scholarly journals Vacuum quantum effects on Lie groups with bi-invariant metrics

2019 ◽  
Vol 16 (08) ◽  
pp. 1950122
Author(s):  
A. I. Breev ◽  
A. V. Shapovalov
Keyword(s):  
Scalar Field ◽  
Lie Groups ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Particle Creation ◽  
Vacuum Expectation ◽  
Rotation Group ◽  
Momentum Tensor ◽  
Invariant Metrics ◽  
Field Equations

We consider the effects of vacuum polarization and particle creation of a scalar field on Lie groups with a non-stationary bi-invariant metric of the Robertson–Walker type. The vacuum expectation values of the energy momentum tensor for a scalar field determined by the group representation are found using the noncommutative integration method for the field equations instead of separation of variables. The results obtained are illustrated by the example of the three-dimensional rotation group.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

The backreaction of massive scalar field on FLRW and de Sitter spaces

2020 ◽  
Vol 17 (03) ◽  
pp. 2050033
Author(s):  
M. R. Setare ◽  
M. Sahraee
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Friedmann Equation ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Scale Factor ◽  
Massive Scalar ◽  
De Sitter ◽  
Massive Scalar Field ◽  
Quantum Energy

In this paper, we obtain the effect of backreaction on the scale factor of the Friedmann–Lemaître–Robertson–Walker (FLRW) and de Sitter spaces. We consider a non-minimally coupled massive scalar field to the curvature scalar. For our purpose, we use the results of vacuum expectation values of energy–momentum tensor, which have been obtained previously. By substituting the quantum energy density into the Friedmann equation, we obtain the linear order perturbation of the scale factor. So, the effect of backreaction leads to the new scale factor.

scholarly journals Quantum Effects in the Spacetime of a Magnetic Flux Cosmic String

2003 ◽  
Vol 18 (12) ◽  
pp. 2093-2098 ◽  
Author(s):  
M. E. X. Guimarães ◽  
A. L. N. Oliveira
Keyword(s):  
Scalar Field ◽  
Magnetic Flux ◽  
Cosmic String ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Expectation Values ◽  
Charged Scalar ◽  
Average Value ◽  
Charged Scalar Field

In this work we compute the vacuum expectation values of the energy-momentum tensor and the average value of a massive, charged scalar field in the presence of a magnetic flux cosmic string for both zero- and finite-temperature cases.

scholarly journals Bulk Viscosity and Particle Creation in Brans - Dicke Theory

1999 ◽  
Vol 52 (6) ◽  
pp. 1039 ◽  
Author(s):  
G. P. Singh ◽  
A. Beesham
Keyword(s):  
Scalar Field ◽  
Bulk Viscosity ◽  
Particle Number ◽  
Particle Creation ◽  
Particle Number Density ◽  
Number Density ◽  
Viscous Stress ◽  
Field Equations ◽  
Bulk Viscous

The effect of bulk viscosity on the evolution of the spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) models in the context of open thermodynamical systems, which allow for particle creation, is analysed within the framework of Brans–Dicke (BD) theory. The BD field equations are modified with the incorporation of a creation pressure and bulk viscous stress. A class of physically plausible models has been taken into consideration. The behaviour of the particle number density and bulk viscosity is discussed with the evolution of the Brans–Dicke scalar field.

scholarly journals Bianchi Type I Cosmological Models with Expansion Driven by Particle Creation

2018 ◽  
Author(s):  
Kalyani Desikan
Keyword(s):  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Particle Creation ◽  
Momentum Tensor ◽  
Conservation Equation ◽  
Type I ◽  
Field Equations ◽  
Bianchi Type I ◽  
Energy Conservation Equation ◽  
The Universe

