Transcript Fundamental equations - uni
COSMOLOGY AS A TOOL FOR PARTICLE PHYSICS
Roberto Trotta University of Oxford Astrophysics & Royal Astronomical Society
Vol. 302, 12/2003
«Cosmos Sits for Early Portrait, Gives Up Secrets »
Feb. 12 th , 2003
Outline
Towards precision cosmology Neutrino properties from high quality cosmological observations Conclusions & Outlook
Cosmological observables
10 -32 s 3 mins Gravitational waves Cosmic Neutrino Background BBN 300’000 yrs Cosmic Microwave Background 1 Gyr Large Scale Structures Lensing Ly systems Clusters counts 13 Gyrs Supernovae Type Ia GRB’s Sunyaev Zel’dovich
The Cosmic Microwave Background
Temperature fluctuation on the 2-sphere: 2-point correlation function: Temperature power spectrum
Cosmology with the CMB
The statistical distribution of temperature anisotropies described by the 2-point angular correlation function, or equivalently by the angular power spectrum For Gaussian fluctuations (as predicted by inflation), the power spectrum contains the full statistical information.
1st peak position (WMAP) Small fluctuations ) linear perturbation theory sufficient.
The power spectrum carries characteristic signatures of interesting physical quantities: • baryon density • angular diameter distance ( “curvature” ) • matter-to-relativistic energy ratio • damping scale (diffusion length)
Cosmological Params (May 05)
Combining CMB + SDSS + HST + SNIa Degeneracy breaking crucial
Flatness Non-Gaussianity Non-adiabaticity Scale invariance Gravity waves ?
Inflationary paradigm
tot = 1.02 § 0.02
Bayesian evidence 18 : 1 -58 < f nl < 134 inflation curvaton
» »
10 -5 1 Planck (2007) > 5 isocurvature < 33% Bayesian evidence > 1000 : 1 in favor of adiabatic pert’ons n s = 0.95 § 0.03
Planck (2007): 90% chance of disproving scale invariance with high evidence r 10 < 0.35
E inf < 10 -5 M pl B-polarization smoking gun !
Direct detection: LIGO, Virgo, LISA
The hidden assumptions
Assumptions about initial fluctuations crucial for precision cosmology BBN b
»
0.022
HST 0.72
§ 0.08
RT, Riazuelo & Durrer (2001) RT & Durrer (2004) Beltran et al (2004) Polarization saves the day Pre-WMAP (2001), but still qualitatively the case Precision cosmology: < 2% error on most parameters
Exploring the cosmic neutrino background
What good is cosmology?
Impact of (light) neutrinos on cosmological observables: log r Background: relativistic energy drives expansion early on Clustering / structure formation: free stream properties (mass/viscosity/couplings) Initial conditions: isocurvature (entropy) perturbations r rad ~ a - 4 time r mat ~ a - 3 r L = const radiation dominated matter dominated lambda dominated log a
Massless families
Matter/radiation equality affected CERN, 1991: N = 2.994 § 0.012 WMAP+ : 2.4 < N BBN : 2.8 < N < 3.2
< 6.8 (2 )
While relativistic, neutrinos free-stream out of fluctuations
Neutrino masses
Structure washed out below scales k nr » (m ) 1/2 ( m h 2 ) 1/2 Mass hierarchy: m 12 2 » 8 x 10 -5 eV 2 m 23 2 » 2.6 x 10 -3 eV 2 Absolute mass: Tritium decay m e < 2.3 eV (95% cl) Cosmology : m < O(1) eV Hu, Eisenstein & Tegmark 1998
Detecting the CNB
Viscosity parameter c vis 2 : controls the free-streaming behaviour c vis 2 = 1/3 : radiative viscosity free streaming c vis 2 = 0 : perfect fluid no anisotropic stress (eg, CDM coupling) acoustic oscillations Hu 1998 RT & Melchiorri 2004
Positive evidence for a CNB
Assuming N = 3 CMB alone CMB+SDSS CMB+SDSS CMB alone +BBN CMB + SLOAN c vis 2 = 0 clearly disfavored (about 2 ) Bayesian model comparison: c vis 2 = 1/3 favored with odds 2:1 RT & Melchiorri 2004
Automatic Occam’s razor
Model comparison tools to assess the need for new parameters CNB 0 RT 2005 n s : scale invariance : flatness f iso : adiabaticity
Prospects for precision cosmology
Almost orthogonal degeneracies Polarization lifts flat directions in Temperature Constraints improve significantly Temperature alone Polarization alone Many polarization-dedicated experiments upcoming (2005-07): POLARBEAR (2005): 100 < ell < 1400 QUEST (2005): 100 < ell < 1000 Bicep (2005): 10 < ell < 1000 SPOrt (ISS, 2005?): full sky Planck (2007): up to ell = 2000
Conclusions and Outlook
Cosmology is a data-driven field with much more to come Moving on from parameter fitting to model testing and model selection Combination of data-sets allows cross-validation and checks of systematics Subtle physics of the Concordance Model and beyond being stringently tested. Expect advances on neutrinos, dark energy/matter, brane-worlds, cosmic strings, topology, axis of evil (?) Watch out for: correlations between observations, high quality polarization data, lensing, GW