Jeans’s criterion using various cosmological terms

الملخص EN

Jeans’s criterion concerning the gravitational instability of a quasi-infinite homogeneous medium is revisited.

The original erroneous derivation is improved by considering the gravitational potential around an extremum.

However, it is shown that the domain of valid approximation is about as large as the instability region, still leaving doubts about the correctness of the criterion.

A derivation using a cosmological constant is obtained which avoids the inconsistency and recovers Jeans’s criterion to a very good approximation.

However, other problems arise.

Moreover, when we use a sensible bilinear cosmological term then a kind of standard instability length results, not the Jeans’s wavelength.

Using a cosmological term quadratic in the density leads again to a good approximation of Jeans’s criterion.

Hence the precise form of the cosmological term turns out to be quite relevant.

The underlying physical mechanism of the instability is explained, confirming theright order of the Jeans’s instability wavelength and Jeans’s mass.

The stability analysis of an infinite gravitational cylinder and of a plane-parallel medium support Jeans’s result too.

Some confirmations on the basis of celestial bodies (Earth, Sun, galaxy, cosmic tessellation) are briefly considered, including the effect of scaling.

This leads to another interpretation of Jeans’s wavelength: it is about (in fact slightly larger than) the diameter of celestial bodies in equilibrium and thus it expresses rather the stability of the body.

The cosmic entropy concept is discussed in the light of Jeans’s criterion.