A study of Bianchi Type I cosmological model is undertaken in the framework of creation of particles. To accommodate the creation of new particles, the universe is regarded as an Open thermodynamical system. The energy conservation equation is modified with the incorporation of a creation pressure in the energy momentum tensor. Exact solutions of the field equations are obtained (i) for a particular choice of the particle creation function and (ii) by considering the deceleration parameter to be constant. In the first model the behavior of the solution at late times is investigated. The physical aspects of the model have also been discussed. In the case of the second model we have restricted our analysis to the power law behaviour for the average scale factor. This leads to a particular form for the particle creation function. The behavior of the solution is investigated and the physical aspects of the model have also been discussed for the matter dominated era.

scholarly journals T-dualization of Gödel string cosmologies via Poisson–Lie T-duality approach

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Ali Eghbali ◽  
Reza Naderi ◽  
Adel Rezaei-Aghdam
Keyword(s):  
Lie Groups ◽  
Effective Action ◽  
Three Dimensional ◽  
Target Space ◽  
Loop Order ◽  
Field Equations ◽  
First Order ◽  
Self Duality ◽  
Duality Approach ◽  
Dual Models

AbstractUsing the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $$\alpha '$$ α ′ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to $$\alpha '$$ α ′ -corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as $$A_2$$ A 2 , $$A_2 \oplus A_1$$ A 2 ⊕ A 1 and $$SL(2, \mathbb {R})$$ S L ( 2 , R ) . In this way, the PL self-duality of $$AdS_3 \times \mathbb {R}$$ A d S 3 × R space is discussed.

scholarly journals UNCERTAINTY RELATIONS FOR COSMOLOGICAL PARTICLE CREATION AND EXISTENCE OF LARGE FLUCTUATIONS IN REHEATING

2011 ◽  
Vol 20 (14) ◽  
pp. 2795-2801
Author(s):  
ALI KAYA
Keyword(s):  
Scalar Field ◽  
Uncertainty Relation ◽  
Particle Creation ◽  
Random Variable ◽  
Vacuum Expectation ◽  
Uncertainty Relations ◽  
Large Fluctuations ◽  
Short Time ◽  
Reheating Process ◽  
Classical Background

We derive an uncertainty relation for the energy density and pressure of a quantum scalar field in a time-dependent, homogeneous and isotropic, classical background, which implies the existence of large fluctuations comparable to their vacuum expectation values. A similar uncertainty relation is known to hold for the field square since the field can be viewed as a Gaussian random variable. We discuss possible implications of these results for the reheating process in scalar field driven inflationary models, where reheating is achieved by the decay of the coherently oscillating inflaton field. Specifically we argue that the evolution after backreaction can seriously be altered by the existence of these fluctuations. For example, in one model the coherence of the inflaton oscillations is found to be completely lost in a very short time after backreaction starts. Therefore we argue that entering a smooth phase in thermal equilibrium is questionable in such models and reheating might destroy the smoothness attained by inflation.

scholarly journals Gravitationally Induced Particle Production through a Nonminimal Torsion–Matter Coupling

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 227
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
Emmanuel N. Saridakis
Keyword(s):  
Particle Production ◽  
Energy Momentum Tensor ◽  
Open Systems ◽  
High Redshift ◽  
Particle Creation ◽  
Irreversible Thermodynamics ◽  
Momentum Tensor ◽  
Covariant Formulation ◽  
Field Equations ◽  
Matter Coupling

We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion–matter coupling. An intriguing feature of this theory is that the divergence of the matter energy–momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard ΛCDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. We consider specific models, and we show that cosmology with a torsion–matter coupling can almost perfectly reproduce the ΛCDM scenario, while it additionally gives rise to particle creation rates, creation pressures, and entropy generation through gravitational matter production in both low and high redshift limits.

scholarly journals Sectional and Ricci Curvature for Three-Dimensional Lie Groups

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Gerard Thompson ◽  
Giriraj Bhattarai
Keyword(s):  
Automorphism Group ◽  
Lie Groups ◽  
Ricci Curvature ◽  
Lie Group ◽  
Systematic Study ◽  
Three Dimensional ◽  
Invariant Metrics ◽  
Curvature Function ◽  
Invariant Metric ◽  
Curvature Tensors

Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.

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