# Lemaître theory of the expansion of the Universe

Georges Henri Joseph Édouard Lemaître, 17 July 1894 – 20 June 1966) was a Belgian Roman Catholic priest, astronomer, and professor of physics at the Catholic University of Leuven.[2] He proposed on theoretical grounds that the universe is expanding, which was observationally confirmed soon afterwards by Edwin Hubble. He was the first to derive what is now known as Hubble's law, or the Hubble-Lemaître law, and made the first estimation of what is now called the Hubble constant, which he published in 1927, two years before Hubble's article. Lemaître also proposed what became known as the "Big Bang theory" of the origin of the universe, originally calling it the "hypothesis of the primeval atom" or the "Cosmic Egg".

Lemaître was a pioneer in applying Albert Einstein's theory of general relativity to cosmology. In a 1927 article, which preceded Edwin Hubble's landmark article by two years, Lemaître derived what became known as Hubble's law and proposed it as a generic phenomenon in relativistic cosmology. Lemaître also estimated the numerical value of the Hubble constant. However, the data used by Lemaître did not allow him to prove that there was an actual linear relation, which Hubble did two years later.

He began the report which brought him international fame when it was published in 1927 in the Annales de la Société Scientifique de Bruxelles (Annals of the Scientific Society of Brussels) under the title "Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques" ("A homogeneous Universe of constant mass and growing radius accounting for the radial velocity of extragalactic nebulae"). In this report, he presented his new idea that the universe is expanding, which he derived from General Relativity; this later became known as Hubble's law, but Lemaître provided the first observational estimation of the Hubble constant. The initial state he proposed was taken to be Einstein's own model of a finitely sized static universe.

The paper had little impact because the journal in which it was published was not widely read by astronomers outside Belgium; Arthur Eddington reportedly helped translate the article into English in 1931, but the part of it pertaining to the estimation of the "Hubble constant" was not included in the translation for reasons that remained unknown for a long time. This issue was clarified in 2011 by Mario Livio; Lemaître omitted the paragraphs when himself initially translating the paper for the Royal Astronomical Society, in favour of reports of new work on the subject, since by that time Hubble's calculations had already improved on his earlier ones.

At this time, Einstein, while not taking exception to the mathematics of Lemaître's theory, refused to accept that the universe was expanding; Lemaître recalled his commenting "Vos calculs sont corrects, mais votre physique est abominable" ("Your calculations are correct, but your physics is atrocious"). In the same year, Lemaître returned to MIT to present his doctoral thesis on The gravitational field in a fluid sphere of uniform invariant density according to the theory of relativity. Upon obtaining his Ph.D., he was named ordinary professor at the Catholic University of Leuven.

In 1931, Arthur Eddington published in the Monthly Notices of the Royal Astronomical Society a long commentary on Lemaître's 1927 article, in which he described the latter as a "brilliant solution" to the outstanding problems of cosmology. The original paper was published in an abbreviated English translation later on in 1931, along with a sequel by Lemaître responding to Eddington's comments. Lemaître was then invited to London to participate in a meeting of the British Association on the relation between the physical universe and spirituality. There he proposed that the universe expanded from an initial point, which he called the "Primeval Atom". He developed this idea in a report published in Nature. Lemaitre's theory appeared for the first time in an article for the general reader on science and technology subjects in the December 1932 issue of Popular Science. Lemaître himself also described his theory as "the Cosmic Egg exploding at the moment of the creation"; it became better known as the "Big Bang theory," a pejorative term coined during a 1949 BBC radio broadcast by the astronomer Fred Hoyle, who was then still a proponent of the steady state universe and remained so until his death in 2001.

Lemaître's proposal met with skepticism from his fellow scientists. Eddington found Lemaître's notion unpleasant. Einstein thought it unjustifiable from a physical point of view, although he encouraged Lemaître to look into the possibility of models of non-isotropic expansion, so it is clear he was not altogether dismissive of the concept. Einstein also appreciated Lemaître's argument that Einstein's model of a static universe could not be sustained into the infinite past.

Friedmann was handicapped by living and working in the USSR, and died in 1925, soon after inventing the Friedmann–Lemaître–Robertson–Walker metric. Because Lemaître spent his entire career in Europe, his scientific work is not as well known in the United States as that of Hubble or Einstein, both well known in the U.S. by virtue of residing there. Nevertheless, Lemaître's theory changed the course of cosmology. This was because Lemaître:

- Was well acquainted with the work of astronomers, and designed his theory to have testable implications and to be in accord with observations of the time, in particular to explain the observed redshift of galaxies and the linear relation between distances and velocities;
- Proposed his theory at an opportune time, since Edwin Hubble would soon publish his velocity-distance relation that strongly supported an expanding universe and, consequently, Lemaître's Big Bang theory;
- Had studied under Arthur Eddington, who made sure that Lemaître got a hearing in the scientific community.

Both Friedmann and Lemaître proposed relativistic cosmologies featuring an expanding universe. However, Lemaître was the first to propose that the expansion explains the redshiftof galaxies. He further concluded that an initial "creation-like" event must have occurred.

#### Friedmann-Lemaître models

Aleksandr A. Friedmann, a Russian meteorologist and mathematician, and Georges Lemaître, independently discovered solutions to Einstein’s equations that contained realistic amounts of matter. These evolutionary models correspond to big bang cosmologies. Friedmann and Lemaître adopted Einstein’s assumption of spatial homogeneity and isotropy (the cosmological principle). They rejected, however, his assumption of time independence and considered both positively curved spaces (“closed” universes) as well as negatively curved spaces (“open” universes). The difference between the approaches of Friedmann and Lemaître is that the former set the cosmological constant equal to zero, whereas the latter retained the possibility that it might have a nonzero value. To simplify the discussion, only the Friedmann models are considered here.

