A New Approach to Testing Dark Energy Models by Observations Page: 3 of 19
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The accelerating expansion of the universe in the present epoch was discovered in 1998
[1, 2] via Type Ia supernova (SN Ia) distance measurement. This has been confirmed by more
recent observations, including SN Ia [3, 4, 5], cosmic microwave background (CMB)  and
large-scale structure (LSS)  observations. Models with a wide variety of strategies have
been proposed to explain this salient phenomenon. One of the approaches invokes an energy
source, generally referred to as "dark energy", that provides a significant negative pressure
and therefore a repulsive gravity (anti-gravity). Examples of dark energy candidates include
a positive cosmological constant [8, 9, 10] and a dynamical scalar field such as quintessence
[11, 12, 13] and phantom .
So far many of these models remain consistent with observational results. In this situation
the dark energy information obtained by comparing the individual theoretical model with
the observational data is indecisive. Responding to this deficiency, recently cosmologists
attempt to extract the generic features of dark energy, such as (the constraints on) the
equation of state (EoS) or the energy density as a function of the redshift, from observational
results by invoking model-independent parametrizations in data analysis [15, 16, 17, 18]. It is
hoped that several generic questions can be addressed through this approach. A particularly
important question is: Is dark energy a cosmological constant? If not, it is essential to explore
how the dark energy density evolves with time. A specific manifestation of this would be
the deviation of the dark energy EoS from -1.
Along a similar line with the utilization of a parametrization, in the present paper we
propose a new approach to the testing of the consistency between observational results and
dark energy models or, more generally, cosmological models. For each category of dark
energy models we suggest introducing a distinct characteristic Q(z) that in general varies
with time and the redshift z but is equivalent to an essential constant parameter within the
scope of that category of models. In general the quantities, Q(z) and dQ(z)/dz, by design
can be reconstructed from data with no reliance on the other parameters of the models. The
consistency between data and models can then be assessed by comparing the observational
constraint on dQ(z)/dz with the theoretical prediction, dQ(z)/dz = 0. This approach
in principle provides a simple "litmus test" for each category of dark energy models. In
addition, for a category of models that passes the test we can further constrain the distinct
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Gu, Je-An; /NCTS, Hsinchu /Taiwan, Natl. Taiwan U.; Chen, Chien-Wen; /Taiwan, Natl. Taiwan U.; Chen, Pisin; /Taiwan, Natl. Taiwan U. /KIPAC, Menlo Park et al. A New Approach to Testing Dark Energy Models by Observations, article, October 24, 2013; United States. (digital.library.unt.edu/ark:/67531/metadc870095/m1/3/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.