We round out this morning's session.

The standard ΛCDM split of the Universe energy budget is wel known: 70%-26%-5% for DE-DM-Atoms. However, at photon decoupling 12.4 billion years ago, it is instead 63%-12%-15%-10% for DM-atoms-photons-neutrinos, with DE utterly negligible. This is obviously relevant for CMB physics. But with neutrinos being such a significant fraction, and so poorly constrained, the question is how things might change with non-standard neutrino physics.

Example 1: neutino masses. Direct experimental limit is only < 7 eV.

Example 2: sterile neutrinos. Various evidence from the short baseline anomalies. Light steriles would have cosmological implications.

Example 3: free streaming? Yes in SM, but BSM interactions (

eV-mass neutrinos become non-relativistic around photon decoupling. They still have a large thermal motion even in this case, hence a large free-streaming scale. The former affects CMB anisotropies, and both modify large scale structure. Potential wells bigger than the free-streaming scale will capture neutrinos. If too small they will not, and the potential will decay.

CMB limit on neutrino masses comes from this effect. Linear calculation (CMB epoch). Some progress in non-linear calculation. Suppression is enhanced on non-linear scales.

CMB limits from weak gravitational lensing. Photons from surface of last scattering are deflected by intermediate matter; we observe slightly distorted picture. Affects small angular scales, less than about 0.2 degrees. Can directly construct the lensing potential power spectrum. Interestingly, current Planck bounds only slightly better than strongest WMAP bounds, but don't rely on low-z (nonlinear) data. Thus under better systematic control. Planck + Lyman-α bounds starting to put pressure on inverted hierarchy parameter space.

Finally, note that KATRIN will give cosmology-independent bound on neutrino masses of 0.6 eV, compared to Planck 0.2 eV bound. This is truly robust and independent.

For cosmology, we just mean a particle that decouples before z ~ 10

In particular, there is an exact degeneravy between the matter density ω

But, when you go through the data, the third CMB peak is the

Including just this new parameter we get N

Comparison to short baseline anomalies. 3+1 scenario features "heavy" sterile, mass spliting 0.5 eV

An alternative way to deal with that needed suppression. Work with effective Fermi-like self-interaction, suppressed by high scale. This works for scales only ~ 1000 times weak scale but again distorts positron spectra. Can also lead to flavour equilibration between active & sterile neutrinos, which would again give too large N

New interactions can also modify free-streaming. In standard picture stream after T ~ 1 MeV. New hidden interactions could keep neutrinos in equilibrium at time of CMB. This would modify the spacetime metric perturbations.

An experiment looking into dark energy. A galaxy survey experiment; the first

Primary goal is to measure DE by looking at galaxy-redshift distribution. Also look for primordial non-Gaussianities better than Planck. Also measure spectral index and its running.

Measuring bispectrum > 1 would exclude all single-field inflation models. Measuring it without corresponding trispectrum would exclude most multi-field inflation models. NG is enhanced at large scales (1/k

**11:00 am:***Neutrinos in Cosmology*, Yvonne WongThe standard ΛCDM split of the Universe energy budget is wel known: 70%-26%-5% for DE-DM-Atoms. However, at photon decoupling 12.4 billion years ago, it is instead 63%-12%-15%-10% for DM-atoms-photons-neutrinos, with DE utterly negligible. This is obviously relevant for CMB physics. But with neutrinos being such a significant fraction, and so poorly constrained, the question is how things might change with non-standard neutrino physics.

Example 1: neutino masses. Direct experimental limit is only < 7 eV.

Example 2: sterile neutrinos. Various evidence from the short baseline anomalies. Light steriles would have cosmological implications.

Example 3: free streaming? Yes in SM, but BSM interactions (

*e.g.*self-interactions or coupling to DM) would change that.__Neutrino masses__eV-mass neutrinos become non-relativistic around photon decoupling. They still have a large thermal motion even in this case, hence a large free-streaming scale. The former affects CMB anisotropies, and both modify large scale structure. Potential wells bigger than the free-streaming scale will capture neutrinos. If too small they will not, and the potential will decay.

