INFLATION AND SQUEEZED STATES: LATTICE SCHRÖDINGER PICTURE

2009 ◽  
Vol 24 (07) ◽  
pp. 497-508 ◽  
Author(s):  
JUNG-JENG HUANG
Keyword(s):  
Scalar Field ◽  
Power Spectrum ◽  
Particle Production ◽  
Squeezed States ◽  
De Sitter ◽  
Squeezed Vacuum ◽  
Slow Roll ◽  
Vacuum States ◽  
Schrödinger Picture ◽  
Inflationary Models

In lattice Schrödinger picture, the wave functionals of the squeezed vacuum states of a free real scalar field in de Sitter space are constructed explicitly in momentum space by using the method of instantaneous Hamiltonian diagonalization. The modified power spectrum and particle production in the general mixed, squeezed initial states are also presented. For the massless minimally coupled scalar field which is relevant to slow roll inflationary models, we recover the power spectrum of scalar fluctuations for the squeezed vacuum states, and show that the evolution of the squeezed vacuum states exhibits an attractor behavior. The case of a massless conformally coupled scalar field is also discussed.

BEHAVIOR OF NON-CLASSICAL INFLATON IN THE FRW UNIVERSE

2013 ◽  
Vol 28 (37) ◽  
pp. 1350168 ◽  
Author(s):  
K. K. VENKATARATNAM
Keyword(s):  
Scalar Field ◽  
Particle Production ◽  
Gordon Equation ◽  
Frw Universe ◽  
Relative Deviation ◽  
Squeezed Vacuum ◽  
Slow Roll ◽  
Vacuum States ◽  
Klein Gordon ◽  
Klein Gordon Equation

We study the semiclassical Einstein equation and inflaton in the oscillatory region of the FRW Universe. We study the relative deviation of particle production in coherent and squeezed vacuum states for a minimally coupled scalar field in the oscillatory region of flat FRW Universe. We also study the behavior of inflaton field in non-oscillatory region. We examine whether the solution obtained in slow-roll approximation satisfies Klein–Gordon equation and commutation relation as well.

Inflationary dynamics in f(𝒢) gravity

2017 ◽  
Vol 26 (04) ◽  
pp. 1750030 ◽  
Author(s):  
M. Sharif ◽  
Ayesha Ikram
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Power Spectrum ◽  
Universe Model ◽  
De Sitter ◽  
Slow Roll ◽  
Homogeneous Universe ◽  
Text Model ◽  
Flow Functions ◽  
Hubble Flow

This paper investigates inflationary dynamics for isotropic and homogeneous universe model in the background of [Formula: see text] gravity. We construct Hubble-flow functions, slow-roll parameters, amplitude of scalar power spectrum, spectral index and tensor–scalar ratio for a particular form of equation of state which describes quasi-de Sitter expansion. The dynamics of inflationary epoch is analyzed for scalar field as well as fluid cosmology with viable power-law [Formula: see text] model. We obtain different potential functions that correspond to chaotic inflation and Starobinsky type models. The graphical behavior of these parameters shows compatible results with observational Planck 2015 data in this gravity.

scholarly journals Bohm Quantum Trajectories of Scalar Field in Trans-Planckian Physics

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jung-Jeng Huang
Keyword(s):  
Scalar Field ◽  
Wave Theory ◽  
Vacuum State ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
De Sitter ◽  
Pilot Wave ◽  
In Trans ◽  
Schrödinger Picture ◽  
Pilot Wave Theory

In lattice Schrödinger picture, we investigate the possible effects of trans-Planckian physics on the quantum trajectories of scalar field in de Sitter space within the framework of the pilot-wave theory of de Broglie and Bohm. For the massless minimally coupled scalar field and the Corley-Jacobson type dispersion relation with sextic correction to the standard-squared linear relation, we obtain the time evolution of vacuum state of the scalar field during slow-roll inflation. We find that there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, which provides a possible mechanism to solve the riddle of the smallness of the cosmological constant.

scholarly journals REAL OR IMAGINARY? ON PAIR CREATION IN DE SITTER SPACE

2010 ◽  
Vol 25 (33) ◽  
pp. 2815-2823 ◽  
Author(s):  
EMIL T. AKHMEDOV
Keyword(s):  
Scalar Field ◽  
Path Integral ◽  
Effective Action ◽  
Particle Production ◽  
De Sitter Space ◽  
Pair Creation ◽  
De Sitter ◽  
Feynman Propagator

Using properly defined Feynman propagator we obtain nonzero imaginary contribution to the scalar field effective action in even-dimensional de Sitter space. Such a propagator follows from the path integral in de Sitter space and obeys composition principle proposed in arXiv:0709.2899. The obtained expression for the effective action shows particle production with the Gibbons–Hawking rate.

scholarly journals PROBING THE VACUUM STRUCTURE OF SPACETIME

2012 ◽  
Vol 12 ◽  
pp. 310-319 ◽  
Author(s):  
SANG PYO KIM
Keyword(s):  
Scalar Field ◽  
Effective Action ◽  
Particle Production ◽  
Constant Electric Field ◽  
Massive Scalar ◽  
De Sitter ◽  
Charged Scalar ◽  
Massive Scalar Field ◽  
Vacuum Structure ◽  
Gravitational Analog

We explore the question of how to probe the vacuum structure of space time by a massive scalar field through interaction with background gravitons. Using the Γ-regularization for the in-/out-state formalism, we find the effective action of a scalar field in a conformally, asymptotically flat spacetime and a four-dimensional de Sitter space, which is a gravitational analog of the Heisenberg-Euler and Schwinger effective action for a charged scalar in a constant electric field. The effective action is nonperturbative in that it sums all one-loop diagrams with arbitrary number of external lines of gravitons. The massive scalar field becomes unstable due to particle production, the effective action has an imaginary part that determines the decay rate of the vacuum, and the out-vacuum is unitarily inequivalent to the in-vacuum.

