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Modern Cosmology:Modern Cosmology:

the Legacy of Christian the Legacy of Christian DopplerDoppler

Sabino Matarrese

Dipartimento Di Fisica Galileo Galilei Universita’ degli Studi Di PadovaPadova, ITALY

Email: matarrese@pd.infn.It

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The standard cosmological The standard cosmological model model IIThe validity of the standard model of cosmology, based on

Einstein’s General Relativity, is confirmed by a number of fundamental observations like

The isotropic expansion of the Universe, as resulting from the measured redshift of distant galaxies discovered by E. Hubble in 1929.

The measured isotropy of the Cosmic Microwave Background (CMB) radiation, which is accurate up to T/T ~ 10-5, after subtracting the dipole anisotropy, T/T ~ 10-

3,, due to the Doppler effect from the peculiar motion of the Local Group of galaxies, at a speed of ~ 600 km/s w.r.t the comoving CMB frame.

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The standard cosmological The standard cosmological model model IIII

Doppler shift

blueshift

redshift

Consider a distant galaxy emitting f wave crests per second. Suppose the galaxy is moving away at speed v. The time between wave crests is 1/f, and the galaxy moves a distance v/f during this time. The observer measures wave crests separated not by 1/f but by 1/f (1+v/c), including the additional time for light to traverse the distance v/f. So the wavelength is increased by the fractional amount v/c; we define this to be the redshift z, i.e. z=v/c:

(obs –em)/em = z

The convention is to measure v away from the observer: a velocity of approach corresponds to negative v or to a blueshift (reduction in wavelength of emission). The redshifted frequency f is reduced:fobs= fem/(1+z) .

Credit: M. White

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The standard cosmological The standard cosmological model model IIIIII

In 1929 Edwin Hubble, studying the redshift of distant galaxies, discovered that the Universe is expanding, with galaxies moving away from each other at a velocity given by an expression known as the Hubble Law: v = H0 r

with v the galaxy recessional velocity, r its distance away from Earth, and H0 is a proportionality constant, called Hubble's constant (now accurately measured to be H0 70 km/s/Mpc).

[1 Mpc ~ 3 million light years 3 x km ]1910

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The standard cosmological The standard cosmological model model

The extraordinary success of the standard Hot Big Bang model has led theoretical cosmologists to speculate on its extrapolation back to the earliest epochs, when the Universe age was a tiny fraction of a second, corresponding to very high energies, thus representing a unique laboratory to test modern theories for the unification of fundamental interactions.

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Structure formation in the Structure formation in the CosmosCosmos

The seeds of structure formation in the Universe were generated in the early Universe, during an epoch of accelerated expansion named “inflation”. The CMB is a snapshot of the Universe at photon “last scattering”, which occurred just after hydrogen “recombination”.

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The Era of Precision The Era of Precision CosmologyCosmology II Very large datasets will soon become available in

Cosmology:

Large galaxy redshift surveys (2dF, SDSS) allow to study the Large-Scale Structure (LSS) of the Universe

Present and ongoing satellite missions like WMAP and Planck allow to measure the temperature anisotropy and polarization of the Cosmic Microwave Background (CMB) radiation with unprecedented precision

The SNAP satellite will collect redshifts for a large number of high-redshift type Ia Supernovae (SN)

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The Anglo-Australian Telescope allowed to obtain redshifts for ~250,000 galaxies selected from the APM catalogue

Observing the LSSObserving the LSS

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The 2dF galaxy redshift The 2dF galaxy redshift survey survey

The 2dFGRS contains about 250,000 galaxies for which angular positions and distances from the observer, in the form of redshift, are measured

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The SDSS survey will collect redshifts for ~ 1,000,000 galaxies. To date 200,000 redshifts have been

measured.

The Sloan Digital Sky SurveyThe Sloan Digital Sky Survey

SDSS observing site: Apache Point Observatory, Sacramento Mountains ( New Mexico)

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The Era ofThe Era of Precision Precision CosmologyCosmology IIII

Present (BOOMERanG, MAXIMA, WMAP) and forthcoming (Planck) satellite experi-ments allow to measure the temperature anisotropy and polarization of the Cosmic Microwave Background (CMB) radiation with high resolution and large or full sky coverage

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The CMB is an almost “perfect” blackbody with a mean

temperature T=2.726 0.005

K

The CMB as a perfect blackbodyThe CMB as a perfect blackbody

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The microwave sky as seen The microwave sky as seen byby WMAP (2003)WMAP (2003)

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The The Doppler peaksDoppler peaks in in CMBCMB temperature temperature anisotropiesanisotropies

Radiation pressure resists the fluid gravitational compression into potential wells and sets up acoustic oscillations in it. The shorter the wavelength of the potential fluctuation the faster the fluid oscillates such that the phase of the oscillation reached at last scattering scales with wavelength. Sites of compression (maxima) represent hot regions and rarefaction (minima) cold ones: there is a harmonic series of peaks in wavelength associated with acoustic oscillations. Their features provide us with an array of cosmological tests.