CMB limit on neutrino masses comes from this effect. Linear calculation (CMB epoch). Some progress in non-linear calculation. Suppression is enhanced on non-linear scales.

CMB limits from weak gravitational lensing. Photons from surface of last scattering are deflected by intermediate matter; we observe slightly distorted picture. Affects small angular scales, less than about 0.2 degrees. Can directly construct the lensing potential power spectrum. Interestingly, current Planck bounds only slightly better than strongest WMAP bounds, but don't rely on low-z (nonlinear) data. Thus under better systematic control. Planck + Lyman-α bounds starting to put pressure on inverted hierarchy parameter space.

Finally, note that KATRIN will give cosmology-independent bound on neutrino masses of 0.6 eV, compared to Planck 0.2 eV bound. This is truly robust and independent.

__Sterile neutrinos__For cosmology, we just mean a particle that decouples before z ~ 10

^{6}while ultra-relativistic, and does not interact with itself or anything else after decoupling. All measured in the standard parameter N_{eff}, number of effective neutrino species. Has obvious, huge effects on CMB that makes it look easy to measure. However, because CMB also used to measure 6 other cosmological parameters, there exist parameter degeneracies that complicate things.In particular, there is an exact degeneravy between the matter density ω

_{m}and N_{eff}in the recombination redshift. Another exact degeneracy exists between ω_{m}and the Hubble rate in the sound horizon. Finally, there are non-physical apparent degeneracies between N_{eff}and the primordial fluctuation amplitude and/or the spectral index.But, when you go through the data, the third CMB peak is the

*first*data point that is*free*of all the degeneracies: the first true probe of N_{eff}. Originally (WMAP) this required*e.g.*HST data to fully break degeneracies. Modern work with ACT/SPT/Planck measuring CMB damping tail lets us do this with CMB data alone.Including just this new parameter we get N

_{eff}= 3.04 ± 0.2. Including neutrino masses the allowed region is 3.2 ± 0.5. However, increased N_{eff}could help resolve the discrepancies in the Hubble rate that exist.Comparison to short baseline anomalies. 3+1 scenario features "heavy" sterile, mass spliting 0.5 eV

^{2}. A careful calculation gives one effective neutrino species and a mass sum of 0.7 eV, in clear contradiction with Planck limits. This requires some non-standard cosmology to suppress the thermalisation of the sterile. Possibilities include a large lepton asymmetry, L ~ 0.01, that creates an effective potential suppressing active-sterile mixing. However, this can create problems itself with the positron distributions, which in turn can effect the neutron/proton ratio for BBN.__Self-interactions__An alternative way to deal with that needed suppression. Work with effective Fermi-like self-interaction, suppressed by high scale. This works for scales only ~ 1000 times weak scale but again distorts positron spectra. Can also lead to flavour equilibration between active & sterile neutrinos, which would again give too large N

_{eff}.New interactions can also modify free-streaming. In standard picture stream after T ~ 1 MeV. New hidden interactions could keep neutrinos in equilibrium at time of CMB. This would modify the spacetime metric perturbations.

**11:45 am:***Cosmology with the HETDEX Survey*, Donghui JeongAn experiment looking into dark energy. A galaxy survey experiment; the first

*blind*large-scale structure survey (no pre-selection of objects). Working at high redshift (1.9 < z < 3.5). Using large (10m) telescope. Start to get data next year.Primary goal is to measure DE by looking at galaxy-redshift distribution. Also look for primordial non-Gaussianities better than Planck. Also measure spectral index and its running.

Measuring bispectrum > 1 would exclude all single-field inflation models. Measuring it without corresponding trispectrum would exclude most multi-field inflation models. NG is enhanced at large scales (1/k

^{2}, where k is wavenumber). Unfortunately degeneracies with gravitational lensing effects.
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