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This short but systematic work demonstrates a link between Chebyshevs 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 $Lambda eq0$ 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. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.
The equivalence between Chern-Simons and Einstein-Hilbert actions in three dimensions established by A.~Achucarro and P.~K.~Townsend (1986) and E.~Witten (1988) is generalized to the off-shell case. The technique is also generalized to the Yang-Mills
BMS symmetry is a symmetry of asymptotically flat spacetimes in the vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quant
In this paper we explore possible extensions of Interacting Dark Energy cosmologies, where Dark Energy and Dark Matter interact non-gravitationally with one another. In particular, we focus on the neutrino sector, analyzing the effect of both neutrin
The effects of bulk viscosity are examined for inflationary dynamics in which dissipation and thermalization are present. A complete stability analysis is done for the background inflaton evolution equations, which includes both inflaton dissipation
We make use of the conformal compactification of Minkowski spacetime $M^{#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{#}]^{-1}$ obtained via conforma