1. Neutrinos and Large-Scale Structure
Daniel Eisenstein
Harvard University
Image: SDSS

2. Large-Scale Structure
Most of the powerful tests and successes of the Hot Big Bang focus not on the homogeneous expansion but on the small perturbations away from homogeneity.
Small ripples grow in time, but different sized ripples grow at different rate due to the detailed composition of the Universe.
From simple initial conditions, we predict complicated final products that we do observe!
Large scales (>30 Mpc) are special because cold dark matter doesn’t move that far: window to the early Universe.
Image from the Deep Lens Survey

3. Large-Scale Structure and the History of the Universe
When perturbations are small, structure grows in a simple way: each Fourier mode is independent.
Growth is a competition between gravitational attraction and the expansion of the Universe.
Gravity will cause all scales to grow, but pressure support or motions can oppose that. Affect small scales preferentially.
“Small” compared to sound speed (or streaming velocity) times the age of Universe.
Variations in the amplitude of structure as a function of scale reveals the history of relativistic and cold components.
Power spectrum analyses measure the rms amplitude of structure as a function of Fourier wavenumber.

4. Cosmic Neutrinos
The thermal production of neutrinos in the early Universe leaves us with a very important relic population.
68% of the energy density of the CMB.
40% of the energy density when Universe has kT between 1 and 106 eV.
Would produce the dark matter if the sum of the masses of the three mass states were ~10 eV.

5. Outline Neutrinos in the Radiation Epoch Neutrinos in the Matter Epoch
Constraints on the total relativistic density.
Discussion of baryon acoustic oscillations.
Neutrinos in the Matter Epoch
Constraints on neutrino mass.

6. Neutrinos in the Radiation-Dominated Era
Cosmology is sensitive to the relic energy density of any long-lived light particle, neutrinos being the familiar example.
We parameterize the search for extra energy density by scaling in units of “one neutrino species”. We call this Neff, with 3 being the canonical value (really, 3.04).
Important: Neff > 3 might have nothing to do with neutrinos!
One “extra species” adds 13% more energy density and therefore increases the Hubble parameter (and decreases the age of the Universe at a given redshift) by 6.5%.

7. Four Routes to Neff
1) Helium-4 abundance from Big Bang Nucleosynthesis.
2) CMB damping tail
3) Comparison of Hubble constant (H0) from Baryon Acoustic Oscillations (BAO) and direct measurements.
4) Use Wm, H0, and measure of redshift of matter-radiation equality.

8. 1) Big Bang Nucleosynthesis
Higher energy density implies faster expansion rate at a given temperature.
More neutrons survive, increasing 4He abundance.
Data continues to favor values of Neff around 3-4.
Coc (2013)

9. 2) CMB Damping Tail
The CMB is smooth at small angular scales because of the diffusion between photons and the electrons.
The size of this scales as the square root of the age of the Universe.
Meanwhile, the acoustic peak angle scales proportionally to the age of the Universe.
The comparison of the two allows a strong measure of the expansion rate at redshift ~1000, which in turn measures Neff.
Planck 2013 reports Neff = 3.3 ± 0.27.
Planck Consortium (2013)

10. 3) Baryon Acoustic Oscillations
Sound waves in the early Universe produce a signature in the clustering of galaxies of calculable physical size.
Depends on the Hubble expansion at z>1000, and hence on the radiation density.
We measure the signature in galaxy samples to infer the distance to a given redshift.
Comparing that distance scale to the one measured through local techniques can allow us to infer the radiation density.

11. Sound Waves in the Early Universe
Before recombination:
Universe is ionized.
Photons provide enormous pressure and restoring force.
Perturbations oscillate as acoustic waves.
After recombination:
Universe is neutral.
Photons can travel freely past the baryons.
Perturbations grow by gravitational instability.
Big Bang
Today
Recombination
z ~ 1000
~400,000 years
Ionized
Neutral
Time

12. Sound Waves
Each initial overdensity (in DM & gas) is an overpressure that launches a spherical sound wave.
This wave travels outwards at 57% of the speed of light.
Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.
Sound speed plummets. Wave stalls at a radius of 150 Mpc.
Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.

13. A Standard Ruler
The acoustic oscillation scale depends on the sound speed and the propagation time.
These depend on the matter-to-radiation ratio (Wmh2) and the baryon-to-photon ratio (Wbh2).
The CMB anisotropies measure these and fix the oscillation scale. Known to 0.4% from Planck data (with Neff = 3!).
When we see this pattern in the clustering data as an angular scale, we can infer the distance to the galaxies.

