Chaplygin gas and the cosmological evolution of alpha

Abstract： The class of Chaplygin gas models regarded as a candidate of dark energy can be realized by a scalar field，which could drive the variation of the fine structure constant α during the cosmic time.This phenomenon has been observed for almost ten years ago from the quasar absorption spectra and attracted many attentions.In this paper，

the authors reconstruct the class of Chaplygin gas models to a kind of scalar fields and confront the resulting Δα/α with the observational constraints.It is found that if the present observational value of the equation of state of the dark energy was not exactly equal to -1，various parameters of the class of Chaplygin gas models are allowed to satisfy the observational constraints，as well as the equivalence principle is also respected.

Key words： cosmology； dark energy； Chaplygin gas； varying alpha

CLC number： O 412.1 Document code： A Article ID： 1000-5137（2014）04-0432-09

1 Introduction

The possibility of varying the fundamental constants over cosmological time-scale has been studied for many years[1].Among these fundamental constants，the time-variation of the fine-structure constant α is deserved to study both from the experimental and theoretical point of view.The observational evidence of time-varying α is firstly from the quasar absorption spectra and reported in 2001 by Webb et al.，and now there are some other independently results can be used to constrain the variation of α ，see [1-3].The variation of α can be due to many possible reasons，one of them is that there is a scalar field coupled to the gauge field.In 1982，Bekenstein first introduced the exponential form for the coupling，which in practice can be taken in the linear form coupling between a scalar field and the electromagnetic field to explain the variation.

5 Conclusions

In this paper，we have reconstructed the class of Chaplygin gas models to a kind of scalar field and study the variation of the fine structure constant α driven by it.This phenomenon was found since ten years ago and attracted many attentions.The resulting Δα/α as a function of the redshif z is presented in Fig.1，F(xiàn)ig.2 and Fig.3.We only consider the case of linear coupling between the scalar field and the electromagnetic field，because the variation of α is much small.The results indicate that if the present observational value of the equation of state of the dark energy was not exactly equal to -1，various parameters of the class of Chaplygin gas models are allowed to satisfy the observational constraints，as well as the equivalence principle is also respected since it requires the constant ζ is much smaller than 10-3 in all the case.

For the generalized Chaplygin gas，there is a parameter 0< σ≤1 in eq. （23）.We find that when the smaller σ is，the larger upper bound of ζ is.In the case of modified generalized Chaplygin gas，the upper bound of ζ becomes more restricted when the running of equation of state w′0 is large.It is worth further studying，since the variation of fundamental constants during the cosmic time is a very interesting area.

References：

[1] UZAN J P.The fundamental constants and their variation：Observational status and theoretical motivations[J].Rev Mod Phys，2003，75（2）：403-455.

[2] OLIVE K A，POSPELOV M，QIAN Y Z，et al.Constraints on the variations of the fundamental couplings[J].Phys Rev D，2002，66（4）：045022.

[3] MARTINS C J A.New constraints on varying alpha[J/OL].arXiv：astro-ph/0405630.

[4] DAMOUR T，DYSON F.The Oklo bound on the time variation of the fine-structure constant revisited[J].Nucl Phys B，1996，480（1）：37-54.

[5] MURPHY M T，WEBB J K，F(xiàn)LAMBAUM V V.Further evidence for a variable fine-structure constant from Keck/HIRES QSO absorption spectra[J].Mon Not Roy Astron Soc，2003，345（2）：609-638.

[6] SRIANAND R，CHAND H，PETITJEAN P，et al.Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars[J].Phys Rev Lett，2004，92（12）：121302.

[7] AVELINO P P，ESPOSITO S，MANGANO G，et al.Early-universe constraints on a time-varying fine structure constant[J].Phys Rev D，2001，64（10）：103505.

[8] NOLLETT K M，LOPEZ R E.Primordial nucleosynthesis with a varying fine structure constant：An improved estimate[J].Phys Rev D，2002，66（6）：063507.

[9] WEI H.Varying alpha driven by the dirac-born-infeld scalar field[J].Phys Lett B，2009，682（1）：98-104.

[10] KAMENSHCHIK A Y，MOSCHELLA U，PASQUIER V.An alternative to quintessence[J].Phys Lett B，2001，511（2-4）：265-268.

[11] BENTO M C，BERTOLAMI O，SEN A A.Generalized chaplygin gas，accelerated expansion and dark energy-matter unification[J].Phys Rev D，2002，66（4）：043507.

[12] BENTO M C，BERTOLAMI O，SEN A A.Generalized chaplygin gas as a scheme for unification of dark energy and dark matter[J/OL].arXiv：astro-ph/0210375.

[13] HAO J G，LI X Z.Generalized quartessence cosmic dynamics：Phantom or quintessence with de Sitter attractor[J].Phys Lett B，2005，606（1-2）：7-11.

[14] MARRA V，ROSATI F.Cosmological evolution of alpha driven by a general coupling with quintessence[J].Journal of Cosmology and Astroparticle Physics，2005（5）：011，1～14.