Geodesic
Cosmological models with homogeneous and isotropic spatial sections
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 219-227 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The assumption that the universe is homogeneous and isotropic is the basis for the majority of modern cosmological models. We give an example of a metric all of whose spatial sections are spaces of constant curvature but the space–time is nevertheless not homogeneous and isotropic as a whole. We give an equivalent definition of a homogeneous and isotropic universe in terms of embedded manifolds.
Keywords: homogeneous isotropic universe, cosmology. 
@article{TMF_2017_191_2_a5,
     author = {M. O. Katanaev},
     title = {Cosmological models with homogeneous and isotropic spatial sections},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {219--227},
     year = {2017},
     volume = {191},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a5/}
}
TY  - JOUR
AU  - M. O. Katanaev
TI  - Cosmological models with homogeneous and isotropic spatial sections
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 219
EP  - 227
VL  - 191
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a5/
LA  - ru
ID  - TMF_2017_191_2_a5
ER  - 
%0 Journal Article
%A M. O. Katanaev
%T Cosmological models with homogeneous and isotropic spatial sections
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 219-227
%V 191
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a5/
%G ru
%F TMF_2017_191_2_a5
M. O. Katanaev. Cosmological models with homogeneous and isotropic spatial sections. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 219-227. http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a5/

[1] C. Clarkson, “Establishing homogeneity of the universe in the shadow of dark energy”, Compt. Rendus Phys., 13:6 (2012), 682–718, arXiv: 1204.5505 | DOI

[2] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York, 1972

[3] A. A. Fridman, “O krivizne prostranstva”, Zhurn. russk. fiz.-khim. o-va, chast fiz., 56:1 (1924), 59–68 ; УФН, 80:3 (1963), 439–446 ; 93:2 (1967), 280–287 | MR | Zbl | DOI | Zbl | DOI

[4] A. A. Fridman, “O vozmozhnosti mira s postoyannoi otritsatelnoi kriviznoi prostranstva”, UFN, 80 (1963), 447-452 | DOI | Zbl

[5] G. Lemaître, “Un univers homogène de masse constante et de rayon croissant, rendant compte de la Vitesse radiale de nébuleuses extra-galacticues”, Ann. Soc. Sci. Bruxelles A, 47 (1927), 49–59 | Zbl

[6] G. Lemaître, “LÚnivers en expansion”, Ann. Soc. Sci. Bruxelles A, 53 (1933), 51–85 | MR | Zbl

[7] H. P. Robertson, “On the foundations of relativistic cosmology”, Proc. Nat. Acad. Sci. USA, 15 (1929), 822–829 | DOI | Zbl

[8] H. P. Robertson, “Relativistic cosmology”, Rev. Modern Phys., 5:1 (1933), 62–90 | DOI | Zbl

[9] H. P. Robertson, “Kinematics and world structure”, Astrophys. J., 82 (1935), 284–301 | DOI | Zbl

[10] R. C. Tolman, “The effect of the annihilation of matter on the wave-length of light from the nebulae”, Proc. Nat. Acad. Sci. USA, 16:4 (1930), 320–337 | DOI | Zbl

[11] R. C. Tolman, “More complete discussion of the time-dependence of the non-static line element for the universe”, Proc. Nat. Acad. Sci. USA, 16:6 (1930), 409–420 | DOI | Zbl

[12] D. Hilbert, “Die Grundlagen der Physik”, Math. Ann., 92:1 (1924), 1–32 | DOI | MR

[13] G. Fubini, “Sugli spazii a quattro dimensioni che ammettono un gruppo continuo di movimenti”, Ann. Mat. Pura Appl. Ser. III, 9:1 (1904), 33–90 | DOI

[14] L. P. Eizenkhart, Rimanova geometriya, IL, M., 1948 | MR | Zbl

[15] R. C. Tolman, “On the estimation of distances in a curved universe with a non-static line element”, Proc. Nat. Acad. Sci. USA, 16:7 (1930), 511–520 | DOI | Zbl

[16] A. G. Walker, “On Milne's theory of world-structure”, Proc. London Math. Soc. Ser. 2, 42:1 (1936), 90–127 | MR | Zbl

[17] M. O. Katanaev, “On homogeneous and isotropic universe”, Modern Phys. Lett. A, 30:34 (2015), 1550186, 5 pp., arXiv: 1511.00991 | DOI | MR | Zbl

[18] R. M. Wald, General Relativity, University of Chicago Press, Chicago, IL, 1984 | MR | Zbl

[19] M. O. Katanaev, Geometric methods in mathematical physics, arXiv: 1311.0733

[20] I. Ya. Arefeva, I. V. Volovich, “Ob izotropnom energeticheskom uslovii i kosmologii”, TMF, 155:1 (2008), 3–12 | DOI | DOI | MR | Zbl

[21] V. A. Rubakov, “Izotropnoe uslovie energodominantnosti i ego narushenie”, UFN, 184:2 (2014), 137–152 | DOI | DOI | MR

[22] G. A. Alekseev, “Collision of strong gravitational and electromagnetic waves in the expanding universe”, Phys. Rev. D, 93:6 (2016), 061501, 6 pp. | DOI | MR

[23] A. K. Guschin, “$L_p$-otsenki nekasatelnoi maksimalnoi funktsii dlya resheniya ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 207:10 (2016), 28–55 | DOI | DOI | MR

[24] A. K. Guschin, “O razreshimosti zadachi Dirikhle dlya neodnorodnogo ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 206:10 (2015), 71–102 | DOI | DOI | MR | Zbl

[25] V. V. Zharinov, “Zakony sokhraneniya, differentsialnye tozhdestva i svyazi uravnenii v chastnykh proizvodnykh”, TMF, 185:2 (2015), 227–251 | DOI | DOI | MR | Zbl

[26] V. V. Zharinov, “O preobrazovanii Beklunda”, TMF, 189:3 (2016), 323–334 | DOI | DOI | MR | Zbl