Massive Neutrinos and the Cosmos

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Massive Neutrinos and the Cosmos

• Neutrinos
• Neutrino Mass
• Neutrinos in Cosmology
• Results
• The Future

Scott Dodelson University of Kansas December 1,
2003
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Radioctivity discovered 1900
Heavy atom decays to lighter atom, emitting
electron.
Why is the spectrum continuous? Why is electron
energy not equal to difference between two atomic
energies?
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Pauli's letter of the 4th of December 1930 Dear
Radioactive Ladies and Gentlemen, I have hit
upon a desperate remedy to save the law of
conservation of energy. Namely, the possibility
that there could exist in the nuclei electrically
neutral particles, that I wish to call neutrons,
which have spin 1/2 and obey the exclusion
principle and which further differ from light
quanta in that they do not travel with the
velocity of light. The mass of the neutrons
should be of the same order of magnitude as the
electron mass and in any event not larger than
0.01 proton masses. The continuous beta spectrum
would then become understandable by the
assumption that in beta decay a neutron is
emitted in addition to the electron such that the
sum of the energies of the neutron and the
electron is constant... I agree that my remedy
could seem incredible because one should have
seen those neutrons very earlier if they really
exist. But only the one who dare can win and the
difficult situation, due to the continuous
structure of the beta spectrum, is lighted by a
remark of my honoured predecessor, Mr Debye,
"Oh, It's well better not to think to this at
all, like new taxes". From now on, every solution
to the issue must be discussed. Thus, dear
radioactive people, look and judge.
Unfortunately, I cannot appear in Tubingen
personally since I am indispensable here in
Zurich because of a ball on the night of 6/7
December.
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Amended picture of beta decay
Courtesy University of Oregon
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After heavy neutrons were discovered
At Solvay conference in Bruxelles, in October
1933, Pauli says, speaking about his particles
"... their mass can not be very much more than
the electron mass. In order to distinguish them
from heavy neutrons, mister Fermi has proposed to
name them "neutrinos". It is possible that the
proper mass of neutrinos be zero...
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Origin of neutrino mass

• Can have masses like electrons, quarks (via
  coupling to Higgs boson). But why are n masses so
  small (at least a million times smaller than
  electrons)?
• See-Saw Mechanism Explanation of small masses
  and hint of physics at high energy scales.

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Mainz
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Direct measurementsmnlt2.2 eV
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There are 3 types of neutrinos

• Corresponding to 3 families of quarks, electrons
• Electron, muon, and tau neutrinos
• These are not necessarily mass eigenstates one
  species can oscillate into another

Only if masses are non-zero
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Note probability depends only on mass squared
difference.
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Two Obvious Sources of neutrinos Sun Cosmic
Rays hitting the atmosphere
Bahcall
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Solar Neutrinos
Bahcall
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The Cl neutrino detector is a tank containing
100,000 gallons of perchloroethylene in the
cavity 4,850 feet below ground in the Homestake
Mine in Lead, S.D. Ray Davis, Jr., principal
scientist of the Cl experiment, is leaning on the
catwalk above the tank. Courtesy of the
Brookhaven National Laboratory (circa 1967)
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Observe fewer (electron) neutrinos than are
produced in Sun
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The SNO experiment detects the missing neutrinos
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Results post-SNO
Solar
Solar Kamland
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Atmospheric neutrinos
Fewer muon neutrinos seen than expected,
consistent with oscillations to tau neutrinos
Fukuda et al. 1998
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Muon and Tau neutrino are maximally mixed
Mass difference squared larger than solar
neutrino difference evidence for at least two
non-zero neutrino masses
Fukuda et al. 1998
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Degenerate m1m2m3
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Neutrinos are also produced in the early universe
Alpher, Herman, Gamow 1953

• Neutrinos interact very weakly need high
  temperatures/energies
• Early on, the universe was much hotter, so, e.g.

