### Beyond the the standard cosmological model: neutrinos and non-Gaussianity

Tristan L. Smith

(UC Berkeley)

**Abstract:**

The cosmic microwave background (CMB) has provided us the laboratory in which we entered the
era of 'precision cosmology'. By and large these observations have confirmed the basic, standard,
cosmological model which supposes a universe seeded with Gaussian initial fluctuations and filled
with non-relativistic matter, photons, and 3 neutrino species. As observations have become more
accurate it has become increasingly pertinent to test some of the assumptions that have gone into
building the standard cosmological model. In this talk I will present some of my recent work on testing
these assumptions.

First I will discuss how recent measurements of the small-scale CMB have hinted at the presence of
extra relativistic energy density within the universe. Any interpretation of these results will necessitate
the measurement of some of the properties of any extra relativistic energy density. Using recent
small-scale measurements of the CMB, along with my colleagues, I have been able to constrain the
clustering properties of the extra relativistic energy density. We show that current observations disfavor
the interpretation that any extra relativistic energy consists of standard neutrinos.

Second, there has been an increasing interest in testing whether the initial fluctuations follow Gaussian
statistics. These tests of 'primordial non-Gaussianity' use estimators constructed from either the CMB
three-point (bispectrum) or four-point (trispectrum) correlation functions. Usually an estimator constructed
from data is assumed to have a Gaussian probability distribution (PDF) as a result of the central limit theorem.
However, in this case the central limit theorem does not apply since the number of terms that appear in these
estimators are much greater than the number of measurements. A complete knowledge of the shape of the
PDF is necessary in order to properly assign confidence limits to any constraint. I will discuss how Monte Carlo
simulations show that the PDF for these estimators are highly non-Gaussian themselves, necessitating more
care in using these estimators, especially for future observations with the Planck satellite. I will also show how
the constraining power of these estimators may be improved by using a realization-dependent normalization.