The ‘fabric’ of the model presented here consists of identical, contiguous cubes of space, each of which is occupied by a simple quantum harmonic oscillator. A possible structure is proposed for the ensemble of cubes, and it is shown also that other configurations, on all scales can exist in the ensemble, even although the members of that collection are absolutely identical.
The expansion of space is considered initially from the standpoint of a universe which is not accelerating, and equations are developed which relate to this ‘coasting’ condition, and, in which the Hubble parameter, H, is shown to be a function of time. These equations are extended by the inclusion of the deceleration parameter of cosmology, q, treating q as a parameter.
Table of Contents
Abstract
Introduction
A stacking structure for the universe
The expansion of space
The cosmic jerk
The Hubble parameter.
The expansion of space relative to an observer.
Discussion
References.
Objectives and Research Themes
This work proposes a model of the universe where the vacuum is structured as a collection of identical, frequency-quantized, simple quantum harmonic oscillators. The research aims to develop a mathematical framework for space expansion that incorporates the transition from a decelerating to an accelerating state, known as the "cosmic jerk," and investigates the resulting temporal behavior of the Hubble parameter and cosmological redshift.
- Mathematical modeling of space expansion using quantum harmonic oscillators.
- Analysis of the "cosmic jerk" as a transition phase in universal expansion.
- Examination of the Hubble parameter as a time-dependent function rather than a constant.
- Investigation of observer-centered geometry in an infinite universe.
Excerpt from the Book
The cosmic jerk
From the results of the surveys of Schmidt, Riess et al* and Perlmutter et al**, it was reported by Riess in 2003 that the universe went suddenly from a decelerating state to an accelerating state approximately five billion years ago. In Mechanics such an effect is called a jerk.
Whilst the following analysis does not explain the origin of the cosmic jerk it will be shown to provide a way in which the speed of expansion of the universe at the jerk may be determined. The equations developed are somewhat complicated and so, for the purpose of illustration, a rough approximation to the speed at the jerk is calculated.
In view of the above mentioned experimental observations we advance the suggestion that the deceleration parameter q is not a constant thing but is a function of time. In the immediate vicinity of the beginning of the universe it is accepted generally that the universe expanded very rapidly. The acceleration then decreased and the universe entered a phase of deceleration. From equation (9) it may then be inferred that q was very large, and negative, although it is moot whether or not this happened instantaneously.
Summary of Chapters
Abstract: Provides an overview of the proposed cubical vacuum model and its derivation of a time-dependent deceleration parameter to explain the cosmic jerk.
Introduction: Discusses the theoretical background of a universe modeled as contiguous cubes and the experimental observations of space expansion.
A stacking structure for the universe: Explores the arrangement of fundamental cubic oscillators and the conditions required to maintain isotropy.
The expansion of space: Develops the fundamental equations for the rate of expansion of space based on the properties of the vacuum oscillators.
The cosmic jerk: Proposes that the deceleration parameter is a function of time to account for the transition from deceleration to acceleration.
The Hubble parameter.: Redefines the Hubble parameter as a temporally-local rate of volumetric strain.
The expansion of space relative to an observer.: Analyzes the geometry of observations from the perspective of an observer located within a cube.
Discussion: Interprets the mathematical results, specifically concerning the relationship between wavelengths of the vacuum and radiation over time.
References.: Lists the supporting literature and previous work by the author on this vacuum model.
Keywords
Quantum harmonic oscillators, Hubble parameter, Cosmic jerk, Vacuum model, Space expansion, Deceleration parameter, FLRW universe, Isotropy, Cosmological redshift, Dark energy, Volumetric strain, Frequency quantization, Observer-centered, Relativity, Quantum mechanics
Frequently Asked Questions
What is the core subject of this publication?
The paper proposes a theoretical model where the universe's vacuum is structured as an ensemble of identical, frequency-quantized quantum harmonic oscillators, rather than a homogeneous continuum.
What are the central thematic fields explored?
The study integrates results from quantum mechanics and general relativity to explain the dynamics of space expansion, the variation of the Hubble parameter, and the cosmic jerk.
What is the primary objective of the research?
The goal is to mathematically model how the speed of space expansion changes over time, specifically addressing the transition from deceleration to acceleration observed five billion years ago.
What scientific methods are utilized?
The author employs differential and integral calculus to derive equations describing the temporal evolution of space, using the deceleration parameter as a non-constant function of time.
What is covered in the main body of the work?
The body covers the geometric stacking of cubic space, the derivation of expansion rates, the mathematical treatment of the cosmic jerk, and the interpretation of the Hubble parameter as a strain rate.
Which keywords best characterize this work?
The key concepts include quantum harmonic oscillators, the cosmic jerk, the Hubble parameter, and the observer-centered nature of an infinite, structured universe.
How does the author interpret the "Hubble parameter"?
The author argues that the Hubble parameter should be viewed as a function of time and interprets it as one-third of the temporally-local rate of volumetric strain.
Does the model support the Big Bang theory?
The model displays hallmarks of a Big Bang, such as singularities in the past, but the author contends that by treating the vacuum as discrete oscillators, it avoids the "infinities and zeros" found in standard models.
What is the significance of the "coasting condition" mentioned in the text?
The coasting condition represents a state where the deceleration parameter is zero, acting as a transition point in the expansion history of the universe.
- Arbeit zitieren
- William Fidler (Autor:in), 2018, Structure and Expansion of a Universe whose Vacuum is modelled as a Set of identical, bi-modal, frequency-quantised, simple quantum harmonic oscillators., München, GRIN Verlag, https://www.grin.com/document/416773
