In this paper the separation of variables is presented in the Dirac equation in open, flat, and closed expanding cosmological Robertson–Walker universes. The equations governing the radial variable and the evolution of the time‐dependent factor are obtained. An exact solution to the Weyl equation is derived for an arbitrary expansion factor of the Robertson–Walker metrics. An exact solution to Dirac equation in a universe filled with radiation is also presented.

1.
J.
Audretsch
and
G.
Schäfer
,
Gen. Relativ. Gravit.
9
,
243
(
1978
).
2.
J.
Audretsch
and
G.
Schäfer
,
Gen. Relativ. Gravit.
9
,
489
(
1978
).
3.
L.
Parker
,
Phys. Rev. D
22
,
1922
(
1980
).
4.
L.
Parker
,
Phys. Rev. Lett.
44
,
1559
(
1980
).
5.
S. W.
Hawking
,
Commun. Math. Phys.
43
,
199
(
1975
);
G. W.
Gibbons
and
S. W.
Hawking
,
Phys. Rev. D
15
,
2738
(
1977
).
6.
V. S.
Otchik
,
Class. Quant. Grav.
2
,
539
(
1985
).
7.
L. P.
Chimento
and
M. S.
Mollerach
,
Phys. Rev. D
34
,
3689
(
1986
);
L. P.
Chimento
and
M. S.
Mollerach
,
Phys. Lett. A
121
,
7
(
1987
).
8.
M. A.
Castagnino
,
C. D.
El Hasi
,
F. D.
Mazzitelli
, and
J. P.
Paz
,
Phys. Lett. A
128
,
25
(
1988
).
9.
A. O.
Barut
and
I. H.
Duru
,
Phys. Rev. D
36
,
3705
(
1987
).
10.
G. V.
Shishkin
and
I. E.
Andrushkevich
,
Vestsi. Akad. Nauk BSSR Fiz.‐Mat. Navuk
4
,
109
(
1986
).
11.
I. E.
Andrushkevich
and
G. V.
Shishkin
,
Theoret. Math. Phys.
70
,
204
(
1987
).
12.
S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).
13.
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1971).
14.
D.
Brill
and
J. A.
Wheeler
,
Rev. Mod. Phys.
29
,
465
(
1957
).
15.
A. S. Davydov, Quantum Mechanics (Pergamon, Oxford, 1965).
16.
J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Springer, New York, 1976).
17.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
18.
P. Berestestskii, E. M. Lifshitz, and L. P. Pitaevskii, Relativistic Quantum Mechanics (Pergamon, Oxford, 1971).
19.
F. M.
Arscott
,
Proc. Roy. Soc. Edinburgh A
67
,
265
(
1967
).
20.
K. M.
Urwin
and
F. M.
Arscott
,
Proc. Roy. Soc. Edinburgh Sect. A
69
,
28
(
1969
).
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