Dark energy as a modification of the Friedmann equation Page: 2 of 12
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The discovery that the expansion of the Universe is speeding up and not slowing down [1, 2]
has presented cosmologists and particle physicists with a profound (and wonderful) puzzle.
In the context of general relativity this surprising result can be accounted for by the existence
of a smooth component of energy with large negative pressure (w - p/p < -1/2), dubbed
dark energy, which accounts for about 2/3 of the critical density .
A number of suggestions for the dark energy have been discussed including quantum
vacuum energy (cosmological constant), a very light and slowly evolving scalar field, and a
frustrated network of topological defects. None is compelling and all have serious conceptual
Another logical possibility is that the phenomenon of accelerated expansion is actually a
sign of a breakdown of the standard Friedmann equation which governs the expansion rate,
which is the idea we explore here.
The high degree of isotropy and large-scale homogeneity observed in the Universe implies
that the metric of our 4-d spacetime can be written in the Robertson - Walker form with
a single function - the cosmic scale factor R(t) - describing the large-scale dynamics of the
Universe. The issue then is the equation(s) that govern the evolution of the cosmic scale
It should be noted that the kinematics of the expansion - acceleration or deceleration -
can be discussed without regard to dynamics, and further, that the current type Ia supernova
(SNIa) data indicate a recent period of acceleration (R/HR2 > 0 for z < 0.5) preceded by
an earlier period of deceleration (R/H2R < 0 for z > 0.5) . Thus, simply allowing for
modified dynamics cannot eliminate the puzzling phenomenon of accelerated expansion.
In this paper, we investigate the addition to the Friedmann equation of a term, (1 -
QM)HO/HO -2, which can arise with theories with extra dimensions . We know that at
early times the Friedmann equation is a good approximation and this fact constrains a to
be < 1. We further show that such a modification has an equivalent description as dark
energy with time varying equation-of-state wef(z). Finally, we show that future supernova
measurements envisioned with SNAP  can constrain a to a precision of about half that of
w, i.e., a ~ 2am, or about a0 ~ 0.1.
In the next Section we discuss some theoretical motivations for a modification to the
Friedmann equation, and in the following Section we discuss the cosmological phenomenology
of "m dark energy." We end with a brief summary.
Both the hierarchy [7, 8] and cosmological constant  problems motivate theories with
large extra dimensions. Extra dimensions that are either compact or have finite volume
manifest themselves exclusively at high energies, above the compactification scale. Such
theories modify laws of gravity only at short distances, below the size of the extra dimensions.
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Dvali, Gia; U., /New York; Turner, Michael S. & /Chicago U., Astron. Astrophys. Ctr. /KICP, Chicago /Chicago U., EFI /Fermilab. Dark energy as a modification of the Friedmann equation, article, January 1, 2003; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1409385/m1/2/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.