SN and Transients Workshop 2012 THCA SNIa and Cosmology Charling TAO
Today’s mysterious Dark Universe ! We know with % precision that we do not know much about the Universe ! What we know is only 4% of the energy density of the Universe Graph source: Wikipedia Definition:W=r/rc (rc=10-29 g/cm3)
Cosmological Density Parameters Definition:W=r/rc (rc=10-29 g/cm3) ~ 0.92 h702 10-26 kg/m3 5.16 h702 109 eV/c2 /m3
大爆炸宇宙学 Big Bang cosmology: 3 pillars Cosmological Principle: 宇宙学原理 Universe homogenous and isotrtopic Observations 宇宙学观测 General Relativity 广义相对论 ?
Cosmological principle • Homogeneous and isotropic Universe (at large scales) • Copernic principle • No privileged space • No privileged direction • Earth, or Sun are not in the center!!!! -The Universe is the same as seen from any point -The same laws of physics apply everywhere A long time for human societies to accept this!
Homogeneous non isotropic Isotropic non homogeneous Universe isotropy and homogeneity Ned Wright Cosmology tutorial Simulation of galaxies
Great Wall North Wall High redshift « surveys » reveal large scale structures in the Universe South Wall Best proof of Universe homogeneity Observations of CMB (Cosmic Microwave Background): photon relic from primordial Universe (back to that later)
Heaven (Religion) Chinese Cosmogony The Anthropocosmic Unity:Heaven, Earth, and Man Earth (Cosmology) Man (Ethics) Panggu Myth The Development and Decline of Chinese Cosmology John Henderson (1984)
Physical Cosmology started with Greek philosophers Raphaël : Athens school 1511 Plato Aristotle Democritos, Leukippos Parmenides Pythagoras Heraclites Euclid
IInd century : Ptolemy’s Almagest Earth is at the center of the Universe Nonetheless a Physical Cosmology Universum C. Flammarion, gravure sur bois, Paris 1888, Coloris : Heikenwaelder Hugo, Wien 1998. Equant Epicycles
Copernician revolution: The Universe is not static ! Observations of SN • 1572 (Tycho Brahe), 1604 (Kepler) • visible during the day
An evolving Universe time Particle physics explains the early evolution of the Universe Us today Lynn Cominsky
大爆炸宇宙学 Big Bang cosmology: 3 pillars Cosmological Principle: 宇宙学原理 Universe homogenous and isotrtopic General Relativity 广义相对论 Observations 宇宙学观测 BB nucleosynthesis
Galileo ( 1564-1642) “Father of modern observational astronomy, modern physics, Modern Science." Observational astronomy Kinematics: motion of uniformly accelerated objects "Eppur si muove" And yet it moves Earth/Sun controversy It is not yet decided (and I believe it will always remain so for human science) that the Universe is finite or infinite The laws of nature are mathematical Dialogue on the great systems in the world(1632)
Large telescopes 1948 : 48-inch Schmidt telescpe on Mt Palomar (-Hubble) 1917 : 100-inch Hooker telescope at Mount Wilson Andromeda is a Galaxy 2 Million light years First Palomar Observatory Sky Survey, maps the entire northern sky.
Slipher, Hubble, Humason (1929): Most galaxies in the Universe show RedshiftedSpectra!!!!!
- observed rest z = rest Redshift Definition redshift z Universe is expanding Shifts to red z = [(1+ v/c)/(1- v/c)]1/2 – 1 ~ v/c -1
Velocity (km/s) SNIa (1996) Author ? Distance(Mpc) Today H0 ~71 +/- 2.5 km/s/Mpc Hubble constant Parameter (1 Mpc= 3.086 1022 m) An expanding Universe Velocity (km/s) Hubble (1929) Distance(Mpc) v = H0D Lemaitre Parameter?
Komatsu, E., et.al., 2011, ApJS, 192, 18 Position 1st peak WT CMB : WMAP 7 years Ratio (2/1) peak Wb
Cf Wikipedia Edwin Powell Hubble November 20, 1889 – September 28, 1953 American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way. Hubble's law: the loss in frequency—the redshift—observed in the spectra of light from other galaxies increase in proportion to the galaxy distance from Earth. (Lemaitre) Hubble doubted the Doppler shift interpretation of the observed redshift that had been proposed earlier by Vesto Slipher, whose data he used, and that led to the theory of the metric expansion of space. He tended to believe the frequency of any beam of light could, by some so far unknown means, be diminished ever stronger, the longer the beam travels through space.
Georges Lemaître Cf Wikipedia 17 July 1894 – 20 June 1966 Belgian priest, astronomer. He was the first person to propose the theory of the expansion of the Universe, widely (mis?)attributed to Edwin Hubble. He was also the first to derive what is now known as the Hubble's law and made the first estimation of what is now called the Hubble constant which he published in 1927, two years before Hubble's article. Lemaître also proposed what became known as the Big Bang theory of the origin of the Universe, which he called his 'hypothesis of the primeval atom'. On Lemaitre/Hubble discovery controversy : 1105.6271, 1106.1195, 1106.3928, 1107.228,1107.0442,1107.5695
Big Bang cosmology 大爆炸宇宙学 Cosmological Principle: 宇宙学原理 Universe homogenous and isotrtopic Observations 宇宙学观测 General Relativity 广义相对论 ?
