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(). Therefore it becomes meaningful to reconstruct V() and the cosmic equation of state w = P / 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
(13) | |
(14) (15) | |
(16) |
Since the Hubble parameter is related to the luminosity distance
(17) |
one can determine both the quintessence potential V() as well as reconstruct its equation of state w_{}(z) provided the luminosity distance d_{L}(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 w_{}(z) is permitted by current SnIa observations. The presence of a cosmological constant is therefore in good agreement with these results.
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 w_{} - 0.8 at z = 0; and -1 w_{} - 0.46 at z = 0.83 (90% CL), _{m} = 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 _{m}. 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. The near degeneracy in the luminosity distance is shown for the pair of cosmological models with {_{m} = 0.3, w_{X} = - 1.0} and {_{m} = 0.25, w_{X} = - 0.8}. |