LOG#134. Chaplygin gas.


Warm Dark Matter candidates: neutrinos, axions, extra relativistic species currently unknown.

Cold Dark Matter candidates: many. Pick one (or many!): Z primes, the lightest supersymmetric particle (LSP), gravitino, gaugino, neutralino, ELKO fields, Majorana spinors, the infinite component Majorana field, unparticles, conformal dark matter, preonic matter, KK resonances,…

Does Dark Matter particles interact with Dark Energy? A unified model? A single toy model: the Chaplygin gas (no microscopic description yet):

A) Chaplygin gas (CG):

    \[ \boxed{p=p(\rho)=A/\rho}\]

B) Generalized Chaplygin Gas (GCG):



n\geq -1

C) Modified Generalized Chaplygin Gas (MGCG)  (in the sense of P.F.Glez-Díaz, in memoriam):

\boxed{p=p(\rho)=A\rho+B/\rho^n}\;\; n\geq 1

D) Cosmic Modified Generalized Modified Chaplygin Gas (CMGMCG):

    \[ \boxed{p=\dfrac{A(\omega)}{\rho^n}-\dfrac{1}{\rho^n}\left(\rho^{n+1}+A(\omega)\right)^{-\omega}}\]

and where


This last Chaplygin gas can be extended a la P.F. Glez-Díaz:

\boxed{p=\mu \rho+\dfrac{A(\omega)}{\rho^n}-\dfrac{1}{\rho^n}\left(\rho^{n+1}+A(\omega)\right)^{-\omega}}

A modification of Chaplygin gas including bulk viscosity \xi is also available:

    \[ p=\mu \rho+\dfrac{A(\omega)}{\rho^n}-\dfrac{1}{\rho^n}\left(\rho^{n+1}+A(\omega)\right)^{-\omega}-\xi H\]

We can allow a variable B term with respect to the cosmic scale factor R(t) in certain way as well. In the above equations,  \omega is a cosmic parameter (a pure number). It determines the properties of the Chaplygin gas and n is a pure number as well. Generally n is real and generally greater than -1 or 1, depending on the concrete model and Chaplygin gas type. The generalized Chaplygin gas can be also rewritten as a function of some unknown mass and the power exponent:

    \[ \boxed{p=\dfrac{M^{4(1+\alpha)}}{\rho^{\alpha}}}\]

Some remarks about the Chaplygin gas:

1st. It is one of the few systems where we can derive fully the scalar potential and admits a supersymmetric description. Its lagrangian is related to D-branes.

2nd. Chaplygin gases have a weird enough equation of state to describe something as rare as Dark Matter and even Dark Energy from a unified viewpoint.

3rd. Issues: there is no microscopic theory of the Chaplygin gas yet. It can manifest superluminality (faster than light speed of sound).

There is also a variation of the Chaplygin gas called silent Chaplygin gas or quartessence.

Dark energy candidates beyond exotic changes in the equation of state as the Chaplygin gases:

1) Pure cosmological constant/Vacuum energy.

2) Quintessence. Scalar field mimics dark energy but, unlike CC, it is dynamical.

3) Phantom energy. Scalar field with wrong kinetic term (negative kinetic term!). It is related to tachyonic scalar models somehow. Recently, PLANCK data seem to prefer this option but there is too much uncertainty to decide that this is the case of curren dark energy.

4) Quintom matter. Crossover between phantom energy and quintessence, through the pure CC regime. It needs at least two scalar fields to be possible. Interesting feature of quintom matter scenarios are that it could avoid  spacetime singularities as the Big-Bang or the Big-Crunch, even the Big Rip.

5) k-essence (kinetic-essence). Scalar field with non-standard kinetic term. It is a big type of theories involving general scalar functionals in the lagrangian. It could also include theories based on non-local lagrangians with infinite number of derivatives as those arising from string field theory with open fundamental or cosmic strings and/or p-adic string theory.

6) Other exotic proposals. Quons and other modified statistical particles (plektons, anyons, …).  Some generalized statistics beyond the Boltzmann statistics and the common Quantum Statistics have been proposed. Quons are a strange type of particles obeying infinite statistics (quantum Boltzmann statistics). There is no local field theory for quons.

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