100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Understanding Our Universe: Current Status and Open Issues 193Fig. 3. Constraints on the possible variation of the dark energy density with redshift.The darker shaded region is excluded by SN observations while the lighter shaded regionis excluded by WMAP observations. It is obvious that WMAP puts stronger constraintson the possible variations of dark energy density. The cosmological constant correspondsto the horizontal line at unity. The region between the dotted lines has w > −1 at allepochs.above, virtually every form of a(t) can be modeled by a suitable “designer”V (φ). (2) These models are degenerate in another sense. Even when w(a)is known/specified, it is not possible to proceed further and determine thenature of the scalar field lagrangian. The explicit examples given aboveshow that there are at least two different forms of scalar field lagrangians(corresponding to the quintessence or the tachyonic field) which could leadto the same w(a). (See Ref. 8 for an explicit example of such a construction.)(3) All the scalar field potentials require fine tuning of the parametersin order to be viable. This is obvious in the quintessence models in whichadding a constant to the potential is the same as invoking a cosmologicalconstant. So to make the quintessence models work, we first need to assumethe cosmological constant is zero! (4) By and large, the potentials used inthe literature have no natural field theoretical justification. All of them arenon-renormalisable in the conventional sense and have to be interpreted asa low energy effective potential in an ad-hoc manner.