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A convergence of ideas, observations and technology have led to the greatest period of cosmological discovery yet. Over the past three years we have determined the basic features of our Universe. We are now challenged to make sense of what we have found. The outcome of planned experiments and observations as well as new ideas will be required. If we succeed, ours truly will be a Golden Age of Cosmology.
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\Title{A Cosmic Perspective from Lapland in 2001}
\vfill

\Author{MICHAEL S. TURNER\footnote{Work supported by the NASA at Fermilab
and the DOE at Chicago and Fermilab.}}

\Address{Center for Cosmological Physics\\
Departments of Astronomy \&
Astrophysics and of Physics\\
Enrico Fermi Institute, The University of Chicago\\
Chicago, IL~~60637-1433, USA}
%\vfill
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\Address{NASA/Fermilab Astrophysics Center\\
        Fermi National Accelerator Laboratory\\
        Batavia, IL~~60510-0500, USA\\
E-mail: mturner@oddjob.uchicago.edu}

\vfill
\begin{Abstract}

A convergence of ideas, observations and technology have led
to the greatest period of cosmological discovery yet.  Over
the past three years we have determined the
basic features of our Universe.  We are now challenged
to make sense of what we have found.  The outcome of
planned experiments and observations as well as new ideas 
will be required.  If we succeed, ours truly will
be a Golden Age of Cosmology.

\end{Abstract}
\vfill
\begin{Presented}
    COSMO-01 \\
    Rovaniemi, Finland, \\
    August 29 -- September 4, 2001
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\section{How Did We Get Here?}

Cosmology is currently in its most exciting period ever.
However, the past hundred years haven't been too bad either.
In 1916, Einstein introduced general relativity, the first theoretical
framework up to describing the evolution of the Universe.
In the next decade, Hubble established the extragalactic
nature of the nebulae and put forth the first systematic
evidence for the expansion of the Universe.  This burst of
activity was powered by ideas -- general relativity --
and technology -- big telescopes on high mountains -- and
marked the beginning of modern cosmology.

Cosmology then stalled for some twenty years.  During that time,
the 100-inch Mt. Wilson telescope and its counterpart at the
Lick Observatory charted only a few
hundred galaxies, with redshifts less than $z=0.1$ \cite{history}.
Most of the Universe lay beyond their reach.  While some important
new theoretical ideas were introduced, most notably the idea of a
hot big bang by Gamow and
his collaborators, theory did little to push things forward either.

First light at the 200-inch Hale telescope on Palomar and the
steady state vs. hot big bang controversy signaled the beginning
of a new period of discovery around 1950.  Once again, it was 
the combination of theory and observation that propelled the field
forward.  The discovery of quasars and
radio-source counts murdered cosmology's most beautiful
theory -- the steady state -- in the early 1960s.  I note the important
role played here by a strong theory -- that is, one that makes
sharp predictions and is therefore easily falsified.
Because the steady state predicts a nonevolving Universe,
any evidence of evolution can falsify it (here, the distribution of
radio sources vs. their strength and the large abundance of quasars
seen at high redshift).

The discovery of the cosmic background radiation in 1964 by Penzias
and Wilson broke things wide open, and cosmology became a legitimate
branch of physics.  The details of Gamow's nucleosynthesis scheme
were worked out in detail and became big-bang nucleosynthesis,
and the large mass fraction of $^4$He predicted by the hot big-bang
model became its first success.  In Chapter 15 of his
influential text, {\em Gravitation and Cosmology}, Steven Weinberg laid
out ``The Standard Cosmology'' and coined the term \cite{weinberg1}.
The Standard Cosmology meant the hot big-bang model, from shortly
before the epoch of big-bang nucleosynthesis to the present.
A convergence of ideas (a better understanding of general relativity
and the careful application of physics to the early Universe) and
observations (the discovery of the cosmic microwave background) again had
powered a significant advance our understanding of the Universe.

According to Weinberg's same text, the period before BBN
($t\la 10^{-4}\,$sec) was ``cosmos incognito'' (cf, Section 15.11).
He recognized quite correctly that the key
to further progress was a better understanding of the elementary
particles.  A subatomic world of strongly interacting particles
with exponentially rising numbers, which was the world view of
subatomic physics then, leads to a maximum temperature
and a breakdown of any simple statistical mechanical treatment.

