Cosmology 259energy. Inflationary cosmology requires that the relaxation time be long compared
to a Hubble time during the first instants after the big bang so that the universe can
undergo the cosmic acceleration necessary to resolve the horizon and flatness prob-
lems and generate a nearly-scale invariant spectrum of density fluctuations. After
inflation, it is essential that the relaxation time become short compared to a Hub-
ble time in order for primordial nucleosynthesis and galaxy formation to proceed
in accordance with observations. The discovery of dark energy, though, means that
the universe entered a new period of cosmic acceleration 10 billion years later, so
the relaxation time must be long compared to a Hubble time today. The situation
seems to call for a relaxation mechanism that transforms magically on cue from
slow to fast and back to slow again, a cosmological somersault that appears to be
anything but simple.
In this comment, I would like to introduce a suggestion by Neil Turok and
myself [l] for reviving the concept of a simple dynamical relaxation mechanism.
Here, rather than seeking a relaxation time that is sometimes shorter and sometimes
longer than a Hubble time, we propose a relaxation time that is always exponentially
long compared to a Hubble time. (Finding ultra-slow relaxation mechanisms turns
out not to be difficult; as illustrated below, some have already been identified in the
literature.) In our picture, A is decreasing excruciatingly slowly throughout cosmic
history at a rate too small to be detected even after 14 billion years. Furthermore,
the relaxation process slows downs as A approaches zero from above. Hence, most of
cosmic history is spent with a small, positive cosmological constant, in accordance
with what we observe.
Before describing how the concept works, it is instructive to compare our picture
of the cosmological constant with the case of the 'Hubble constant,' H. H is about
GeV, exponentially tiny compared to the QCD, electroweak or Planck scale.
If it were truly a constant, physicists would find it hard to understand how its value
could emerge from fundamental physics. Yet, this small value is essential if galaxies,
stars and planets are ever to form. Some might feel driven to introduce an anthropic
principle or multiverse to explain the small value. But, as we already know, this is
not necessary. We understand that Einstein's theory of general relativity tells us
that the 'Hubble constant' is not a constant after all and that gravity incorporates
a dynamical relaxation mechanism that naturally causes H to decrease with time.
H was once large ~ so large that galaxies could not form - but after 5 billion yearsit reached a value small enough for structure to evolve. Furthermore, the Hubble
constant decreases more slowly as its value shrinks, so most of cosmic history is
spent with a small positive Hubble constant. So, as far as the Hubble constant is
concerned, we live at a typical location in space and time. Its small value today is
not considered a deep mystery; it is just a sign that the universe is old compared
to a Planck time.
The key difference is a matter of timescale.
The Hubble constant changes by a factor of lo1'' in 14 billion years. For theOur proposal for A is similar.