14. Galaxy and Quasar Surveys
The easiest way to map the density of the Universe at low redshift is with galaxy surveys.
We make two-dimen. maps with imaging and then add the third dimension with spectroscopy.
Largest 3-d maps use about a million galaxies.
SDSS redshift survey image credit: Blanton

15. The Sloan Digital Sky Survey
The SDSS is the world’s largest galaxy redshift survey.
Took digital pictures of one third of the sky in 5 bandpasses.
Catalogued 500 million objects.
Then performed spectroscopy of about 5 million objects, mostly galaxies.
Project began in 1990, started taking data in 1998.
Completing SDSS-III in 2014!
Support from Sloan Foundation, DOE, NSF, and over 50 member institutions from around the world.

16. SDSS-III Baryon Oscillation Spectroscopic Survey
Latest results come from over 1 million galaxies over 8500 deg2, about 20% of the sky.
Two samples:
CMASS (0.43<z<0.7) with 777K galaxies. Median redshift 0.57.
LOWZ (0.15<z<0.43) with 268K galaxies. Median redshift 0.32.
Papers: Anderson et al. (arXiv: ), supported by Manera et al. ( ), Percival et al. ( ), Ross et al. ( ), Tojeiro et al. ( ), and Vargas-Magana et al. ( ).

17. Galaxy Correlation Functions

18. Galaxy Correlation Functions

19. Galaxy Correlation Functions

20. Galaxy Correlation Functions

21. Galaxy Correlation Functions

22. Galaxy Correlation Functions

23. Galaxy Correlation Functions

24. Galaxy Correlation Functions

25. Galaxy Correlation Functions

26. Galaxy Correlation Functions

27. Acoustic Peak in 2013
With SDSS-III we have a strong detection, yielding a 1.0% distance measurement to z=0.57.
s2 x(s) (Mpc/h)2
P(k)/Psmooth
Anderson et al. (2013b)

28. Acoustic Peak in 2013
Also a detection in the lower redshift sample, giving a 2.1% distance measurement to z=0.32.
s2 x(s) (Mpc/h)2
P(k)/Psmooth
Tojeiro et al. (2014)

29. The Cosmic Distance Scale
Anderson et al. (2013)

30. The Cosmic Distance Scale
Planck curve is a Prediction, not a Fit!
Anderson et al. (2013)

31. Zooming In
Anderson et al. (2013)

32. Cosmological Constraints
For non-flat wCDM, Planck+BAO finds: WK = ± 0.005, w = –0.98 ± 0.11, Wm = ± 0.020, H0 = 67.3 ± km/s/Mpc

33. Measuring the Expansion and Density of the Universe
The combination of CMB, BAO, and Supernova (Union-2) data give superb constraints on H0 and Wm, essentially independent of model of low-z dark energy or curvature.
H0 = 67.5 ± 1.7 km/s/Mpc
Wm = ± 0.016
A reverse distance ladder:
CMB calibrates z=1000 at 0.4%.
BAO transfers to z~0.5 at 0.9%.
SNe carries to z=0 at ~2%.
Anderson et al (2013b)

34. Direct Measures of H0
Most direct measures using Cepheid variables and various calibrations give H0 values in the low 70’s.
E.g., 72.5 ± 2.5 km/s/Mpc.
This difference from ~68 is not statistically significant.
But it does have people thinking about Neff as a way to reconcile.

35. What about H0?
Does the CMB+LSS+SNe really measure the Hubble constant? What sets the scale in the model?
The energy density of the CMB photons plus the assumed a neutrino background gives the radiation density.
The redshift of matter-radiation equality then sets the matter density (Wmh2).
Measurements of Wm (e.g., from distance ratios) then imply H0.
What if the radiation density were different, i.e. more/fewer neutrinos or something new?
Sound horizon would shift in scale. LSS inferences of Wm, Wk, w(z), etc, would be correct, but Wmh2 and H0 would shift.
Minor changes in baryon fraction, age of Universe, and CMB damping.
So comparison of H0 from direct measures to CMB-based inferences are a probe of “dark radiation”.
1% in H0 is 0.2 effective neutrino species.
DJE & White (2004)

36. DESI on the Kitt Peak 4-m telescope!
What’s after SDSS BOSS and eBOSS?
DESI on the Kitt Peak 4-m telescope!
15x faster than BOSS.
30 million galaxies, <0.3% BAO distance!
Powerful measurement of cosmic acceleration. 36

37. 4) Beyond BAO
We measure the redshift of matter-radiation equality from the CMB acoustic peaks and from the shape of the galaxy power spectrum.
Measurements of Wm and H0 yield the matter density.
Combining gives the radiation density and hence Neff.
Currently not the leading method, but it does give consistent answers.

