Fetching the paper…

Reading the bibliography…

Friedmann's Equations in All Dimensions and Chebyshev's Theorem · Around

2014

Friedmann's Equations in All Dimensions and Chebyshev's Theorem

Chen, Shouxin, Gibbons, Gary W., Li, Yijun et al.

Original
PDF
Post on X

Understand

This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time $t$ and conformal time $\eta$ of the Friedmann equations in all dimensions and with an arbitrary cosmological constant $\Lambda$.

More precisely, it is shown that for spatially flat universes an explicit integration in $t$ may always be carried out, and that, in the non-flat situation and when $\Lambda$ is zero and the ratio $w$ of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension $n$ of space and $w$ obey some specific relations among an infinite family.
The situation for explicit integration in $\eta$ is complementary to that in $t$.
More precisely, it is shown in the flat-universe case with $\Lambda\neq0$ that an explicit integration in $\eta$ can be carried out if and only if $w$ and $n$ obey similar relations among a well-defined family which we specify, and that, when $\Lambda=0$, an explicit integration can always be carried out whether the space is flat, closed, or open.

Built on

Harrison E R,
1967
Earlier work this paper cites.
Wald R M,
1984
Earlier work this paper cites.
Barrow J D,
1993
Earlier work this paper cites.
Marchisotto E A and Zakeri G-A,
1994
Earlier work this paper cites.
Caldwell R R, Dave R, and Steinhardt P J,
1998
Earlier work this paper cites.
Fischler W and Susskind L,
1998
Earlier work this paper cites.
Faraoni V,
1999
Earlier work this paper cites.
Kaloper N and Linde A,
1999
Earlier work this paper cites.
Bahcall N A, Ostriker J P, Perlmutter S, and Steinhardt P J,
1999
Earlier work this paper cites.
de Bernardis P
2000
Earlier work this paper cites.

Similar

Lima J A S,
2001
Cited alongside, same era.
Uzan J-P and Lehoucq R,
2001
Cited alongside, same era.
Campos A and Sopuerta C F,
2001
Cited alongside, same era.
van Holten J W,
2002
Cited alongside, same era.
Steinhardt P J and Turok N,
2002
Cited alongside, same era.
Nojiri S, Odintsov S D, and Ogushi S,
2002
Cited alongside, same era.
Stephani H, Kramer D, Maccallum M, Hoenselaers C, and Herlt E,
2003
Cited alongside, same era.
Linder E V,

Then

Copeland E J, Sami M, and Tsujikawa S,
2006
Later among the works it cites.
Dunajski M and Gibbons G W,
2008
Later among the works it cites.
Watanabe M, Kanno S, and Soda J,
2009
Later among the works it cites.
Farajollahi H and Salehi A,
2011
Later among the works it cites.
Gibbons G W,
2012
Later among the works it cites.
Sonego S and Talamini V,
2012
Later among the works it cites.
Planck Collaboration,
2013
Later among the works it cites.
Burgess C P, Cicoli M, and Quevedo F,

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2003

Cited alongside, same era.

Chernin A D, Nagirner D I, and Starikova S V,

2003

Cited alongside, same era.

Tchebichef M P,

Cited in the paper.

http://planetmath.org/integrationofdifferentialbinomial

Cited in the paper.

2013

Later among the works it cites.

Peebles, P J E,

2014

Closest in time.