Acoustic oscillations of the baryon-photon fluid

Springs represent photon pressure and balls the effective mass of the fluid

Credits: W. Hu

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WMAP WMAP

The temperaturefluctuations can be expanded in spherical harmonics

Angular power-spectrum

of temperature anisotropies of WMAP data

W. Hu 2003

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CMB anisotropy dataCMB anisotropy data

The angular power-spectrum as determined by various experiments in recent years

W. Hu 2003

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The Planck Surveyorwhich will be launched in 2007 is an ESA satellite to measure the temperature anisotropy and polarization of theCMB with unprecedentedresolution

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Simulated maps of the CMB anisotropies expected in a CDM model. Upper picture: a simulated COBE map with a resolution of FWHM=7°. Lower panel: the same realization of the sky at the much higher angular resolution and signal-to-noise of PLANCK (Liguori, Matarrese & Moscardini 2003)

COBE

PLANCK

The basic scientific goal of the PLANCK mission is to measure the CMB anisotropies at all angular scales larger than 10 arcminutes, with an accuracy set by astrophysical limits.

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The Dark Matter distributionThe Dark Matter distribution

The dark matter component forms the LSS of the Universe. The ordinary baryonic material falls in the DM potential wells.

Jenkins et al. 1998

N-body Simulation by the Virgo Consortium

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The galaxy distributionThe galaxy distribution

Galaxies preferentially form at the density peaks of the underlying DM distribution, thus providing a generally “biased” picture of the matter distribution

Benson et al. 2001

N-body Simulation by the

Virgo Consortium

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Success of the Success of the “concordance” model“concordance” model

The predicted power- spectrum of density fluctuations of the Lambda Cold Dark Matter (CDM) or “concordance” model fits a variety of independent datasets spanning more than four decades in scale

CDM model

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The Era ofThe Era of Precision Precision CosmologyCosmology IIIIII

Type Ia Supernovae are being used as astronomical “standard candles” (their intrinsic luminosity being stable and well-known); their recent observation at redshifts z~1 by the High Z SN team and the Supernovae Cosmology Project changed our vision of the Universe: the magnitude-redshift relation

deceleration parameter

for these objects is only consistent with the Universe undergoing a phase of accelerated expansion (q0 < 0), which requires the existence of some unknown form of Dark Energy, whose negative pressure contrasts the attractive gravitational force by both the dark and ordinary baryonic matter.

)1(086.15525 00 qLogczLogHMm apparent magnitude absolute magnitude

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The SNAP (SuperNovae Acceleration Probe) satellite which will be launched by NASA is expected to detect 2,000 type Ia SN per year in the redshift range z < 1.7

High-redshift SN search

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Independent datasets give a consistent determination of the amount of Dark Energy and Dark Matter in the Universe. The relative weights being measured by their density parameter

_i = _i / _cr

where _cr 10 g/cm is

the critical density to close the Universe

The cosmic budget The cosmic budget II

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-29 -3

Credits: P. de Bernardis

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The cosmicThe cosmic budget budget IIII

Only about 5% of the cosmic energy budget is in the form of ordinary “baryonic” matter, out of which only a small fraction shines in the galaxies (quite likely most of the baryons reside in filaments forming the Warm- Hot Intergalactic Medium (WHIM), a sort of cosmic web connecting the galaxies and clusters of galaxies).

About 25% of the cosmic budget is made of Dark Matter, a collision-less component whose presence we only perceive gravitationally. The most likely candidates are hypothetical particles like neutralionos, axions, etc….

About 70% of the energy content of our Universe is in the form of some exotic component, called Dark Energy, also called “Quintessence”, which causes a large-scale cosmic repulsion among celestial objects, thereby mimicking a sort of anti-gravity effect.

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ConclusioConclusionsns

The Doppler effect, dating back to Christian Doppler studies in 1842, not only forms the basis for the standard Big Bang theory, according to which the Universe is isotropically expanding (as resulting from the measured redshifts of distant galaxies), but also underlies some fundamental recent discoveries in Cosmology:The existence of a Dark Matter component, which makes the LSS of the Universe.The discovery that the Universe is spatially flat and ever expanding, from the CMB Doppler peaks. The discovery that some exotic form of Dark Energy has recently started to dominate the Universe dynamics, leading to a phase of accelerated expansion.