Primordial quantum perturbations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Slow Roll ◽  
Inflationary Models

This chapter shows that fluctuations of quantum origin are generated during inflation and that this process supplies initial conditions compatible with the observations. These fluctuations are therefore an important prediction of inflationary models. The chapter thus begins with a study of perturbations during inflation, proceeding in a similar manner to the previous chapter by finding the perturbation of the energy–momentum tensor of the scalar field. Another method of deriving the equations of motion of the perturbations is to start from the action of general relativity coupled to a scalar field, and expand to second order in the metric and scalar field perturbations. The chapter then proceeds with the determination of the initial conditions and the slow-roll inflation.

scholarly journals Interaction between Maxwell field and charged scalar field in de Sitter universe

2015 ◽  
Vol 30 (16) ◽  
pp. 1550088 ◽  
Author(s):  
Cosmin Crucean ◽  
Mihaela-Andreea Băloi
Keyword(s):  
Scalar Field ◽  
Particle Production ◽  
Perturbation Expansion ◽  
Maxwell Field ◽  
De Sitter ◽  
Charged Scalar ◽  
Gravitational Fields ◽  
Sitter Background ◽  
Charged Scalar Field ◽  
De Sitter Universe

We study the theory of interaction between charged scalar field and Maxwell field in de Sitter background. Solving the equation of interacting fields, we define the in–out fields as asymptotic free fields and construct the reduction formalism for scalar field. Then we derive the perturbation expansion of the scattering operator. The first-order transition amplitudes corresponding to particle production from de Sitter vacuum and pair production in an external field are analyzed. We show that all these effects are important only in strong gravitational fields and vanish in the flat limit.

PILOT-WAVE SCALAR FIELD THEORY IN DE SITTER SPACE: LATTICE SCHRÖDINGER PICTURE

2010 ◽  
Vol 25 (01) ◽  
pp. 1-13 ◽  
Author(s):  
JUNG-JENG HUANG
Keyword(s):  
Scalar Field ◽  
Vacuum State ◽  
De Sitter Space ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
De Sitter ◽  
Minimal Coupling ◽  
Pilot Wave ◽  
The Difference ◽  
Schrödinger Picture

In the lattice Schrödinger picture, we find the de Broglie–Bohm quantum trajectories for the eigenstates of a generically coupled free real scalar field in de Sitter space. For the massless minimally coupled scalar field which has exact quantum trajectory, we evaluate both the time evolution of vacuum state and the possible effects of initial quantum nonequilibrium on the power spectrum of the primordial inflaton and curvature fluctuations in the slow-roll approximation. We reproduce the results that were already presented by Valentini who considered only the massless minimal coupling case. In addition we cover both massive minimal and massive non-minimal coupling cases which are the extension of Valentini's work. Finally we discuss the difference between de Broglie's first-order dynamics and Bohm's second-order dynamics in finding the quantum trajectories.

EXCITED STATES OF DE SITTER SPACE SCALAR FIELDS: LATTICE SCHRÖDINGER PICTURE

2006 ◽  
Vol 21 (22) ◽  
pp. 1717-1725 ◽  
Author(s):  
JUNG-JENG HUANG
Keyword(s):  
Scalar Field ◽  
Excited States ◽  
Momentum Space ◽  
Scalar Fields ◽  
De Sitter Space ◽  
De Sitter ◽  
Minimal Coupling ◽  
Real Scalar ◽  
Schrödinger Picture

In lattice Schrödinger picture, the wave functionals of a free real scalar field in de Sitter space for the Bunch–Davies vacuum and the corresponding excited states are given explicitly in momentum space for the following coupling cases: (i) massless conformal couplng, (ii) massless minimal coupling, and (iii) massive minimal coupling. Implications of these solutions for inflationary scenarios in cosmology are also discussed.

scholarly journals Generation of Coherent and Spatially Squeezed States of an Electromagnetic Beam in a Planar Inhomogeneous Dielectric Waveguide

Photonics ◽  
2019 ◽  
Vol 6 (3) ◽  
pp. 84 ◽  
Author(s):  
Anna Bogatskaya ◽  
Andrey Schegolev ◽  
Nikolay Klenov ◽  
Alexander Popov
Keyword(s):  
Single Mode ◽  
Waveguide Structure ◽  
Squeezed States ◽  
Practical Applications ◽  
Electromagnetic Beam ◽  
Squeezed Vacuum ◽  
Inhomogeneous Dielectric ◽  
Vacuum States ◽  
Mode Excitation ◽  
Index Gradient

We use slow-varying amplitude approximation (SVA) for the wave equation to study both analytically and numerically propagation of an electromagnetic beam in the waveguide structure with parabolic susceptibility spatial dependence. Such a structure is similar to the harmonic oscillator in quantum mechanics. We analyze this structure as a single mode guide and introduce the notion of number of “photons” in the mode. In particular, we pay special attention to the possibility of effective build-up of the coherent and spatially squeezed vacuum states of the mode that can be of interest for a number of practical applications. The way to provide these types of mode excitation is suggested. Several applications for controlling the mode composition of an electromagnetic wave in the parabolic index-gradient waveguide for various frequency ranges are considered.

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