of galaxies in clusters

• Now lots of evidence: galactic rotation Now lots of evidence: galactic rotation curves (curves (Vera Vera Rubin, Kent FordRubin, Kent Ford, 1975), gravitational lensing, etc, 1975), gravitational lensing, etc

• Arno Penzias, Robert Wilson Arno Penzias, Robert Wilson (1964 Bell Labs, New (1964 Bell Labs, New Jersey); at Princeton (< 40 miles away) Jersey); at Princeton (< 40 miles away) Dicke, Dicke, Peebles, WilkinsonPeebles, Wilkinson writing paper on how CMB should writing paper on how CMB should be Burke (MIT) told Penzias of Peebles’ work: be Burke (MIT) told Penzias of Peebles’ work: and the Big Bang was there !and the Big Bang was there !

• Alan Guth Alan Guth ‘80,‘80,Katsuhiko Sato Katsuhiko Sato ‘81,‘81,Andrei LindeAndrei Linde: : inflationinflation Also: Also: A Albrecht, P Steinhardt, A Starobinsky A Albrecht, P Steinhardt, A Starobinsky. . And And Ya BYa B Zel’dovich, S Coleman Zel’dovich, S Coleman (decay of false (decay of false vacuum), …vacuum), …

• Quantum fluctuations + chaotic inflation Quantum fluctuations + chaotic inflation multiversemultiverse

• Hawking+TurokHawking+Turok instantoninstanton ’98 ’98 NoBoundary (NoBoundary (HHHH) vs chaotic inflation) vs chaotic inflation

• A Riess B SchmidtA Riess B Schmidt ’98, ’98, SS PerlmutterPerlmutter ’99: ’99: acceler acceler expan! expan! Dark Energy Dark Energy

Friedmann equation (matter,radiation,curvature)

Multiply by a2 to get

When a increases, each term on rhs decreases:the universe should be decelerating (a decreases)

.

a

tBig Bang Sean Carroll, CaltechSSI 2009

Two groups looked for the ‘deceleration’ of the universe expansion, using type Ia

supernovae as standardizable candles

SN 1994d

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

F(R) Modified Gravity RfRgxd

GSg

4

16

1

Cosmic Expansion Cosmic Structure Solar-System Test

Cosmological Tests 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

To summarize …To summarize …

•Astronomical ObservationsAstronomical Observations– Are not enoughAre not enough

•Scientific TheoriesScientific Theories– Are not enoughAre not enough

Observations + Theory Observations + Theory Understanding the Understanding the

Universe !Universe !

Thank You Thank You

ArigatoArigato