Juan P. Beltran Almeida

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

CERN-PH-TH/2009-260 Abstract: We apply the time-renormalization group approach to study the effect of pri- mordial non-Gaussianities in the non-linear evolution of cosmological dark matter density perturbations. This method improves the standard perturbation approach by solving renor- malization group-like equations governing the dynamics of gravitational instability. The primordial bispectra constructed from the dark matter density contrast and the velocity fields represent initial conditions for the renormalization group flow. We consider local, equilateral and folded shapes for the initial non-Gaussianity and analyze as well the case in which the non-linear parameter fNL parametrizing the strength of the non-Gaussianity depends on the momenta in Fourier space through a power-law relation, the so-called run- ning non-Gaussianity. For the local model of non-Gaussianity we compare our findings for the power-spectrum with those of recent N-body simulations and find that they accu- rately fit the N-body data up to wave-numbers k � 0.25h/Mpc at z = 0. We also present predictions for the (reduced) matter bispectra for the various shapes of non-Gaussianity.

On the stability and causality of scalar-vector theories

Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations, such models require to introduce non-standard couplings between vector fields on the one hand, and either gravity or scalar fields on the other hand. In this article, we study models involving a vector field coupled to a scalar field. We derive restrictive necessary conditions for these models to be both stable (Hamiltonian bounded by below) and causal (hyperbolic equations of motion).

THE SUYAMA–YAMAGUCHI CONSISTENCY RELATION IN THE PRESENCE OF VECTOR FIELDS

We consider inflationary models in which vector fields (VF) are responsible for part or eventually all of the primordial curvature perturbation ζ. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity (NG) is generated due to the superhorizon evolution, we use the δN formalism to do a complete tree level calculation of the NG parameters fNL and τNL in the presence of VF. We isolate the isotropic pieces of the NG parameters, which anyway have contributions from the VF, and show that they obey the Suyama–Yamaguchi (SY) consistency relation . Other ways of defining the NG parameters, which could be observationally relevant, are stated and the respective SY-like consistency relations are obtained.

On the 4D generalized Proca action for an Abelian vector field

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stuckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stuckelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field

Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation

A_\mu

de Sitter symmetries and inflationary scalar-vector models

, the Faraday tensor

Scale and shape dependent non-Gaussianity in the presence of inflationary vector fields

F_{\mu \nu}

The different varieties of the Suyama-Yamaguchi consistency relation and its violation as a signal of statistical inhomogeneity

and its Hodge dual

de Sitter symmetries and inflationary correlators in parity violating scalar-vector models

\tilde{F}_{\mu \nu}

Arbitrarily coupled

.