Comments on the Paper astro-ph/0103335 by C. Rubano and P. Scudellaro

Abstract

We briefly comment on a paper by Rubano and Scudellaro [astro-ph/0103335] where they found general exact solutions for two classes of exponential potentials in a scalar field model for quintessence. In that paper the authors were led to some interesting conclusions after a proper choice of the integration constants. By using dimensionless variables we show that the integration constants can be found explicitly without additional assumptions. In consequence we revise some results and conclusions in that paper. We also reproduce observations for Type-Ia supernovae with good accuracy.

Model of the universe including dark energy accounted for by both a quintessence field and a (negative) cosmological constant

“…and 17) where u 1 , u 2 , v 1 and v 2 are the integration constants. These can be related with the initial conditions for u and v (and their τ -derivatives) thoughout the following equations, 18) and…”

“…Also, we use the experimental fact of a spatially flat universe [16]. We apply the same technique of adimensional variables we used in [17] to determine the integration constants without additional assumptions.…”

Some remarks about non-minimally coupled scalar field models

“…In the reference [136], it was investigated a scalar field non-minimally coupled to the Ricci scalar evolving in Higgs-like (quadratic) potentials plus a negative cosmological constant. Double exponential potential and exponential coupling function were discussed in [91] as well as in [92,93,95,98], under the ansatzφ = λH.…”

“…The potential have been considered as positive and negative exponential [84], single and double exponential [85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106], etc. Multiple scalar fields can be found at [107,108,109,110,111,112,113,114,115,116,117,118].…”

Phase space analysis of quintessence cosmologies with a double exponential potential

“…We use the Friedmann-Robertson-Walker (FRW) ansatz with a non-trivial lapse function to obtain the equations of 1 The general analytic solution of flat FRW universe and a scalar field with a single exponential potential was recently found in ref. [29], while for certain values of parameters general analytic solutions are also known when barotropic matter is added [30,31,32]. 2 When this manuscript was in preparation, ref.…”