How did the universe begin?

Table of Contents:

Abstract………………………………………………………………………………………….1

Introduction……………………………………………………………………………………..1

Rise of the Big Bang Model…………………………………..……………………………….2

Mathematical Basis of Big Bang Cosmology………………………………………………..3

1. Friedmann-Robertson-Walker(FRW) Metric………………..………………………..3
2. Friedmann Equations……………………………………………….………………….4

3 Pillars of the Big Bang Model……………………………………..…………………………5

1. Hubble’s Law……………………………………………………………………………..6
2. Cosmic Microwave Background Radiation(CMBR) …………………………………7
3. Big Bang Nucleosynthesis………………………………………………………………8

Implications(?) of the Big Bang Model

Conclusion

Bibliography

Abstract

(Insert abstract)

Introduction

Cosmology is the study of the entire universe i.e the origin, evolution and its ultimate fate. Within the past 100 years, tremendous advances have been made. The universe was first thought of as static by Einstein but was later confirmed by Hubble’s observation that the universe is in fact expanding. This discovery led to the development of the Big Bang theory which is still currently being refined. This paper aims to offer an explanation of the origins of the universe by using Big Bang model. In the first section, we would briefly look at the history of modern cosmology, followed by a summary of the mathematical basis that forms the Big Bang theory as well as present the three main lines of evidence that support the Big Bang theory. Lastly, attention is drawn to the relationship between the scientific theories/models and the real world, pointing out that models can only partially represent reality and

Rise of the Big Bang Model:

Soon after Einstein had formulated the general theory of relativity, in 1917 he postulated that the universe is homogenous, isotropic, static, with a constant mean mass density and curvature of space. However, this model was not permitted by his field equations as they suggested that the universe would collapse due to the gravitational force acting on matter. Therefore, he added a cosmological constant, Λ to the field equation to counteract this effect.

In 1922, Alexander Friedmann used Einstein’s field equations to show that a dynamical universe was also allowed. Five years later, George Lemaître, a physicist and Belgian Roman Catholic priest, unaware of Friedmann’s work, independently came up with a dynamical model that included mass and pressure. He managed to theoretically derive a linear relation between the recession velocity and distance of the nebulae using the latest observations provided by Slipher (whose data was published in Eddington’s book of 1923) and Hubble [2]. This relationship is currently known as Hubble’s Law. Lemaître interpreted the observed redshifts as an effect of cosmic expansion. He published his findings that year in an obscure journal in French and sent a copy to his former mentor, Eddington. Unfortunately, it went unnoticed. During the 1927 Solvay congress, Lemaître took the opportunity to give a copy of the reprint of his findings to Einstein, who found it abominable as it made no sense to him from a physical point of view.  According to Lemaître, it seemed like Einstein was unaware of the cosmological observations then [3].

In 1929, Hubble published a paper which led to the realisation of an expanding universe. Using data on Doppler redshifts mostly given by Slipher combined with the measured distances to the spiral nebulae, he too found a linear correlation between distances and velocities [4]. Hubble’s work was very similar to Lemaître’s, however he merely interpreted them as Doppler effects and never considered them as a consequence of an expanding universe.

During the Royal Astronomical Society (RAS) meeting that took place in 1930, Eddington discussed the instability of Einstein’s model and called for the search of new explanations for the recession of velocities using dynamical models [5]. Lemaître read the proceedings of the meeting and immediately wrote to Eddington to remind him of his paper published in 1927. Eddington was impressed and arranged for it to be translated into English. It was published in the monthly notices of the RAS in 1931. The paragraphs concerning Hubble’s law were deleted by Lemaître himself and thus he was never credited for Hubble’s law and the discovery of an expanding universe [6]. In the same year, Lemaître hypothesised that the universe came into being, governed by the laws of quantum mechanics, from an initial point known as the “Primeval Atom” [7]. However, the idea was poorly received by the scientific community due to Lemaître’s personal religious beliefs.

In 1949, Thomas Gold, Hermann Bondi together with Fred Hoyle came up with the “steady-state theory” which asserts that the universe was unchanging and eternal; matter is continuously created to maintain a constant density in the universe [12]. Hoyle opposed the idea of an expanding universe from a singularity and made fun of it on a radio interview. He accidentally coined the term “Big Bang”, which was since then popularised even though it was meant in a pejorative sense.

Mathematical Basis of Big Bang cosmology:

1. Friedmann-Robertson-Walker(FRW) Metric:

In General Relativity, the metric used to describe the geometry of spacetime is a fundamental quantity. In order to allow for a dynamic universe, that is also homogeneous and isotropic, Robertson and Walker independently came up with the most generic metric that allowed the radius of curvature to be a function of time [8]. In spherical polar coordinates, this can be written as:

${\text{d}s}^2=\mathrm{ }–{c^2\text{d}t}^2–\mathrm{ }{\left(\frac{\text{d}\bar{r}}{\sqrt{1–K{r}^2}}\right)}^2– {\left(\bar{r} \text{d}\theta \right)}^2– {\left(\bar{r} \text{sin }\mathit{\theta }\text{d}\varphi \right)}^2$

.                       (1)

By introducing a cosmic scale factor that is dependent on time

$t$

,

$a\left(t\right)$

, the radial coordinate is transformed to a comoving coordinate:

$\bar{r}\left(t\right)=\mathit{ a}\left(t\right)\bullet r$

  . (2)

Furthermore, the radius of curvature is also affected by cosmic expansion so it can be expressed in terms of the scale factor and a constant

$k$

that is independent of time:

$K\left(t\right)= \frac{k}{a^2\left(t\right)}$

  .   (3)

After making substitutions for

$\bar{r}\left(t\right)$

and

$\mathit{ K}\left(t\right)$

into equation (1), the following is obtained:

${\text{d}s}^2=\mathrm{ }–{c^2\text{d}t}^2–\mathrm{ }{a}^2\left(t\right)\left[\frac{{\text{d}r}^2}{1–k{r}^2}+r^2\left({\text{d}\theta }^2+{\text{sin}}^2\mathit{\theta }{\text{d}\varphi }^2 \right)\right]$

    (5) 

With a final change of variables

$r\to S_k\left(r\right)$

, the metric can also be expressed as