Cosmology E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

This book presents the main aspects of cosmology such as:
the cosmological principle, Hubble's law and the recession of galaxies
Newtonian and relativistic cosmology
the problems of flatness and the horizon, the De Sitter and Lemaitre models
the cosmological theories of the Big Bang and steady state
cosmological thermodynamics and cosmological eras
the role of dark matter

Leseprobe

Table of Contents

"Cosmology"

INTRODUCTION

BASIC CONCEPTS

NEWTONIAN COSMOLOGY

RELATIVISTIC COSMOLOGY

COSMOLOGICAL THEORIES

COSMOLOGICAL ERAS

DARK MATTER AND THE ORIGIN OF GALAXIES

"Cosmology"

SIMONE MALACRIDA

This book presents the main aspects of cosmology such as:

the cosmological principle, Hubble's law and the recession of galaxies

Newtonian and relativistic cosmology

the problems of flatness and the horizon, the De Sitter and Lemaitre models

the cosmological theories of the Big Bang and steady state

cosmological thermodynamics and cosmological eras

the role of dark matter

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I - BASIC CONCEPTS

Cosmological principle

Redshift

Hubble's law

Recession of galaxies

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II - NEWTONIAN COSMOLOGY

Introduction

Newtonian cosmological models

Critical density and effective density

Evolution in the Newtonian case

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III - RELATIVISTIC COSMOLOGY

Introduction

The curvature of space-time

Scale factor and metric

Density of matter-energy and pressure

Flatness problem

Horizon problem

De Sitter and Lemaitre models

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IV - COSMOLOGICAL THEORIES

Theory of the Big Bang and the steady state

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V - COSMOLOGICAL ERA

Cosmological thermodynamics

Brief overview of particles and fundamental interactions

Cosmological eras

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VI - DARK MATTER AND ORIGIN OF GALAXIES

First models _

Dark matter

INTRODUCTION

Cosmology is the science that deals with the study of the structure, origin and evolution of the Universe and, as such, represents one of the highest points of current physical knowledge.

In fact, all the previous theories converge in it, such as mechanics, thermodynamics, general relativity, but also quantum, nuclear and particle physics.

Therefore, a full understanding of cosmology cannot be separated from an awareness of the rudiments of these sectors of physics.

Nonetheless, in this book references to nuclear and particle physics and to general relativity will be presented, at least in their specific aspects.

For an in-depth study of these sectors, please refer instead to other specialized writings.

The purpose of cosmology is not to study the solutions of Einstein's equations for the gravitational field, but to apply these solutions on a universal scale and draw conclusions about the overall structure of space-time.

This book presents the main cosmological studies that have been substantially investigated over the last hundred years, with the fundamental contributions of general relativity and quantum physics.

The cosmological theories resulting from the reconciliation of these two sectors at the level of the structure of the Universe have made it possible to make a thermodynamic and temporal classification of the evolution of the Universe, without however solving all the problems in this regard.

The still mysterious role of dark matter, its entity and its composition, remains one of the most fascinating challenges of contemporary science.

THE

BASIC CONCEPTS

Cosmological principle

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Cosmology studies the structure, origin and evolution of the universe.

The foundation of modern cosmology is the so-called cosmological principle enunciated by Milne in 1933.

According to this principle, the universe must be fundamentally homogeneous (its appearance does not depend on the point of observation) and isotropic (its appearance is the same in all directions) on a large scale and subject everywhere to the same physical laws, so that any observer, placed at any point of it, is able to observe the same characteristics and to arrive at the same results.

It is, if you like, an extension of the Copernican principle according to which the earth is not a privileged place in our solar system.

The cosmological principle is not a demonstrable law, but a rational requirement of our intellect, which could not make the object of scientific knowledge a universe not subject everywhere to the same laws of nature.

A direct consequence of the cosmological principle is that the universe, to respect the conditions of homogeneity and isotropy, must be static or characterized by a homogeneous motion (expansion or contraction).

Experimental data collected in the second decade of the twentieth century confirm this prediction by demonstrating that the universe is in a state of homogeneous expansion.

The term "homogeneous" does not refer to the rate of expansion (which in fact, as we shall see, decreases with time), but to the fact that the expansion uniformly affects the entire universe (there is no portion that expands faster than another).

Redshift

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When we observe the spectra coming from bodies moving relative to us, they appear deformed.

In particular, the lines are displaced towards longer wavelengths if the light source has a relative moving away, while they are displaced towards shorter wavelengths if the source is animated by a relative moving towards.

Since in the visible spectrum the longer wavelengths correspond to red, while the shorter wavelengths correspond to blue, the phenomenon of wavelength "stretching" from a receding body is referred to as a redshift or red-shift, while the phenomenon of "compression" of the wavelength coming from an approaching body is referred to as blue-shift or blue-shift.

Naturally this does not mean that a radiation that has undergone a red-shift or a blue-shift actually appears red or blue to us, it only means that it appears to us with a wavelength respectively greater or less than the one it possessed at the moment of emission.

The intensity of the phenomenon is greater the greater the radial speed of departure or approach.

The phenomenon is analogous, as Doppler pointed out in 1842 and as Fizeau experimentally demonstrated in 1848, to that which occurs in acoustic waves.

It is in fact known that an approaching sound source produces a more acute sound, while moving away produces a more serious sound (Doppler effect).

Suppose now that a light source emits electromagnetic waves of period T and that the source is moving away from the observer at a speed v.

After having emitted the first crest, the second will be emitted after a time T.

But in the time T between one emission and the next, the source moves away by a space vT.

This distance increases the time required for the second crest to reach the observer by an amount vT/c.

The observer will therefore no longer measure a period T, but a longer period.

The time between the arrival of one crest and the arrival of the next will in fact be equal to

On the basis of this new period the observer will calculate a wavelength equal to

while the outgoing wavelength is related to the original period T

By dividing member by member the last two relations we obtain

from which simplifying

and finally

This parameter is commonly referred to as 'z', red-shift parameter.

It is therefore shown that if z is due to the Doppler effect it is equal to the ratio between the relative speed of the emitting body and the speed of light.

Since it is quite simple to calculate how much the wavelength of a line spectrum has increased or decreased by comparing it with the standard spectra of the various elements and compounds obtained in the laboratory, consequently the speed of departure or approach is immediately determined, expressed as percentage of the speed of light.

By determining the red-shift parameter (z) of some celestial bodies, values greater than 1 have been calculated.

Of course, this cannot mean that such bodies have speeds greater than those of light.

Instead, it means that they move away with speeds so close to those of light (relativistic speeds) that it is necessary to use a relativistic relation for the calculation of z.

In other words, Lorentz transformations are to be used.

In special relativity z is related to the departure velocity v by the following relations:

With these relations, it is seen that z can never be greater than 1.

In 1925 Slipher measured the red shifts of 45 galaxies.

With the exception of Andromeda and a few other galaxies which had shown a blueshift, and therefore a relative motion of approach, all the others showed a more or less marked redshift.

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