Cosmology and Gravitation

I will review recent developments in our theoretical understanding of the abundance and clustering of dark matter haloes. In the first part of this talk, I will discuss a toy model based on the statistics of peaks  of Gaussian random field (Bardeen et al 1986) and show how the clustering properties of such a point set can be easily derived from a generalised local bias expansion. In the second part, I will explain how  this peak formalism relates to the excursion set approach and present parameter-free predictions for the  mass function and bias of dark matter halos.

We
employ the effective field theory approach for multi-field inflation which is a
generalization of Weinberg's work. In this method the first correction terms in
addition to standard terms in the Lagrangian have been considered. These terms
contain up to the fourth derivative of the fields including the scalar field
and the metric. The results show the possible shapes of the interaction terms
resulting eventually in non-Gaussianity in a general formalism. In addition
generally the speed of sound is different but almost unity. Since in this
method the adiabatic mode is not discriminated initially so we define the
adiabatic as well as entropy modes for a specific two-field model. It has been
shown that the non-Gaussianity of the adiabatic mode and the entropy mode are
correlated in shape and amplitude. It is shown that even for speed close to
unity large non-Gaussianities are possible in multi-field case. The amount of
the non-Gaussianity depends on the curvature of the classical path in the
phase-space in the Hubble unit such that it is large for the large curvature.
In addition it is emphasized that the time derivative of adiabatic and entropy
perturbations do not transform due to the shift symmetry as well as the
original perturbations. Though two specific combinations of them are invariant
under such a symmetry and these combinations should be employed to construct an
effective field theory of multi-field inflation.

Screened Scalar-Tensor gravity such as chameleon and symmetron theories allow order one deviations from General Relativity on large scales whilst satisfying all local solar-system constraints. A lot of recent work has therefore focused on searching for observational signatures of these
models and constraining them. If these models are to be viable then our own solar system is necessarily screened, however, this may not be the case for stars in Dwarf Galaxies, which can exhibit novel and unique phenomena. These new effects can be exploited to produce constraints that are far more competitive than laboratory and cosmological tests and in this talk, I will describe some recent and ongoing work using these phenomena to place new constraints.

Ultra-light axions (m_a<10^{-18} eV), motivated by string theory, can be a powerful probe of the energy scale of inflation if they exist as a sub-dominant component of the Dark Matter. In contrast to heavier axions the isocurvature modes in the ultra-light axions can coexist with observable gravitational waves. Here it is shown that existing (2005) large scale structure constraints severely limit the parameter space for axion mass, density fraction and isocurvature amplitude. It is also shown that radically different CMB observables for the ultra-light axion isocurvature mode additionally reduce this space. The results of a new, accurate and efficient method to calculate this isocurvature power spectrum are presented, and can be used to constrain ultra-light axions and inflation.
I will also present preliminary results of constraints to this model using up-to-date cosmological observations, which verify the above picture. The parameter space is interesting to explore due to a strongly mass dependent covariance matrix, motivating comparisons between Metropolis-Hastings and nested sampling. Finally I discuss fine-tuning and naturalness in these models.