occurred frequently
Expect about as many neutrinos in the universe
today as photons (100 cm3 )
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50 eV mass n would dominate the energy density in
the Universe

• There is non-baryonic dark matter in the universe
  (i.e., something beyond the standard model)
• Simplest extension which gives dark matter is
  neutrino mass
• But

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Massive Neutrinos affect large scale structure
Bond, Efstathiou, Silk 1980, Melott 1982 Bond
Szalay 1983 White, Frenk Davis 1983
Shandarin, Dorshkevich, Zeldovich 1983

• We know the neutrino abundance in the universe
• Neutrinos stream out of overdense regions when kT
  1 eV.
• Less clustering in universe with massive
  neutrinos

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Cold Dark Matter (no neutrino mass)
If neutrinos are important, they smooth out the
distribution no small scale structure
Colombi, Dodelson, Widrow 1995
Hot Cold Dark Matter (non-zero neutrino mass)
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Musical Acoustics

• Middle C
• Middle C on a piano

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Quantitative Measure Power Spectrum
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Probes of the Power Spectrum

• Galaxy distribution
• Lyman alpha forest
• Weak Lensing

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Sloan Digital Sky Survey

• 2.5 meter telescope in Apache Point, New Mexico
• Collaboration of Fermilab, Princeton, U.
  Chicago, U.Washington, Johns Hopkins, New Mexico
  State, Max Planck, Japan, Pittsburgh,
• Scheduled to end in 2005 may be extended until
  2007 will cover ¼ of the sky

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Two surveys in one

• Photometric survey hundreds of millions of
  objects in 5 bands
• Spectroscopic survey 1 million objects with
  spectra
• Spectroscopic survey targets objects found in
  photometric survey. Reduces systematic effects
  (typically objects targeted for redshifts are
  found in different survey, leads to complicated
  selection function).

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5 Filters very efficient
Ultimately will get redshifts for 750,000
galaxies 100,000 QSOs
I and z bands especially important for high
redshift QSOs. Lyman alpha line (1215Ang)
redshifted to 1215(1z) Ang. Can get zgt6 QSOs.
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Galaxy Power Spectrum

• Brighter galaxies are more clustered than faint
  galaxies.
• Brighter galaxies are seen from furthest away
  (smallest k)
• Blind averaging leads to luminosity bias

Tegmark et al. 2003
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SDSS Galaxy Power Spectrum
Corrects for luminosity bias
Pixelize and then apply FKP, etc.
Tegmark et al. 2003
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Cmbgg OmOl
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Cmbgg OmOl
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Cmbgg OmOl
CMB
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Cmbgg OmOl
CMB

LSS
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Lyman alpha forest
Photons with energy gt (n1 to n2 transition
energy) get absorbed along the line of sight as
they lose energy due to cosmic redshift. Every
absorption line corresponds to cloud of neutral
hydrogen.
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Fluctuations in density mimicked by fluctuations
in forest
Gnedin Hui, 1997
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SDSS Lyman Alpha Forest
3000 QSOs withabsorption lines from redshifts 2
to 4.2
Hui et al., 2003 Seljak et al., 2003
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Results

• Dashed lines are from Kecksolid from SDSS
• 3 sets of curves from low (bottom) to high (top)
  redshift
• SDSS goes to larger scales, but doesnt have
  small scales resolution

Good agreement with Keck!
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Convert 1D Flux Spectrum to 3D Linear Matter
Power Spectrum

• Run many simulations with CDM-like spectra
• Extract Flux power spectra from each simulation
• Fit amplitude and slope of power at 1 Mpc

Lidz et al.
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3D Power Spectrum
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Weak Gravitational Lensing
Future
Unlike galaxy surveys and Lyman alpha,
lensing directly probes mass distribution!
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Lensing is sensitive to neutrino mass

• Break up background galaxies into distinct
  redshift bins
• Probe time evolution of gravitational potential
  (sensitive to neutrino mass)

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Weak Lensing
Future

• Measure power spectrum AND/OR measure growth of
  spectrum at late time
• Sensitive to n mass AND dark energy
• Accelerator n experiments will teach us about
  dark energy!

