Licia Verde ICREA & ICC-UB-IEEC CERN Theory Division http://icc.ub.edu/~liciaverde
AIMS and GOALS Observational cosmology has been evolving very rapidly over the past few years Theoretical cosmology is older and well established My aim is to bring you up to date and give you enough information that you will be able to go to a colloquium (not specialized seminar) in the area of cosmology and understand it I will not be complete and sometime not rigorous and I will often skip the maths. There are very good books out there (see course web page). My goal is to transmit what is not usually in the books. Lectures and additional material will appear at http://icc.ub.edu/~liciaverde/cfcosmo.html
Cosmology Program: Introduction, Hubble law, Freedman-Robertson Walker metric Dark matter and large-scale cosmological structure, clustering Cosmic microwave background Large-scale structure Inflation and dark energy The standard cosmological model The successes of cosmology over the past 10 years or so Outlook for the future Lectures and additional material will appear at http://icc.ub.edu/~liciaverde/cfcosmo.html
Cosmology Cosmos= Universe, Order, beauty -logy= study Greek! Study of the Universe as a whole Aim at getting an understanding of: -its origin -its structure and composition (where do galaxies, stars, planets, people come from?) -its evolution -its fate In general for cosmologists galaxies are points.
What to expect Concepts are mind-bending but maths are simple Quick learning curve: a first year graduate student or a good undergraduate can do new work worth of publication
Scales involved! 3d19Km 1d18Km 1.2d4Km 40AU=6d9Km
New units of measure For distance, we use pc, Kpc & Mpc For comparison, mean Earth-Sun distance (Astronomical Unit): " Cosmologists often express masses " in units of the solar mass:
Looking far away is looking back in time! 8 minutes ago 28000 years ago Cosmic archeology We are here Andromeda, M31 2.2 million years ago 3 billion years ago Looking far away in space= looking back in time
Hubble deep field
Not only pretty pictures Nature is written in the mathematical language (Galileo) The laws of physics are the same in the entire Universe The universe is comprehensible (by us) Need physics and maths (physical cosmology) Deep links to fundamental physics
MOTIVATION Cosmology over the past 15 years has made the transition to precision cosmology Cosmology has moved from a data-starved science to a data-driven science Cosmology has now a standard model. The standard cosmological model only needs few parameters to describe origin composition and evolution of the Universe Big difference between modeling and understanding
Motivation: Why should you care about observational cosmology?
Deep connections between cosmology and fundamental physics
Testing fundamental physics by looking up at the sky is not new The interplay between astrophysics and fundamental physics has already produced spectacular findings (e.g. the solar neutrino problem) Cosmology has entered the precision era very recently Cosmological data can be used to test fundamental physics Dark matter 4 Areas Neutrinos Inflation Dark energy
Fundamental assumptions Physics as we know it can describe the Universe On the largest scales the driving force is gravity (forget about gastrophysics ) General Relativity rules! (for many applications you can be Newtonian) Homogeneity and isotropy on large scales FLRW metric Thee possible global geometries only
Some assumptions The Universe is homogeneous and isotropic on large scales
Supported by observations The universe is isotropic it looks the same in every direction HDF-North HDF-South
The universe is homogeneous each volume is about like every other volume Large volumes of the sky in different directions, 100 s of Mpc in size, look about the same.
The smooth Universe: content Gives the global geometry/curvature
The standard cosmological model: parameters Different type of parameters { Parameters that govern the The smooth global geometry of space-time Universe Parameters that govern the expansion rate GR geometry, fate of Universe, content (but not much details) Inhomogeneous Universe { Parameters that characterize inhomogeneities Statistically speaking: clustering, galaxies etc Parameterizing our ignorance { Derived parameters Beyond the minimal model: extra parameters test: which is which?
