# “All that Matter … in One Big Bang …”, &Other Cosmological Singularities

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## Abstract

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## 1. Introduction

## 2. The Very Origins: Leavitt, Slipher, Hubble, Lemaître, Einstein, …

#### 2.1. Old Models of the Universe

#### 2.2. Henrietta Leavitt

#### 2.3. Vesto Slipher

#### 2.4. A Great Debate

#### 2.5. An Island Universe

“FINDS SPIRAL NEBULAE ARE STELLAR SYSTEMS; Dr. Hubbell Confirms View That They are ‘Island Universes’ Similar To Our Own.WASHINGTON, Nov. 22. Confirmation of the view that the spiral nebulae, which appear in the heavens as whirling clouds, are in reality distant stellar systems, or “island universes”, has been obtained by Dr. Edwin Hubbell of the Carnegie Institution’s Mount Wilson observatory, through investigations carried out with the observatory’s powerful telescopes.”

#### 2.6. Hubble’s Law

“… your velocities and my distances…”

“… the first steps in a new field are the most difficult and the most significant. Once the barrier is forced further development is relatively simple.”

#### 2.7. The Interpretation of Hubble’s Law

“ … we use the term ‘apparent velocities’ in order to emphasize the empirical feature of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.”

#### 2.8. George Lemaître and the Expanding Universe: A Perfect Example of Stigler’s Law of Eponymy

“No scientific discovery is named after its original discoverer”.

## 3. “All Matter … in One Big Bang …”

#### 3.1. Some Common Popular Sources on the Big Bang

#### 3.2. Fred Hoyle

“The concept of nucleosynthesis in stars was first established by Hoyle in 1946”.

“… for it’s an irrational process, and can’t be described in scientific terms”; “… belief in the first page of Genesis”.

#### 3.3. The ‘Free Lunch’ Concept

“… a closed universe can equal zero energy. All mass/energy is positive and all gravitational energy is negative, and they may cancel each other out, leading to a universe of zero energy”.

#### 3.4. A Big Bang!

“[Lemaître’s model implies that] … all matter in the universe was created in one Big Bang at a particular time …”.

“Everybody knows that the rival Big Bang theory won the battle of the cosmologies, but few (not even astronomers) appreciate that the mathematical formalism of the now-favored version of Big Bang, called inflation, is identical to Hoyle’s version of the Steady State model”.

## 4. The Many Different Faucets of the Concept of Big Bang

#### 4.1. The Big Bang Singularity

#### 4.1.1. The Belinsky–Khalatnikov–Lifshitz and the Misner Singularities

#### 4.1.2. The Classical Singularity Theorems

**Theorem 1**(Big Bang)

**.**

**Theorem 2**(Black Holes)

**.**

#### 4.1.3. On the Borde–Guth–Vilenkin Theorem

#### 4.2. A Quick Sketch of the Possible Origin of the Universe

- In fundamental classical physics, the ultimate theory is GR, and there, the vacuum solution is the de Sitter solution (the zero-energy one) of Einstein’s field equations.
- In quantum physics, on the other hand, ‘nothing’ means the vacuum state of the quantum system at hand, e.g., in our case, the one at the very beginning of all, as far as we can go into the past.
- It needs little explanation that we are missing here the actual theory that we would need in order to answer the question with more property, namely the theory of quantum gravity (QG).
- However, it is not clear at all that, even in possession of QG, we would be allowed to penetrate the Planck domain, which establishes a limit to all known theories of physics (quite probably also to this unknown QG).

- Just quantum spacetime, and nothing else! In spite of some attempts to do that (as most recently by Lawrence Krauss and Frank Wilczek), nobody has convincingly succeeded yet.
- In addition, a scalar field Hamiltonian (or two), namely the Higgs, an inflaton, … This seems of course a more feasible possibility, at the expense of having to explain from where do these additional necessary fields come.

#### 4.3. Big Bang Cosmological Models

#### 4.3.1. The Hot Big Bang Model

“The evolution of the world can be compared to a display of fireworks that has just ended; some few red wisps, ashes and smoke. Standing on a cooled cinder, we see the slow fading of the suns, and we try to recall the vanishing brilliance of the origin of the worlds.”

- The Universe’s expansion.
- The origin of the CMB.
- The primordial nucleosynthesis of the light elements.
- The formation of the galaxies and of large-scale structures.

#### 4.3.2. The Cold Big Bang and Other Models

“If matter existed as a single atomic nucleus, it makes no sense to speak of space and time in connection with this atom. Space and time are statistical notions that apply to an assembly of a great number of individual elements; they were meaningless notions, therefore, at the instant of first disintegration of the primeval atom.”

## 5. Acceleration: New Singularities

- $w=-1$, the cosmological constant case. It is the simplest and most natural in general relativity, but difficult to explain, and it seems to need a symmetry no one has been able to find yet, in a convincing way, in order to solve the associated cosmological constant problem.
- $w>-1$, the so-called quintessence case. This is the most ordinary case and usually involves an evolving scalar field.
- $w<-1$, the phantom case. This involves a so-called phantom field (of negative kinetic energy) and leads to a number of future singularities at finite (or infinite) time.

