# Presentation: 829317

## Massive Neutrinos and the Cosmos

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

- Scott Dodelson
- University of Kansas
- December 1, 2003

## 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?

**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. *

## Amended picture of beta decay

- Courtesy: *University of Oregon*

## 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... *

## Origin of neutrino mass

- Can have masses like electrons, quarks (via coupling to Higgs boson). But why are 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.

- Mainz

## Direct measurements:m eV

## 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

- Note: probability depends only on mass squared difference.

*Bahcall*

- Two Obvious Sources of neutrinos:
- *Sun
- * Cosmic Rays hitting the atmosphere

## Solar Neutrinos

- Bahcall

**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)

## Observe fewer (electron) neutrinos than are produced in Sun

## The SNO experiment detects the missing neutrinos

## Results post-SNO

- Solar

- Solar + Kamland

## Atmospheric neutrinos

- Fewer muon neutrinos seen than expected, consistent with oscillations to tau neutrinos

*Fukuda et al. 1998*

## 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*

-   _Degenerate  _
**   ****m****1****~m****2****~m****3**

## Neutrinos are also produced in the early universe

- 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 )

*Alpher, Herman, & Gamow 1953*

## 50 eV mass  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 ...

## Massive Neutrinos affect large scale structure Bond, Efstathiou, & Silk 1980, Melott 1982; Bond & Szalay 1983; White, Frenk & Davis 1983;   Shandarin, Dorshkevich, & Zel’dovich 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

- Cold Dark Matter
- (no neutrino mass)

- Hot + Cold Dark Matter
- (non-zero neutrino mass)

- If neutrinos are important, they smooth out the distribution: no small scale structure

*Colombi, Dodelson, & Widrow 1995*

## Musical Acoustics

- Middle C
- Middle C on a piano

## Quantitative Measure: Power Spectrum

- Weak Lensing

- Probes of the Power Spectrum

## 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 1⁄4 of the sky

## 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).

## 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*(1+z) Ang. Can get z>6 QSOs.

## Galaxy Power Spectrum

- Tegmark et al. 2003

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

## SDSS Galaxy Power Spectrum

- Tegmark et al. 2003

- Corrects for luminosity bias

- Pixelize and then apply FKP, etc.

## Cmbgg OmOl

## Cmbgg OmOl

## Cmbgg OmOl

**CMB**

## Cmbgg OmOl

**CMB**

**+**

**LSS**

## Lyman alpha forest

- Photons with energy > (n=1 to n=2 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.

## Fluctuations in density mimicked by fluctuations in forest

*Gnedin & Hui, 1997*

## SDSS: Lyman Alpha Forest

- 3000 QSOs withabsorption lines from redshifts 2 to 4.2

*Hui et al., 2003*
*Seljak et al., 2003*

## Results

-  Dashed lines are from Keck;solid from SDSS
-  3 sets of curves from low (bottom) to high (top) redshift
-  SDSS goes to larger scales, but doesn’t have small scales resolution

- Good agreement with Keck!

## 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.

## 3D Power Spectrum

## Weak Gravitational Lensing

*Future*

- Unlike galaxy surveys and Lyman alpha, lensing
- directly probes mass distribution!

## Lensing is sensitive to neutrino mass

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

## Weak Lensing

*Future*

- Abazajian & Dodelson (2003)

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

- Dark energy equation of state

- Neutrino mass (eV)

## Conclusion

- Cosmological constraints on neutrino mass (<1.8 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, ...

## Galaxy Distribution

- Large surveys with >200k galaxy redshifts: 2dF and SDSS
- 2dF takes redshifts of galaxies first observed by APM
- Restrict to linear scales

*Probes of The Power Spectrum*

- Percival et al. 2002

- Mainz

## Goal: 1D Flux power spectrum

-  Subtract mean flux and divide by mean flux. This gives 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.

## Systematics Check

- Cross-correlate distant lines of sight. No intrinsic correlations: any observed must be due to improper continuum fitting.

- Possible problems on large scales. No problems on small scales.

- Sophisticated estimate

- Simple continuum estimate

- 2dF + BBNprior
- With no external info on matter density,

*Results*

*Elgaroy et al. (2002)*

## WMAP Spectra

*Results*

*Bennett et al. (2003)*

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

##  WMAP: Matter Density

*Results*

*Page et al. (2003)*

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

- WMAP + 2dF + small angle CMB +  Lyman alpha

*Results*

- Spergel et al. (2003)

*Results*

- Croft et al. (2002)

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

## Running and Neutrino Mass

*Results*

- Abazajian, Dodelson, & Gates (2003)

- Very preliminary result: running does alleviate bound on neutrino mass

- CMB Anisotropies

*Probes of The Power Spectrum*

*Modern Cosmology (2003)*

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

- Fourier amplitude

- Recombination

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

*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

*Probes of The Power Spectrum*

-  “First Peak” Mode                     “First Trough” Mode

*Degeneracies*

-  This is virtually degenerate with non-zero neutrino mass

*Degeneracies*

*Modern Cosmology (2003)*

- Scale Factor

- Gravitational Potential

-  Net result: suppression of power as matter density decreases

## CMB

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

*Degeneracies*

*Modern Cosmology (2003)*

## WMAP gets a better fit with spectral index n not constant: A “running” spectrum

- Running complicates things

*Degeneracies*

## Running is degenerate with neutrino mass

*Degeneracies*

*Abazajian, Dodelson, & Gates (2003)*

## Degeneracies

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

## Power spectrum depends only on massive neutrino energy density

- Sterile  typically thermalize (*Abazajian, 2002*) so cosmological constraints apply (but see *Foot & Volkas, 1997*)