The decision to abandon a static model meant that the Friedmann models evolve with time. As such, neighbouring pieces of matter have recessional (or contractional) phases when they separate from (or approach) one another with an apparent velocity that increases linearly with increasing distance. Friedmann’s models thus anticipated Hubble’s law before it had been formulated on an observational basis. It was Lemaître, however, who had the good fortune of deriving the results at the time when the recession of the galaxies was being recognized as a fundamental cosmological observation, and it was he who clarified the theoretical basis for the phenomenon.

The geometry of space in Friedmann’s closed models is similar to that of Einstein’s original model; however, there is a curvature to time as well as one to space. Unlike Einstein’s model, where time runs eternally at each spatial point on an uninterrupted horizontal line that extends infinitely into the past and future, there is a beginning and end to time in Friedmann’s version of a closed universe when material expands from or is recompressed to infinite densities. These instants are called the instants of the “big bang” and the “big squeeze,” respectively. The global space-time diagram for the middle half of the expansion-compression phases can be depicted as a barrel lying on its side. The space axis corresponds again to any one direction in the universe, and it wraps around the barrel. Through each spatial point runs a time axis that extends along the length of the barrel on its (space-time) surface. Because the barrel is curved in both space and time, the little squares in the grid of the curved sheet of graph paper marking the space-time surface are of nonuniform size, stretching to become bigger when the barrel broadens (universe expands) and shrinking to become smaller when the barrel narrows (universe contracts).

It should be remembered that only the surface of the barrel has physical significance; the dimension off the surface toward the axle of the barrel represents the fourth spatial dimension, which is not part of the real three-dimensional world. The space axis circles the barrel and closes upon itself after traversing a circumference equal to 2πR, where R, the radius of the universe (in the fourth dimension), is now a function of the time t. In a closed Friedmann model, R starts equal to zero at time t = 0 (not shown in barrel diagram), expands to a maximum value at time t = t_{m} (the middle of the barrel), and recontracts to zero (not shown) at time t = 2t_{m}, with the value of tm dependent on the total amount of mass that exists in the universe.

Imagine now that galaxies reside on equally spaced tick marks along the space axis. Each galaxy on average does not move spatially with respect to its tick mark in the spatial (ringed) direction but is carried forward horizontally by the march of time. The total number of galaxies on the spatial ring is conserved as time changes, and therefore their average spacing increases or decreases as the total circumference 2πR on the ring increases or decreases (during the expansion or contraction phases). Thus, without in a sense actually moving in the spatial direction, galaxies can be carried apart by the expansion of space itself. From this point of view, the recession of galaxies is not a “velocity” in the usual sense of the word. For example, in a closed Friedmann model, there could be galaxies that started, when R was small, very close to the Milky Way system on the opposite side of the universe. Now, 10^{10} years later, they are still on the opposite side of the universe but at a distance much greater than 10^{10} light-years away. They reached those distances without ever having had to move (relative to any local observer) at speeds faster than light—indeed, in a sense without having had to move at all. The separation rate of nearby galaxies can be thought of as a velocity without confusion in the sense of Hubble’s law, if one wants, but only if the inferred velocity is much less than the speed of light.

On the other hand, if the recession of the galaxies is not viewed in terms of a velocity, then the cosmological redshift cannot be viewed as a Doppler shift. How, then, does it arise? The answer is contained in the barrel diagram when one notices that, as the universe expands, each small cell in the space-time grid also expands. Consider the propagation of electromagnetic radiation whose wavelength initially spans exactly one cell length (for simplicity of discussion), so that its head lies at a vertex and its tail at one vertex back. Suppose an elliptical galaxy emits such a wave at some time t_{1}. The head of the wave propagates from corner to corner on the little square grids that look locally flat, and the tail propagates from corner to corner one vertex back. At a later time t_{2}, a spiral galaxy begins to intercept the head of the wave. At time t_{2}, the tail is still one vertex back, and therefore the wave train, still containing one wavelength, now spans one current spatial grid spacing. In other words, the wavelength has grown in direct proportion to the linear expansion factor of the universe. Since the same conclusion would have held if n wavelengths had been involved instead of one, all electromagnetic radiation from a given object will show the same cosmological redshift if the universe (or, equivalently, the average spacing between galaxies) was smaller at the epoch of transmission than at the epoch of reception. Each wavelength will have been stretched in direct proportion to the expansion of the universe in between.

A nonzero peculiar velocity for an emitting galaxy with respect to its local cosmological frame can be taken into account by Doppler-shifting the emitted photons before applying the cosmological redshift factor; i.e., the observed redshift would be a product of two factors. When the observed redshift is large, one usually assumes that the dominant contribution is of cosmological origin. When this assumption is valid, the redshift is a monotonic function of both distance and time during the expansional phase of any cosmological model. Thus, astronomers often use the redshift z as a shorthand indicator of both distance and elapsed time. Following from this, the statement “object X lies at z = a” means that “object X lies at a distance associated with redshift a”; the statement “event Y occurred at redshift z = b” means that “event Y occurred a time ago associated with redshift b.”

Lemaître was the first theoretical cosmologist ever nominated in 1954 for the Nobel Prize in physics for his prediction of the expanding universe. Remarkably, he was also nominated for the 1956 Nobel prize in chemistry for his primeval-atom theory.

A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of...REFERENCES

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Encyclopædia Britannica. Available in: https://www.britannica.com/science/cosmology-astronomy/Relativistic-cosmologies. Access in: 19/11/2018.

Encyclopædia Britannica. Available in: https://www.britannica.com/biography/Georges-Lemaitre. Access in: 19/11/2018.

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