Quantum Field Theory in Curved Spaces and Its Applications to Cosmology

Quantum field theory in curved spaces and its applications to cosmology.

The development of the quantum theory of gravity is one of the most important problems of theoretical physics. Such a theory should become an important part of the theory of elementary particles and fundamental interactions. The study of different aspects of the quantum field theory in curved spacetimes is a natural step in this direction. Besides, quantum field theory in curved spaces has numerous applications to cosmology, which during the last decades had become an observational science.

One of the main topics which constitutes a bridge between cosmological observations and the theoretical cosmology is the study of the primordial cosmological fluctuations which influence both the large scale structure of the universe and the cosmic microwave background radiation. In modern cosmology

these fluctuations are treated as having a quantum origin. To study them one

construct the correlation functions. There are some consistency relations between

the 2-point correlation functions and the 3- and higher point correlation functions.

These relation have been throughly studied for the case when the quantum state

of the corresponding fluctuation modes is the well-known Bunch-Davies vacuum.

It is interesting also to study more general and less invariant quantum states.

Usually, in quantum field theory and in its applications to the particle physics one considers a scattering processes such that in the infinitely distant past and in the infinitely distant future the particles and fields are free and it is possible neglect their interactions. However, the finite-time processes can be also important and their importance is especially significant in cosmological studies, where there is an initial

(and, sometimes, final) moments of time. Thus, the problem of the construction of initial quantum states at some finite moment of time is very interesting. To solve this problem, it is possible to construct some kind of perturbation theory, starting from the standard free field theory.

Another interesting effect, which arises when we depart from the standard Bunch-Davies quantum initial state choice is connected with such a choice when the scalar and tensor perturbations are entangled. In this situation the rotational symmetry is broken and non-diagonal terms appear. Moreover, the structure of diagonal terms

is also modified.

Another direction of research connected with the application of the quantum field theory methods to inflationary cosmology is the study of mixed initial quantum states of the universe. The study of the cosmological perturbations in such a scheme is a technically challenging task, which can have interesting phenomenological aspects.

All the directions of research mentioned above are unified by an intention to

develop and apply the quantum field theoretical methods suitable for working

with time dependent Hamiltonians, naturally arising in the cosmological context.