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Dictionary of the History of Ideas | ||

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*VI. THE DE SITTER EMPTY*

EXPANDING UNIVERSE

EXPANDING UNIVERSE

When Einstein first obtained his static universe the-

ory, it seemed to be just what was wanted, for it agreed

with the
astronomical observations as they were known

in 1917. The measured
velocities of the stars were

small, and the large scale speed of recession
of the

distant galaxies had not yet been detected. It thus

over, it appeared to Einstein at the time that the

solution of the field equations he had obtained with

the introduction of the cosmical constant λ

*gij*was a

logical necessity which intimately linked up space and

matter, so that one could not exist without the other.

He was led to this opinion because he thought that

the field equations (2) with a positive value of λ have

no solution for

*Tij*= 0 (that is, in the absence of mat-

ter). But, as de Sitter (1917) later showed, this con-

clusion was wrong. He found a solution for empty

space; that is, for

*Tij*= 0 everywhere. Now such a

universe is an expanding one in the sense that if a test

particle (a particle of negligible mass) is placed at any

point in the universe, it recedes from the observer with

ever increasing speed. In other words, the speed of

recession increases with distance from the observer. In

fact, if the de Sitter universe had test particles distrib-

uted throughout, they would all recede from each

other. The reason for this is found in the cosmical term

λ

*gij*in the field equations. If we place

*Tij*= 0 in the

field equations (2) they reduce to

*Rij*= λ

*gij*, or Rij - λ

*gij*= 0, (1)

and since the term

*Rij*represents the ordinary New-

tonian gravitation of attraction, the term -λ

*gij*repre-

sents repulsion, owing to the minus sign.

The de Sitter universe aroused interest initially be-

cause it showed that the cosmological field equations

(2) do not
have a unique solution, and that more than

one model of a universe based on
these equations can

be constructed. Beyond this, however, the de
Sitter

model of the universe was not taken seriously, since

it seemed
to contradict the observations in two re-

spects: it is an empty universe, whereas the actual

universe
contains matter; it is an expanding universe,

whereas the observations
seemed to indicate that the

actual universe was static. But then, in the
early 1920's,

the recession of the distant nebulae was discovered by

Hubble, Slipher, Shapley, and others. The work of

these investigators on
the Doppler displacement (to-

wards the red) of
the spectral lines of the extragalactic

nebulae (or galaxies) indicates
that the universe is, in-

deed, expanding.
Moreover, the rate of recession of

the galaxies increases with distance
(the famous Hubble

law, 1927) in line with what one would expect from

the de Sitter universe. These discoveries demonstrated

the inadequacies of
the Einstein universe and brought

the de Sitter model into prominence.

Another difficulty associated with the Einstein static

universe is that it
is not a stable model but must un-

dergo either
expansion or contraction if there is the

slightest departure from the
precise balance between

the gravitational attraction and the cosmic repulsion.

Thus, if by some process or other some of the mass

were to be
changed into energy, or if condensations

were to occur, the universe would
have to begin to

expand or collapse. This point, taken together with
de

Sitter's work and the observed recession of the distant

galaxies,
led cosmologists to the idea that the actual

model of the universe might be
an expanding one, that

is, intermediate between the empty de Sitter
model

and the Einstein static model. One must therefore look

for
solutions of the field equations which give models

that are expanding, but
not empty. Such models were

first obtained by the Russian mathematician
Friedmann

in 1922 when he dropped Einstein's assumption that

the
density of matter in the universe must remain

constant. By dropping this
assumption, Friedmann was

able to obtain nonstatic solutions of the field
equations

which are the basis of most cosmological models. This

same
problem was independently investigated later by

Weyl (1923),
Lemaître (1931), Eddington (1933),

Robertson (1935), and Walker
(1936). Since the treat-

ment of this problem
as given by Robertson, and,

independently, by Walker, is the most general
one, we

shall use their analysis as a guide in our discussion of

the
current models of the expanding universe.

Dictionary of the History of Ideas | ||