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3.3. Reconstructing the cosmic equation of state

Although fundamental theories such as Supergravity or M-theory do provide a number of possible candidates for quintessence they do not uniquely predict its potential V(phi). Therefore it becomes meaningful to reconstruct V(phi) and the cosmic equation of state w = P / rho directly from observations in a model independent manner [49, 50, 51, 52]. This is possible to do if one notices that the scalar field potential as well as its equation of state can be directly expressed in terms of the Hubble parameter and its derivative

Equation 13 (13)
Equation 14 (14)


Equation 16 (16)

Since the Hubble parameter is related to the luminosity distance

Equation 17 (17)

one can determine both the quintessence potential V(phi) as well as reconstruct its equation of state wphi(z) provided the luminosity distance dL(z) is known from observations. A three parameter ansatz for estimating the luminosity distance was proposed in [49]. Results from that paper reproduced in figure 3 indicate that only a small amount of evolution in wphi(z) is permitted by current SnIa observations. The presence of a cosmological constant is therefore in good agreement with these results.

Figure 3

Figure 3. The equation of state of dark energy/quintessence is reconstructed from observations of Type Ia high redshift supernovae in a model independent manner. The equation of state satisfies -1 leq wphi leq - 0.8 at z = 0; and -1 leq wphi leq - 0.46 at z = 0.83 (90% CL), Omegam = 0.3 is assumed. From Saini, Raychaudhury, Sahni and Starobinsky [49].

A word of caution should be added: as shown in figure 4 a near degeneracy exists between the equation of state of dark energy and the value of Omegam. The latter should therefore be known to better than 5% accuracy for the reconstruction program to yield very accurate results (see also [51]).

Figure 4

Figure 4. The near degeneracy in the luminosity distance is shown for the pair of cosmological models with {Omegam = 0.3, wX = - 1.0} and {Omegam = 0.25, wX = - 0.8}.

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