arXiv subjects

Tereza Vardanyan

Publications and source records attributed to Tereza Vardanyan.

15 recordsLinked to original sources

arXiv2026

Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation

We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent functions, and show that these functions approximate the time evolution of the correlation functions of the stochastic theory reasonably well. Second, we apply the technique of autonomous equations to the Borel-Le Roy transforms of correlation functions, and use solutions of these equations to perform Borel resummation. The results match the time evolution obtained in the stochastic picture substantially better. In addition, we propose an alternative method for extracting perturbative coefficients and provide a new derivation of our autonomous equation by truncating a system of Schwinger-Dyson-type differential equations.

hep-th↗

arXiv2022

Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree-Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We also demonstrate that the long-wavelength expectation value of the commutator of two fields is equal to zero both for spacelike and timelike separated points.

gr-qc↗

arXiv2021

Time and Evolution in Quantum and Classical Cosmology

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.

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arXiv2020

Renormalization group inspired autonomous equations for secular effects in de Sitter space

We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The exact solutions of these equations are free of secular terms and approach a finite limit at late times. This technique is illustrated for the well-known problem of secular growth of correlation functions of a massless scalar field with a quartic self-interaction in de Sitter space. For the expectation value of the product of two fields at coinciding space-time points we obtain a finite late-time result that is very close to the one following from Starobinsky's stochastic approach.

hep-th↗

arXiv2020

Spatial Kasner solution and an infinite slab with constant energy density

We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and Weyl-Levi-Civita spacetimes outside the slab. We also show that there are solutions that can be matched with general anisotropic Kasner spacetime outside the slab. In any case, it is impossible to avoid the presence of the Kasner type singularities in contrast to the well-known case of spherical symmetry, where by matching the internal Schwarzschild solution with the external one, the singularity in the center of coordinates can be eliminated.

gr-qc↗

arXiv2019

Exact solutions of the Einstein equations for an infinite slab with a constant energy density

We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic, while in the second solution the tangential components of the pressure are equal to zero. In both cases the pressure vanishes at the boundaries of the slab. Outside the slab these solutions are matched with the Rindler spacetime and with the Weyl-Levi-Civita spacetime, which represent special cases of the Kasner solution.

gr-qc↗

arXiv2019

Non-Canonical Inflation and Primordial Black Holes Production

We study a mechanism for the amplification of the inflationary scalar perturbation when the inflaton field action is non-canonical, i.e. the inflaton kinetic term has a non-standard form. For such a case the speed of sound of the perturbations generated during inflation is less than one and in general changes with time. Furthermore in such models, even when the scalar field potential is negligible, diverse inflationary attractors may exist. The possible effects of a speed of sound approaching zero during some stage of inflation may lead to a large amplification for the amplitude of the scalar spectrum which, on horizon re-entry during the radiation dominated phase, can collapse and form primordial black holes (PBH) of a mass $M_{\rm BH}\sim 10^{-15}M_{\odot}$ which may constitute a large fraction of the total Dark Matter (DM) today.

gr-qc↗

arXiv2018

Duality between static spherically or hyperbolically symmetric solutions and cosmological solutions in scalar-tensor gravity

We study static spherically and hyperbolically symmetric solutions of the Einstein equations in the presence of a conformally coupled scalar field and compare them with those in the space filled with a minimally coupled scalar field. We then study the Kantowski-Sachs cosmological solutions, which are connected with the static solutions by the duality relations. The main ingredient of these relations is an exchange of roles between the radial and the temporal coordinates, combined with the exchange between the spherical and hyperbolical two-dimensional geometries. A brief discussion of questions such as the relation between the Jordan and the Einstein frames and the description of the singularity crossing is also presented.

gr-qc↗

arXiv2018

Time in quantum theory, the Wheeler-DeWitt equation and the Born-Oppenheimer approximation

We compare two different approaches to the treatment of the Wheeler-DeWitt equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints, while the other uses the Born-Oppenheimer method. We apply both to a very simple cosmological model and observe that they give similar predictions. We also discuss the problem of time in non-relativistic quantum mechanics and some questions concerning the correspondence between classical and quantum theories.

gr-qc↗

arXiv2018

Comment about the vanishing of the vacuum energy in the Wess-Zumino model

We check the cancellation of the vacuum energy in the Wess-Zumino model at the two-loop order in the component field formalisms with and without auxiliary fields. We show that in both cases the vacuum energy is equal to zero. However, in the formalism where the auxiliary fields are excluded, the vanishing of the vacuum energy arises due to the cancellation between the potential and kinetic energies, while in the formalism with the auxiliary fields, both terms vanish separately.

hep-th↗

arXiv2017

The quantum Fokker-Planck equation of stochastic inflation

We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

hep-th↗

arXiv2016

Entangled Scalar and Tensor Fluctuations during Inflation

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the $T$, $E$, and $B$ modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.

hep-th↗

arXiv2014

A Cosmological Slavnov-Taylor Identity

We develop a method for treating the consistency relations of inflation that includes the full time-evolution of the state. This approach relies only on the symmetries of the inflationary setting, in particular a residual conformal symmetry in the spatial part of the metric, along with general properties which hold for any quantum field theory. As a result, the consistency relations that emerge, which are essentially the Slavnov-Taylor identities associated with this residual conformal symmetry, apply very generally: they are true of the full Green's functions, hold largely independently of the particular inflationary model, and can be used for arbitrary states. We illustrate these techniques by showing the form assumed by the standard consistency relation between the two and three-point functions for the primordial scalar fluctuations when they are in a Bunch-Davies state. But because we have included the full evolution of the state, this approach works for a general initial state as well and does not need to have assumed that inflation began in the Bunch-Davies state.

hep-th↗

arXiv2014

Renormalizing an initial state

The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable `renormalization conditions' on the Green's functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.

hep-th↗

arXiv2014

Do Mixed States save Effective Field Theory from BICEP?

The BICEP2 collaboration has for the first time observed the B-mode polarization associated with inflationary gravitational waves. Their result has some discomfiting implications for the validity of an effective theory approach to single-field inflation since it would require an inflaton field excursion larger than the Planck scale. We argue that if the quantum state of the gravitons is a mixed state based on the Bunch-Davies vacuum, then the tensor to scalar ratio r measured by BICEP is different than the quantity that enters the Lyth bound. When this is taken into account, the tension between effective field theory and the BICEP result is alleviated.

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