The breakthrough came in the mid 1970s with the emergence of the standard
model of particle physics and its point-like quark/lepton
constituents with asymptotically weak interactions.  The grander
ideas about unification of the strong and electroweak interactions (GUTs)
that came somewhat later were even more influential.
Asymptotically free gauge theories, GUTs and the sturdy framework of the
hot big-bang fueled a decade of very fertile speculation about the
early Universe in the 1980s (``the go-go junk bond days
of early-Universe cosmology'').  

There was optimism  that the marriage
of ideas about unification with early-Universe cosmology could solve
some of the most pressing questions in cosmology.  The puzzles at
the time included \cite{swogu}: What is the origin
of the baryon asymmetry?  Why is the Universe so smooth, flat, and old?
How did the primeval lumpiness that seeded all structure arise?  What is
the dark matter?  And the marriage brought a new problem:  the glut of
superheavy magnetic monopoles expected from the GUT phase transition (about
one per baryon!).

Grand ideas, clever scenarios, and interesting schemes were suggested -- topological
defects, baryogenesis, particle dark matter, phase transitions, inflation,
superheavy relics, superconducting cosmic strings, unstable relics,
colored relics, relics produced by the decay of other relics, hot dark
matter, cold dark matter, warm dark matter, shadow
worlds, mirror worlds, parallel universes, and on and on.  It was a
fantastic time for theorists.

A handful of these ideas stood the test of time.  In the go-go 80s,
that meant surviving more than a month without being falsified, being
replaced by a better idea, or going out of style.  The survivors --
particle dark matter, inflation, topological defects, and baryogenesis
-- began to form the basis of a new cosmological framework.  However,
only a few years later, the very beautiful idea that topological defects
seeded large-scale structure was killed by cosmic microwave background
measurements that began to show a series of well formed acoustic peaks. 
(Only adiabatic density perturbations lead to such a structure in
the CMB power spectrum.)

Inflation and cold dark matter survived the cut.   Moreover,
they were expansive and eminently testable.
Theorists like to think (and with some good reason) that the
tremendous growth in observational cosmology over the
past decade has something to do with how powerful their ideas are.
Technology -- the advent of large format CCDs, 6-meter, 8-meter,
and 10-meter ground based telescopes, the Hubble Space Telescope,
HEMTs, bolometers and large-scale computing -- of course played
a role too.  An avalanche of data, which has made cosmological
phenomenology possible and the term ``precision cosmology'' a reality,
started in the mid 1990s.  And there is no end in sight.

We are now in the midst of a great period of cosmic discovery.  Once 
again, it came about through a convergence of ideas and technology.
Thus far, we have determined the basic features of our Universe, which
are pointing to a new standard cosmological model.  While we learned
much about the Universe, we still have much more to understand.

\section{The New Cosmology}

Over the past three years a New Cosmology
has been emerging.  It incorporates the highly successful standard
hot big-bang cosmology \cite{weinberg1,hbb_std} and may extend our
understanding of the Universe to times as early as
$10^{-32}\,$sec, when the largest structures in the Universe
were still subatomic quantum fluctuations.

This New Cosmology is characterized by

\begin{itemize}

\item Flat, critical density accelerating Universe

\item Early period of rapid expansion (inflation)

\item Density inhomogeneities produced from quantum fluctuations during inflation

\item Composition:  2/3 dark energy; 1/3 dark matter; 1/200 bright stars

\item Matter content:  $(29\pm 4)$\% cold dark matter; $(4\pm 1)$\% baryons;
$\ga 0.3$\% neutrinos

\item $T_0=2.725\pm 0.001\,$K

\item $t_0 = 14 \pm 1\,$Gyr

\item $H_0= 72\pm 7\,{\rm km\,s^{-1}\,Mpc^{-1}}$

\end{itemize}

The New Cosmology is not as well established as the
standard hot big-bang cosmology.  However, the evidence is growing.

\subsection{Mounting Evidence:  Recent Results}

The position of the first acoustic peak in the multipole power
spectrum of the anisotropy of the cosmic microwave background
(CMB) radiation provides a powerful means of determining the
global curvature of the Universe.  With the recent DASI observations
of CMB anisotropy on scales of one degree and smaller,
the evidence that the Universe is at most very slightly curved is
quite firm \cite{flat}.  The curvature radius of the Universe
($\equiv R_{\rm curv}$) and the total energy density parameter
$\Omega_0= \rho_{\rm TOT}/ \rho_{\rm crit}$, are related:
$$ R_{\rm curv} = H_0^{-1}/|\Omega_0-1|^{1/2}$$
The spatial flatness is expressed as $\Omega_0 = 1.0\pm 0.04$,
or said in words, the curvature radius is at least 50 times greater
than the Hubble radius.

