The model of the future behaviour of the universe developed here is an extension of that developed in [1] and [2] from the indefinite past until the present time.
The first part of the trajectory of the deceleration parameter of cosmology into the future is obtained by extending the exponential variation with time of the trajectory from the end of the cosmic jerk until the present time, as developed in [1]. It is shown, in the future, when the magnitude of the deceleration parameter becomes, -1, that the universe attains a state where the volumetric strain rate becomes a minimum. It is argued that, for this reason, the universe then remains in this state indefinitely.
The trajectory of the deceleration parameter of the universe from the present time into the indefinite future, as shown in the diagram in the body of the work, is then simply an exponential curve followed by a horizontal straight line.
Table of Contents
Introduction
The acceleration of space at the boundary of the universe
The future trajectory of the deceleration parameter
The special character of the state of the universe along the line q = -1
Discussion
References
Objectives and Topics
This work aims to present a model for the future evolution of the universe by extending existing trajectories of the deceleration parameter. It investigates the long-term state of the cosmos under the condition where the deceleration parameter reaches a limit of -1, analyzing the implications for the volumetric strain rate and the expansion of space.
- Modeling the future trajectory of the deceleration parameter
- Mathematical determination of expansion limits at q = -1
- Analysis of volumetric strain rates and cosmic stability
- Calculation of scale factors and vacuum properties
Excerpt from the Book
The future trajectory of the deceleration parameter
It was shown in [1] that the trajectory of the deceleration parameter from the time of the end of the cosmic jerk until the present time, under the assumptions shown there, was given explicitly by: q = exp (0.8160679 * 10^-18 * (t0 - t)) - 1.4.
We now extend this trajectory into the future, not, it should be emphasised, indefinitely. Now, Hubble’s parameter, H may be expressed as: H = 1/a da/dt, where a is the scale factor. If this expression is differentiated wrt t, we get: dH/dt = 1/a d^2a/dt^2 - 1/a^2 (da/dt)^2, Which may be written: dH/dt = 1/a d^2a/dt^2 - H^2.
The deceleration parameter, q, is defined as: q = - a / (da/dt)^2 d^2a/dt^2. Combining (9) and (10) we obtain: 1/H^2 dH/dt + (1 + q) = 0. Examination of (11) shows that, if q exceeds -1 then, dH/dt becomes positive, and hence, thereafter, the Hubble parameter increases with the passage of time. We cannot advance any plausible argument in support of an increasing Hubble parameter with time and hence we take q = -1 to be the absolute negative limit of the deceleration parameter.
Summary of Chapters
Introduction: This chapter contextualizes the research within existing cosmological literature and defines the scope of the proposed model as an extension of previous work.
The acceleration of space at the boundary of the universe: This section establishes the fundamental mathematical relationships regarding the linear acceleration of space at the cosmic boundary and defines key variables.
The future trajectory of the deceleration parameter: This chapter mathematically derives the path of the deceleration parameter into the future and justifies the limit of q = -1.
The special character of the state of the universe along the line q = -1: This chapter explores the physical state of the universe at the limit where the deceleration parameter is -1, focusing on volumetric strain rates.
Discussion: This chapter reviews the model's implications, calculates specific physical dimensions such as the Planck Universe volume, and concludes with a synthesis of the findings.
References: This section lists the scientific sources and theoretical frameworks underpinning the research.
Keywords
Cosmology, Deceleration Parameter, Hubble Parameter, Volumetric Strain Rate, Expansion of Space, Scale Factor, Vacuum Frequency, Planck Universe, Cosmic Evolution, Physical Constants
Frequently Asked Questions
What is the primary focus of this work?
This paper focuses on modeling the long-term future evolution of the universe by extending existing mathematical trajectories of the deceleration parameter.
What are the central thematic fields?
The core themes include theoretical cosmology, the dynamics of space expansion, the behavior of the deceleration parameter, and the calculation of cosmic physical properties.
What is the primary goal of this research?
The goal is to determine the future state of the universe and identify the limit of the deceleration parameter, providing a stable model for the indefinite future.
What scientific method is employed?
The author uses mathematical modeling, specifically analyzing differential equations related to the scale factor, Hubble’s parameter, and the deceleration parameter.
What does the main body of the text cover?
The main body covers the mathematical derivation of future cosmic trajectories, the definition of the q = -1 limit, and the interpretation of volumetric strain rates.
Which keywords characterize this work?
Key terms include Cosmology, Deceleration Parameter, Hubble Parameter, Volumetric Strain Rate, and Cosmic Evolution.
What significance does the value q = -1 hold in this model?
It represents the absolute negative limit of the deceleration parameter, where the volumetric strain rate reaches a minimum, suggesting a stable indefinite state for the universe.
How is the volume of the 'Planck Universe' calculated in this model?
It is calculated by multiplying the number of enclosures (based on the Eddington number of baryons) by the cube of the Planck Wavelength.
What conclusion is drawn about the 'Planck Grain'?
The author suggests that at a time prior to the inception of the universe, its volume was roughly equivalent to the size of a grain of sugar.
- Quote paper
- William Fidler (Author), 2018, A possible future evolution of the universe, Munich, GRIN Verlag, https://www.grin.com/document/416774
