In a recent paper by C. Gao, M. Kunz, A. Liddle and D. Parkinson
[arXiv:0912.0949], the unification of dark matter and dark energy was explored
within a theory containing a scalar field of non-Lagrangian type. This scalar
field, different from the classic quintessence, can be obtained from the scalar
field representation of an interacting two-fluid mixture described in the paper
by L.P. Chimento and M. Forte [arXiv:0706.4142

Chimento, Luis P.

Forte, Mónica

The Open Nuclear & Particle Physics Journal

English

arXiv

In a recent paper by C. Gao, M. Kunz, A. Liddle and D. Parkinson [1] the unification of dark matter and dark energy was explored within a theory, which they say is not of the Lagrangian type, containing a scalar field. This scalar field, different from the classic quintessence, can be obtained from the scalar field representation of an interacting twofluid mixture described in the paper by L.P. Chimento and M. Forte [2]. The corresponding Lagrangian of the model is just the equation (7).Fil: Chimento, Luis Pascual. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Forte, Monica. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

Chimento, Luis Pascual

Forte, Monica

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Comments on Unified dark energy and dark matter from a scalar field different from quintessence

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 The Open Nuclear & Particle Physics Journal, 2011, 4, 25-26 25   1874-415X/11 2011 Bentham Open Open Access Comments on Unified Dark Energy and Dark Matter from a Scalar Field Different from Quintessence Luis P. Chimento and Mónica Forte* Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina Abstract: In a recent paper by C. Gao, M. Kunz, A. Liddle and D. Parkinson [1] the unification of dark matter and dark energy was explored within a theory, which they say is not of the Lagrangian type, containing a scalar field. This scalar field, different from the classic quintessence, can be obtained from the scalar field representation of an interacting two-fluid mixture described in the paper by L.P. Chimento and M. Forte [2]. The corresponding Lagrangian of the model is just the equation (7). Keywords: Unified models, quintessence, interaction, dark sector. 1. INTRODUCTION  Due to the additivity of the stress-energy tensor it is possible to describe the quintessence field in terms of two interacting fluids, namely, stiff matter and vacuum energy. Besides, the total energy-momentum conservation is equivalent to the Klein-Gordon equation [3, 4]. This description was generalized assuming a mixture of two fluids with constant equations of state, which interact between them in a flat Friedmann-Robertson-Walker model [2]. There, a scalar field  representation of the mixture of two interacting fluids was introduced by imposing the condition that 2 is an appropriate linear combination of the energy densities 1  and 2  of both fluids. Under these conditions, the resulting model was called exotic quintessence. 2. EXOTIC QUINTESSENCE  We present the exotic quintessence model developed in [2] including two extra matter components, with energy densities 3  and 4 , which separately satisfy their own equations of conservation. In this case, the Einstein equations read: 3H 2 = 1 + 2 + 3 + 4 ,  (1)  1+ 2 + 3H[(1+ w1 ) 1 + (1+ w2 ) 2 ] = 0,  (2)  3+ 3H (1+ w3 ) 3 = 0,  (3)  4+ 3H (1+ w4 ) 4 = 0,  (4) where we have adopted constant equations of state wn = pn / n  for each fluid with n  = 1,2,3,4. Units are    *Address correspondence to this author at the Departamento de Fsica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina;  Tel: 54-11-4576-3390,  Ext. 830; Fax: 54-11-4576-3357;  E-mail: forte.monica@gmail.com chosen so that the gravitational constant is set to 8 G =1  and c =1 . We introduce a scalar field  representation of the interacting two first fluids associating  2 with the following linear combination of 1  and 2  2 = (1+ w1 ) 1 + (1+ w2 ) 2 .  (5)  From Eqs. (2) and (5) we obtain the total energy density and pressure of the four-fluid mixture, and the dynamical equation for the scalar field  =21+ w1+w1 w21+ w12 + 3 + 4 ,  (6)  p =w121+ w1w1 w21+ w12 + w3 3 + w4 4 ,  (7) +32(1+ w1 )H +w1 w222 = 0.  (8)  These equations define the exotic quintessence model. CONCLUSIONS  Choosing w1 = 0 , w3 = 0 , w4 = 1 / 3 , and making the substitutions / 2  and w2 2 ( ) , the Einstein and the exotic quintessence equations are reduced to the expressions (21)-(23) of the paper [1]. On the other hand, if we impose the integrability condition mentioned in [2]  2+ A 2 = 0,  (9) on the field equation (8) with a constant A , we get 2 ( ) exp( A )  after integrating the Eq. (9). Then, the exotic quintessence model with the integrability condition (9) leads to an exotic scalar field driven by an exponential potential and thus to obtain the model investigated in ref. [1]. As was already pointed in ref. [2], this model is integrable and can be solved exactly. 26    The Open Nuclear & Particle Physics Journal, 2011, Volume 4 Chimento and Forte REFERENCES [1] Gao C, Kunz MAR. Liddle, D Parkinson. Unified dark energy and dark matter from a scalar field different from quintessence. Phys Rev D 2010; 81: 043520. [2] Chimento LP, Forte M. Unified model of baryonic matter and dark components. Phys Lett B 2008; 666: pp. 205. [3] LP Chimento. Symmetry and inflation. Phys Rev D 2002; 65: 063517. [4] LP Chimento. Interacting fluids generating identical, dual and phantom cosmologies. Phys Lett B 2006; 633: 9.   Received: July 26, 2011 Revised: September 12, 2011 Accepted: September 15, 2011  © Chimento and Forte; Licensee Bentham Open.  This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.   

Monica Forte

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Comments on Unified Dark Energy and Dark Matter from a Scalar Field Different from Quintessence

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