- The Big Rip or Type I singularity (occurring in a phantom-dominated universe) [135]. In the limit $t={t}_{s}$ (a finite value of time in the future), all quantities, namely the scale factor, effective energy density and pressure of the universe, diverge.
- Type III or Big Freeze future singularity. In this case, only the scale factor remains finite, while both the effective energy density and pressure of the universe diverge at $t={t}_{s}$. These can be either weak or strong singularities, which are geodesically-complete solutions.
- Type IV or Generalized Sudden singularity. In the limit $t={t}_{s}$, none of these, the scale factor, effective energy density or pressure, diverge. However, higher derivatives of the Hubble rate H become divergent (not H itself and its first derivative), as discovered in [140], where a full classification was given. In this case, a weak singularity appears, and geodesics are complete.

- There is still the case of the so-called Little Rip universes, where the future singularities occur asymptotically, at infinite time only. Typically, this happens when the scale factor increases rapidly, as $a\left(t\right)=exp[exp(t\left)\right]$ or higher exponentials [142,143]. However, different combinations are also possible, such as an oscillating universe (bounce). Furthermore, the very important point must be remarked that quantum gravity effects may affect this future evolution, preventing a Big Rip from occurring due to such quantum effects [144,145] or by a similar Casimir-type effect or other (see, e.g., [145,146,147,148]).

- The Q-singularity, which appears in models where there is an interaction between dark matter and dark energy. On top of the above future singularities, a divergence of the time derivative of w may give rise to a singular interaction. In fact, perturbations may be sensitive to it, since the adiabatic sound speed in a barotropic fluid depends on w’ [151].

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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1 | This being one of the reason why it is my inescapable duty to explain all that here with such emphasis. |

2 | Theoretical cosmologists may, alternatively, consider the year 1915, when Einstein completed his formulation of the gravity field equations, incorporating his revolutionary principle of equivalence, as the one actually marking the beginning of modern cosmology. This is, in particular, the opinion of one of the referees of the present paper. Indeed, the moment Einstein had his “most happy thought” unveiling the relativistic role of the equivalence principle is another seminal event from which the whole theoretical framework stems. Furthermore, the expansion of the universe was first apparent in the work of Friedmann, and partly on de Sitter’s 1917 contributions. I am myself a theoretician, and although I recognize that GR is probably the most beautiful and transcendental theory of physics ever conceived and constructed, I still stand by my opinion, as expressed above; which is also supported by the fact that the very important developments of 1912 preceded those of 1915 and 1917. |

3 | Andrzej Wróblewski brings to my attention the two papers by Carl Wirtz [42,43], of 1922–24, where he derived a linear relation of recession of spiral nebulae with their distance. Wirtz used the assumption that all galaxies have approximately the same size and estimated their relative distance from their apparent diameters. For unknown reasons, Wirtz’s papers were not noticed or soon forgotten (although they are certainly mentioned by historians of astronomy). |

4 | After completion of Version 1 of the present paper, I got through a very interesting preprint [51,52], which presents a nice account of names and concepts associated with finite-age cosmological models from the 1920s to the 1970s, including the many meanings of the Big Bang name. This reference is quite complementary to what I am describing here; it does not go, however, in any detail, into the most crucial point of the actual meaning of a Big Bang in the Theory of General Relativity, which is the essential issue in this section. |

5 | It is to be mentioned that there were at the time other competing models of the cosmos, as, e.g., the interesting contribution of H.P. Robertson [53]. |

6 | John Barrow has told me that he had always suspected that the term ‘Big Bang’ had been remembered in Cambridge, before that episode, from its use by Eddington in his book “The Nature of the Physical World” [71], based on his famous Gifford Lectures of 1927 at the University of Edinburgh [72] (probably the most famous public lecture series in the world then). Eddington writes, “As a scientist, I simply do not believe that the Universe began with a bang”; see also [73], pp. 123–318. Furthermore, according to Barrow, Eddington had a more sophisticated view of the origin of the Universe than others, and he regarded the Eddington–Lemaître models, which are geometrically past eternal, as having a finite thermodynamic age because only a finite number of non-equilibrium events would have happened in the past. |

7 | In particular, very few realize the radical difference between a ‘bang’ and the ‘Big Bang’ concept, in spite of the fact that (or maybe precisely because) everybody knows what ‘big’ means. That a bang was necessary at the origin of the world was naturally understood by everybody accepting Hubble’s law, and this included many cosmologists of the time (and a lot of educated people nowadays). In this precise way was it used in Cambridge (see the previous footnote, reflecting Barrow’s interesting observation). However, it turns out that ‘the Big Bang’ in the sense of Hoyle is not just a Big Bang in the common sense, namely of a very huge bang of the ordinary sort, giving the objects in the Universe a very large recession speed. The crucial point is that of matter creation (since the objects were not there to start with), almost instantly, in a very brief inflationary process (as it is called now) at the very origin of the cosmos. I hope this is clear already. |

8 | |

9 | See also [141], where this type of sudden and other finite time singularities were first introduced in order to show that closed Friedmann universes need not collapse even if they satisfy the strong energy condition; although the terminology ‘sudden singularity’ was introduced by Barrow in 2004, as already mentioned. |

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Elizalde, E.
“All that Matter … in One Big Bang …”, &Other Cosmological Singularities. *Galaxies* **2018**, *6*, 25.
https://doi.org/10.3390/galaxies6010025

**AMA Style**

Elizalde E.
“All that Matter … in One Big Bang …”, &Other Cosmological Singularities. *Galaxies*. 2018; 6(1):25.
https://doi.org/10.3390/galaxies6010025

**Chicago/Turabian Style**

Elizalde, Emilio.
2018. "“All that Matter … in One Big Bang …”, &Other Cosmological Singularities" *Galaxies* 6, no. 1: 25.
https://doi.org/10.3390/galaxies6010025