Alexey Golovnev

Cosmological perturbations from vector inflation

We analyze the behavior of linear perturbations in vector inflation. In contrast to scalar field inflation, the linearized theory with vector fields contains couplings between scalar, vector, and tensor modes. The perturbations decouple only in the ultraviolet limit, which allows us to carry out the canonical quantization. Superhorizon perturbations can be approximately analyzed due to suppressed mixing between different modes in the small field models. We find that the vector perturbations of the metric decay exponentially, but the scalar and tensor modes could remain weakly coupled throughout the evolution. As a result, vector inflation can produce significant correlations of the scalar and tensor modes in the CMB. For realistic models the effect is rather small, but not negligible.

Gravitational waves in vector inflation

We discuss the gravitational waves (GW) in the context of vector inflation. We derive the action for tensor perturbations and find that tachyonic instabilities are present in most (but not all) of the inflationary models with large fields. In contrast, the stability of the small field inflation () is ensured by the usual slow-roll conditions, where N is the total number of fields. For example, the Coleman–Weinberg potential and the power-law inflation are always stable in the small fields limit with an approximately flat spectrum of GW. We also provide some examples which lead to a rapid decay of GW and predict the absence of tensor modes in the CMB.

Linear perturbations in vector inflation and stability issues

We continue the analysis of perturbations in vector inflation. The dominant theme of this paper is the long wavelength limit of perturbations in small fields inflation and the controversial issue of its linear stability. We explain the nature of longitudinal modes, describe how they evolve, and show that they are not as harmful as it could seem at the first glance. On the other hand, the gravitational waves instability in large fields models is shown explicitly. It strongly limits a potential applicability of the recently proposed {delta}N-type approach to vector inflationary perturbations. Finally, we expose a problem of an extra (gravitational) degree of freedom which appears whenever the vector fields are nonminimally coupled to gravity.

Canonical quantization of motion on submanifolds

This is an extended version of the talk given by the Author at the 40th Symposium on Mathematical Physics held in Torun, Poland, June 25-28, 2008. We review the methods of canonical quantization of free particle motion on curved submanifolds considered as a system with second class constraints. The work is based on our previous articles, quant-ph/0508044 and quant-ph/0508111. However, some new results are also presented.

On hyperbolicity violations in cosmological models with vector fields

Cosmological models with vector fields received much attention in recent years. Unfortunately, most of them are plagued with severe instabilities or other problems. In particular, it was noted in ref. [1] that the models with a non-linear function of the Maxwellian kinetic term do always imply violations of hyperbolicity somewhere in the phase space. In this work we make this statement more precise in several respects and show that those violations may not be present around spatially homogeneous configurations of the vector field.

An invariant variational principle for Hamiltonian mechanics

It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure

Effectively nonlocal metric-affine gravity

omega

Non-Gaussian Probability Distribution of the CMB Angular Power Spectra

without any need to choose some 1-form

On covariantisation of teleparallel gravity

gamma

Cosmological perturbations in modified teleparallel gravity models

, such that