Neutrino mass (eV)
Abazajian Dodelson (2003)
Dark energy equation of state
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Conclusion

• Cosmological constraints on neutrino mass (lt1.8
  eV total) arise from power spectrum
• Wide variety of techniques/experiments needed to
  eliminate systematics
• We must all become familiar with Big Bang
  cosmology, large scale structure, dark energy,
  inflation, cosmic microwave background,

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Galaxy Distribution
Probes of The Power Spectrum

• Large surveys with gt200k galaxy redshifts 2dF
  and SDSS
• 2dF takes redshifts of galaxies first observed by
  APM
• Restrict to linear scales

Percival et al. 2002
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Mainz
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Goal 1D Flux power spectrum

• Subtract mean flux and divide by mean flux. This
  gives d open squares
• Composite QSO spectrum crosses
• Principle Component Analysis Allow each QSO
  spectrum to vary linear combination of training
  set reference points

Simple thing works. Composite spectrum works very
well.
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Systematics Check
Sophisticated estimate
Cross-correlate distant lines of sight. No
intrinsic correlations any observed must be due
to improper continuum fitting.
Simple continuum estimate
Possible problems on large scales. No problems on
small scales.
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Results

• 2dF BBNprior
• With no external info on matter density,

Elgaroy et al. (2002)
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WMAP Spectra
Results
Bennett et al. (2003)

• Position and height of firsttwo peaks pinned
  down
• Polarization helps by determining extent of
  reionization

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WMAP Matter Density
Results

• First peak position determinescombination of
  matter densityand Hubble constant
• Height of first peaks determineseach separately

Page et al. (2003)
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Results

• WMAP 2dF small angle CMB Lyman alpha

Spergel et al. (2003)
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Results

• Lyman alpha some info from large scale
  structure (pre-2dF)COBE normalization

Croft et al. (2002)
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Running and Neutrino Mass
Results
Very preliminary result running does alleviate
bound on neutrino mass
Abazajian, Dodelson, Gates (2003)
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Probes of The Power Spectrum
CMB Anisotropies

• Amplitude of given Fourier mode remains constant
  until horizon entry
• Upon horizon entry, acoustic oscillations begin

Fourier amplitude
Modern Cosmology (2003)
Recombination
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Probes of The Power Spectrum
First Peak Mode First
Trough Mode

• Initial amplitude for given k is randomly chosen
• If phase was randomly chosen as well disaster!

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Probes of The Power Spectrum
First Peak Mode First
Trough Mode

• The phases were synchronized when the universe
  was very young Inflation
• Detection of peaks and troughs confirm basic
  model makes neutrino mass limits more robust

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Degeneracies

• Lowering the matter density suppresses the power
  spectrum
• This is virtually degenerate with non-zero
  neutrino mass

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Degeneracies
Gravitational Potential

• Potential wells decay for sub-horizon modes in
  radiation era
• Decreased matter density ? later epoch of
  equality ? more decay
• Net result suppression of power as matter
  density decreases

Modern Cosmology (2003)
Scale Factor
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CMB
Degeneracies

• Decrease in matter density leads to enhanced
  peaks
• Position of first peak (in flat universe) is
  affected by matter density
• CMB can break degeneracy

Modern Cosmology (2003)
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WMAP gets a better fit with spectral index n not
constant A running spectrum
Running complicates things
Degeneracies
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Running is degenerate with neutrino mass
Degeneracies
Abazajian, Dodelson, Gates (2003)
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Degeneracies

• Lowering the matter density suppresses the power
  spectrum
• This is virtually degenerate with non-zero
  neutrino mass

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Power spectrum depends only on massive neutrino
energy density
Sterile n typically thermalize (Abazajian, 2002)
so cosmological constraints apply (but see Foot
Volkas, 1997)