38. Neff Today
All of these lines of argument favor Neff in the 3 to 4 range.
Remarkably, Neff of 0 is sharply disfavored; we have inferred a dark radiation at the level of the expected cosmic neutrino background!
Also important, Neff > 5 is disfavored. The Universe apparently does not contain a large density of long-lived sub-eV relic particles!

39. Neff Tomorrow
These constraints will improve substantially in the coming decade.
Small-scale CMB polarization has lots of reach on this. E.g., CMB-S4 forecasts offer Neff to ~0.02! (Abazajian et al. Snowmass contribution)
Planck + DESI gets to , depending on forecasting assumptions.
A 1% H0 measurement combined with BAO+SNe would push to 0.2 rms by a different method.

40. Neutrino Mass
The growth of structure is always a competition between gravity driving the instability and the expansion of the Universe trying to freeze it.
Giving the neutrinos mass means that some of the dark matter has velocities that are too large to stay in the overdensities.
This suppresses the growth of structure on small scales.

41. Power Spectrum
Suppression of 3% in power for 0.4% dark matter mass fraction in neutrinos (0.05 eV as sum of the three masses).
1.5% drop in amplitude of small-scale clustering.
For masses around 0.1 eV, we primarily measure the suppression at small scales relative to the prediction from the CMB, not the anomalous tilt.
Abazajian et al (2013)

42. Measuring the Suppression
We measure the clustering amplitude at z=1000 from the CMB.
We then predict the clustering at low redshift.
This depends on the expansion history, but we can measure that well enough.
Also depends on assumption of GR.
We measure the clustering at low redshift by various methods.

43. Clustering at z=1000
Our measurement of the clustering amplitude from the CMB is degenerate with the amount of scattering of the CMB due to free electrons at z<100.
We measure this “optical depth to last scattering” by its imprint on large-scale CMB polarization.
Unfortunately, this is limited to about % precision.

44. Clustering at Low Redshift
This can be measured in a variety of ways:
Counts of clusters of galaxies
Weak lensing, either of galaxies or the CMB.
Lyman a forest.
Redshift-space distortions.
We want to measure at multiple redshifts, so as to separate possible effects from dark energy (which dominates only recently) from massive neutrinos (which build cumulatively since z=1000).

45. Redshift-Space Distortions
Structure grows because of the non-zero divergence of the velocity field.
The velocities are measurable along the line of sight because we measure redshifts, not distances.
Can compare clustering along line of sight to across line of sight to isolate the size of the velocities.
Viewer
Velocity

46. Current Data The current observational situation is … unsettled.
Planck predicts a relatively high amplitude.
Several data sets (clusters, galaxy lensing, and RSD) suggest lower values.
Planck weak lensing itself gives a higher value.
Current errors are eV (rms). Central values can reach 0.4 eV, or be down around 0.
Amplitude
Matter Density
Beutler et al.(2014)

47. Future Opportunities
Data are improving rapidly, with major new surveys, e.g.
Galaxy lensing,
CMB lensing measurements,
Cluster samples,
Galaxy redshift surveys.
Multiple routes to 1% amplitude measurements and better.
Forecasts reach around 0.02 eV rms, at the threshold of being able to distinguish 0 eV from 0.05 eV from 0.10 eV.

48. Conclusions Cosmological surveys are improving rapidly.
Galaxy imaging, galaxy spectroscopy, CMB anisotropies, 21 cm mapping, etc.
We expect strong improvements on most aspects of cosmology.
Today, we constrain the relativistic density to about 10% of the cosmic neutrino background, and the neutrino masses to about 0.1 eV (rms), with several methods for each measurement.
In the coming decade, this can shrink by a factor of 5 in mass and 10 in number!

50. The Lyman a Forest
Neutral H absorption observed
in quasar spectrum at z=3.7
Neutral H simulation (R. Cen)
The Lya forest tracks the density of the intergalactic medium along each line of sight.
A grid of sightlines can map the 3-d density at z>2.
An efficient way to measure the BAO at z>2. Requires only modest resolution and low S/N.
White (2004); McDonald & DJE (2006)

51. BAO in the Forest in DR11
In April, we released an analysis with triple the quasar sample.
BAO is well-detected (>5s) in the auto-correlation of the Ly a forest!
Tight measurement of the Hubble parameter and angular diameter distance at z=2.4.
BAO detection along the line of sight from correlations between 140,000 z>2 quasar spectra.
Delubac et al. (2013)

52. Observing Dark Energy
Weinberg et al. (2012; arXiv: ) provides a review of all of the major observational methods for the study of dark energy.