Content: Baryons: stars HST image of stars being born, but it has no direct use for Cosmology; exploding stars (supernovae) are very useful (you ll see later on) By the way, we are star-dust
galaxies M31 the Andromeda Galaxy LMC SMC
galaxies
galaxies
galaxies Collections of ~10 11~ 10 12 Stars nearly spherical halo of "dark matter" Schematic of the Milky Way globular clusters of ~10 6 old stars contains ~10 11 stars bulge flattened, about 6 Kpc by 1 Kpc disk, about 0.3 kpc thick and 12.5 kpc in radius
The local group Entering the regime of cosmology.
groups
Groups and clusters
Distribution of local galaxies
Hubble deep field
Expanding Universe
On step back: Distances are difficult: velocities are easy Thank you Edwin Hubble
REDSHIFT or In relativity: For small velocity or
Hubble s Law 1912-1920s: Vesto Slipher finds most galaxies are redshifted nebulae
Hubble s Law cz = v = H d 0 Ho=74.2 +- 3.8 km/s/mpc Hubble 1929 (PNAS vol 15)
Aside: the great debate (1920) http://antwrp.gsfc.nasa.gov/htmltest/gifcity/cs_nrc.html Harlow Shapley Herber Curtis 1924: Hubble closes the Shapley-Curtis debate Galaxy Universe & Hubble classified galaxies
The many uses of Hubble LAW Determine distances (caveats ) The universe is expanding ( is it? Into what?)
Is the expansion of the Universe surprising? Einstein s view of Newton s considerations. How bright would the night sky be if the distribution of stars was infinite? Olbers paradox: (1826 but from 1576)
Olbers paradox How bright would the night sky be if the distribution of stars was infinite? Flux from a star Intensity of radiation form a shell of stars per sterradiant r dr Density, for simplicity assume constant If the Universe is infinite: Olbers: but the night sky is actually dark! Woops!
Solutions to Olber s Paradox - The brightness of stars goes down as 1/r 2. - BUT The number of stars goes UP by r 2! - Dust clouds obscure the light from distant stars/ galaxies. - BUT Those clouds would heat up and we would see THEM! Something has to GIVE: Either the Universe is not INFINITE OR the Universe is not STATIC. EINSTEIN believed in the STATIC Universe: - cosmological constant - uniform distribution of galaxies - UNSTABLE
The universe had a beginning! The extremely successful BIG BANG theory!
The scale factor a time r(t)=r(t 0 ) a(t) Comoving coordinates!.. v 12 =dr 12 /dt=a r 12 (t 0 )=a/a r 12 (t) Looks like Hubble law H= a. a Important!
How old is the Universe? t 0 =r/v=r/(h 0 r)=1/h 0 Hubble time Remember Olbers? Hubble radius c/h 0 Also called Hubble horizon Exercise: compute numerical values for H 0 =70km/s/Mpc.
Another interpretation (historical interest only) The steady state Universe (Fred Hoyle) Infinitely old;infinitely big;constant density Expanding (Hubble s Law) CONTINUOUS MATTER CREATION Exercise (for the end of this unit): how did I get this number?
The importance of the Cosmological Principle The isotropic and homogeneous nature of the universe are often spoken of together as the cosmological principle. Basically, it says that the universe is more or less the same everywhere, and it looks more or less the same from any location. Two consequences: there is no preferred location (i.e., a center) in the universe; and our own Milky Way (and Sun and ) is not in any particularly special place.
Geometry
Geometry & Metrics α+β+γ=π flat ds 2 =dr 2 +r 2 dθ 2 Area of triangle α+β+γ=π-α/r 2 ds 2 =dr 2 +R 2 sinh 2 (r/r)dθ 2 Negatively curved dr R α+β+γ=π+α/r 2 Positively curved Finite area, max separation ds 2 =dr 2 +R 2 sin 2 (r/r)dθ 2
In 3D and in general dθ 2 ---> dθ 2 + sin 2 θdφ 2 =dω 2 R ds 2 =dr 2 +S k 2 dω 2 k may be taken to belong to the set { 1,0,+1}# Changing coordinate system x=s k (r):
Freedman-Robertson Walker metric In 4 dimensions and introducing back the scale factor x k x x c 2 If k=0 Minkowski OR Comoving coords again! t is COSMIC TIME: time seen by an observer who sees the universe expanding uniformly Knowing a(t),k, and R 0 is all you need!
Compute distances: At fixed time spatial geodesic (angles are fixed) ds=a(t)dr Proper distance: Hubble law again:
Redshift, again Photons travel along null geodesics t only r only t e The next crest r t o Should remind you of z If an object has z=3, what was the size of the Universe?
How do we measure the geometry then? K=+1--> finite size: circumference In the past even smaller If????? Angular size of objects If I happen to know dl. Standard ruler, angular diameter distance brightness Standard candle Ah! Ah! ah!
Key concepts The expansion of the Universe Hubble s Law Redshift Olbers paradox Geometry FRW metric