Relativity and Cosmology General Relativity: Einstein’s equation Geometry of space-time islinked to energymomentum distribution • At large scale, the Universe is homogeneous and isotropic • Cosmological Principle Basic element in cosmology : Galaxy
1915 General Relativity and curved space time • Gravitation ( 引 力) is not a force! • Space is not always flat • Mass (or energy) curves space-time • There is no absolute time in GR. • Different observers measure different times between events. Lecture Notes Sean Caroll http://pancake.uchicago.edu/~caroll/notes/
Postulates of GR • An uniform gravitational field like the one close to Earth is equivalent to an uniform acceleration • A person cannot make the difference between • - gravity effects on Earth • - an elevator accelerating at 9.81 m/s2
Einstein’s Equations Encodes distribution of matter in space-time Encodes geometry of space-time Marcel Grossman and Michele Besso introduced Albert Einstein to multiple algebra and tensors. Ricci Tensor R-1/2 g(R-) = 8 G T Curvature defined by a metric (distance function between elements of a set)
From Einstein to Friedmann’s Equations Principle of equivalence Uniform gravitation <=> acceleration • Metric of Friedmann-Lemaitre-Robertson-Walker (FLRW metric) ds2= c2dt2 - (dx2+dy2+dz2) = c2dt2 - a2(t) [dr2/(1- kr2) + r2 d2+r2sin2 d2] (k=-1,0,1 : curvature ) a(t) =scale factor = R(t)/ R0 • Tensor algebra Reduction of Einstein equations to 2 Friedmann equations Most general solution to Einstein’s equations include a cosmological constant 宇宙学常数 .
Scale factor a(t) • a(t) proportional to distances between galaxies D(t) = Dx a(t) Parameter describing the Universe expansion Reduced scale factor = a0arbitrary constant, usually == 1 for t=t0 today not to confuse with t=0 !
A one dimensional derivation of the Hubble/Lemaitre law a(t) is scale factor Dx = comoving coordinate Hubble parameter =
Friedmann’s equations (cosmological constant included) This set of 2 equations is called the Friedmann’s equations, describe the evolution of the Universe associated with the Friedmann Robertson Walker metric.
Cosmology 1970: a measurement of 2 parameters Sandage, Allan, “Cosmology: A Search for Two Numbers,” Physics Today 23, 34-41 (1970). a(t) a priori unknown Limited expansion a(t) = a0 ( 1 + H0t -1/2 q0 (H0t)2 + … ) A. Sandage: Annu. Rev. Astron. Astrophys. 1988. 26: 561-630 http://nedwww.ipac.caltech.edu/level5/Sept01/Sandage/Sand_contents.html
Hubble law Friedmann’s equation
Deceleration parameter Mass terms slow down the expansion Expected deceleration for a Matter dominated Universe a(t) = a0 ( 1 + H0t -1/2 q0 (H0t)2 + … )
Surprise 1998:An accelerating Universe! 2 collaborations SN SCP +HST q0 negative
Distance measurements are difficult Distance scales
Cosmology: Measuring distances with standard candles Cosmology: additional a(t) scale factor D(t) = a(t) D(t0) a(t) = a0(1+ H0t -1/2 q0 (H0t)2 + …) H0 = Hubble parameter measures the expansion rate of the Universe H0= ( a/a)0 = 100 h km/s/Mpc , h= 0.72 +/- 0.05 (?) q0 = deceleration parameter A Universe with only matter is expected to decelerate .
Luminosity distance with standard candles z = redshift a(t)=a0 /(1+z) 1stterm: Hubble law (z~v/c) 2nd term: deceleration ? SNIa
Supernovae type Ia Best known « standard » candles Red giant White dwarf Chandrasekhar mass 1.4 MO SNIa : 2 stars accretion (a white dwarf +…) Chandrasekhar mass 1.4 MO
Discovery: Two cameras (one wide field) 1.2 m ground based telescopes: NEAT/QUEST Lightcurve follow-up with YALO Photo-spectro follow-up with Field IntegralSpectrometre(SNIFS) at UH 2.2m telescope (Hawaii) SN for cosmologyeg SNLS, SNFactory
SN Ia are not exact standard candles! The light of SNIa explosions can be followed up for several weeks with telescopes magnitude SNIa Light curves
Different standardisation methodscf N. Chotard Standardisation to Dm =0.2 Before:mB After, eg, stretch correction: mBcor = mB – a (s-1) stretch (SCP), MLC2k2 (HiZ), Dm15, .. WangXiaofeng : DC12 + other new ideas, to test on real data
SNIa and Cosmology 1998 SURPRISE: Indication for negative deceleration parameter q0 Acceleration!!! But only 2s effect! B magnitude at maximum W = r(t)/rc(t) = WM+ WL • = 1- Wk L = L/3H02 q0= 1/2 WM- WL < 0 Hubble diagram Redshift z
Determination of cosmological parameters with SNIa • Fit Hubble diagramme • Many software available, eg Kosmoshow (Andre Tilquin) . Introduction to statistical data analysis (cf Andre Tilquin)
Current Supernova Surveys “Concordance” M ~ 0.3 ~ 0.7 Science Goals: cosmology rates physics CfA,CSP,LOSS,SNF,, PTF, Skymapper... SDSS ESSENCE,SNLS Higher-Z
Latest results SNLS3 + other SNIa Existence of L: > 10 s (combination of probes) Conley et al. Jan 2011
Universe with matter, , and curvature 0 = m,0 + ,0 George Lemaître (1894-1966) and Albert Einstein in Pasadena 1933
Cosmological Constant R-1/2 g(R-) = 8 G T The most general form of Einstein’s equations has a constant, a priori arbitrary