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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 [1], 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 [2].

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 [5], 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 aquintessence 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 [6].

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.