Evolving Dark Energy with w =/ -1 Page: 2 of 5
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Evolving Dark Energy with w 0 -1
Lawrence J. Hall, Yasunori Nomura, Steven J. Oliver
Department of Physics, University of California, Berkeley, and
Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Theories of evolving quintessence are constructed that generically lead to deviations from the
w = -1 prediction of non-evolving dark energy. The small mass scale that governs evolution,
m0 10--33 eV, is radiatively stable, and the "Why Now?" problem is solved. These results
rest crucially on seesaw cosmology: in broad outline, fundamental physics and cosmology can be
understood from only two mass scales, the weak scale, v, and the Planck scale, M. Requiring
a scale of dark energy pDE governed by v2/M, and a radiatively stable evolution rate m9 given
by v4/M3, leads to a distinctive form for the equation of state w(z) that follows from a cosine
quintessence potential. An explicit hidden axion model is constructed. Dark energy resides in the
potential of the axion field which is generated by a new QCD-like force that gets strong at the scale
A v2/M ' pDj. The evolution rate is given by a second seesaw that leads to the axion mass,
mo z A2/f, with f M.
1. Introduction The dominant energy density
in the universe has negative pressure, causing a recent
acceleration in the expansion of the universe , and
is known as dark energy. What is the physical picture
for this unusual fluid? How can the size of its energy
density, pDE (it3 eV)4, be understood and how can
the underlying physics be probed?
One interpretation of dark energy is in terms of a pa-
rameter A that determines a fixed energy and pressure for
the vacuum Einstein's cosmological constant. While
the size of the small mass scale, 10-3 eV, has not been
derived from a more basic theory, it could, perhaps, be
broadly understood from mild anthropic arguments .
Alternatively, dark energy may be associated with the
dynamics of some scalar field which is uniform in space,
p(t) [3, 4]. Perhaps the simplest possibility is that the
potential for this field, V(O), is determined by the single
meV mass scale together with dimensionless couplings of
order unity. Such theories of "acceleressence" are easy
to construct , including radiative stability of the meV
scale, but lead to generic observational consequences
for dark energy identical to those from a cosmological
constant. Since the time scale for 0 evolution, meV1 ~
10-12 sec., is much less than the present age of the
universe, to 1018 sec., the field has already evolved
to a local minimum of the effective potential.
An equation of state differing from that of the cosmo-
logical constant results if the time scale for 0 evolution is
of order to. Taylor expanding the potential V(O) about
00, todays value of the field, such theories of quintessence
require a dynamical scale
m = 7"(0o) Ho 10-33 eV. (1)
The appearance of such a low mass scale immediately
raises questions. Can such a mass scale be protected
from radiative corrections? If a mechanism can be found
to stabilize m9 to 10-33 eV, then presumably it could
protect much smaller scales as well, corresponding to a
quintessence theory where 0 is effectively frozen today,
with V(O) acting as a cosmological constant. It is
for these reasons, perhaps, that there is a theoretical
expectation that w= p/p will be found to be -1 and
time independent. However, this expectation ignores the
constraints that will be placed on any theory of dark
energy by requiring that it solves the radiative stability
constraints and the "Dark Energy Why Now?" problem.
Why do we live during an era when the energy densities
in dark matter and dark energy are comparable? This
is the well-known "Dark Energy Why Now?" prob-
lem. Particle physics provides a simple solution to this
problem, at least at the order of magnitude level .
Particle physics can be broadly understood in terms of
two fundamental mass scales: the reduced Planck scale,
M 1018 GeV, and the electroweak scale v 103 GeV.
There is an induced seesaw scale, v2/M, that is also
of great interest. Both the Planck and weak eras were
undoubtedly interesting periods in the evolution of the
universe, and we expect that the seesaw era, with a
temperature of order v2/M iZ 10-3 eV , 10 K, will also
be an interesting epoch. It is significant that the observed
background radiation temperature is within an order of
magnitude of this value we do indeed live during the
seesaw era. During this era, at a temperature of v2/M,
any particle species, or fluid, with an energy density that
depends parametrically on M and v as (v2/M)4 would
be expected to contribute a significant fraction to the
energy density of the universe. The "Dark Energy Why
Now?" problem is solved if theories for dark energy and
dark matter can be constructed that have this parametric
form for their energy densities.
If an evolving quintessence field gives a significant
departure of w from -1, there is a "Quintessence Why
Now?" problem: why do we live during an era when the
p field is just starting to evolve? From (1) this becomes:
why is m9 Ho 0 10--33 eV and not much smaller?
In seesaw cosmology the present value of the Hubble
parameter is given by Ho 0 v4/M3. Once again, seesaw
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Hall, Lawrence J.; Nomura, Yasunori & Oliver, Steven J. Evolving Dark Energy with w =/ -1, article, March 31, 2005; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc928064/m1/2/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.