I will discuss the evidence for accelerated
expansion and dark energy later.

The series of acoustic peaks in the CMB multipole power spectrum and
their heights indicate a nearly scale-invariant spectrum
of adiabatic density perturbations with $n=1\pm 0.07$.
Nearly scale-invariant density perturbations and a flat Universe
are two of the three hallmarks of inflation.  Thus, we are beginning
to see the first significant experimental evidence for inflation,
the driving idea in cosmology for the past two decades.

The striking agreement of the BBN determination of the baryon
density from measurements of the primeval deuterium
abundance \cite{tytler,baryon_density},
$\Omega_B h^2 = 0.020\pm 0.001$, with those from from recent
CMB anisotropy measurements \cite{flat}, $\Omega_Bh^2 = 0.022\pm 0.004$,
make a strong case for a small baryon density, as well as the
consistency of the standard cosmology ($h=H_0/100\,{\rm km\,
sec^{-1}\,Mpc^{-1}}$).  There can now be little doubt that baryons
account for but a few percent of the critical density.

Our knowledge of the total matter density is improving, and becoming
less linked to the distribution of light.  This makes determinations
of the matter less sensitive to the uncertain relationship between the
clustering of mass and of light (what astronomers call the bias
factor $b$) \cite{turner2001}.  Both the CMB and clusters of galaxies allow
a determination of the ratio of the total matter density (anything that
clusters -- baryons, neutrinos, cold dark matter) to that in baryons alone:
$\Omega_M/\Omega_B = 7.2\pm 2.1$ (CMB) \cite{cmbratio},
$9\pm 1.5$ (clusters) \cite{mohr}.  Not only are these numbers consistent, they
make a very strong case for something beyond quark-based matter.  When
combined with our knowledge of the baryon density, one infers a total
matter density of $\Omega_M = 0.33\pm 0.04$ \cite{turner2001}.

The many successes of the cold dark matter (CDM) scenario  -- from
the sequence of structure formation (galaxies first, clusters
of galaxies and larger objects later) and the structure of the intergalactic
medium, to its ability to reproduce the power spectrum
of inhomogeneity measured today -- makes it
clear that CDM holds much, if not all, of the truth in describing
the formation of structure in the Universe.

The two largest redshift
surveys, the Sloan Digital Sky Survey (SDSS) and the 2-degree Field
project (2dF), have each recently measured the power spectrum
using samples of more than 100,000 galaxies and found that it is
consistent with that predicted in a flat accelerating Universe comprised
of cold dark matter \cite{powerspectrum}.  The SDSS will eventually
use a sample of almost one million galaxies to probe the power spectrum.
[Interestingly enough, according to the 2dF Collaboration, bias appears
to be a small effect, $b= 1.0 \pm 0.09$ \cite{bias}.]

All of this implies that
whatever the dark matter particle is, it moves slowly (i.e., the
bulk of the matter cannot be in the form of hot dark matter such
as neutrinos) and interacts only weakly (e.g., with strength much
less than electromagnetic) with ordinary matter.

The evidence from SuperKamiokande \cite{superK} for neutrino oscillations
makes a strong case that neutrinos have mass ($\sum_i m_\nu
\ga 0.1\,$eV) and therefore contribute to the mass budget of the
Universe at a level comparable to, or greater than, that of bright stars.
Particle dark matter has moved from the realm of a hypothesis to
a quantitative question -- how much of each type of particle
dark matter is there in the Universe?  Structure
formation in the Universe (especially the existence of small scale
structure) suggests that neutrinos contribute at most 5\% or 10\%
of the critical density, corresponding to $\sum_i m_nu = \sum_i
m_\nu /90h^2\,{\rm eV} \la 5\,$eV \cite{cosmo_nulimit}.

Even the age of the Universe and the pesky Hubble constant have
been reined in.  The uncertainties in the ages of the oldest globular clusters
have been better identified and quantified, leading to a more precise
age, $t_0 = 13.5\pm 1.5\,$Gyr \cite{krauss}.  The CMB
can be used to constrain the expansion age, independent of direct
measurements of $H_0$ or the composition of the Universe,
$t_{\rm exp} = 14\pm 0.5\,$Gyr \cite{knox}.

A host of different techniques are consistent
with the Hubble constant determined by the HST key project,
$H_0 = 72\pm 7\,{\rm km\,s^{-1}\,Mpc^{-1}}$.  Further, the error
budget is now well understood and well quantified \cite{H0}.
[The bulk of the $\pm 7$ uncertainty is systematic, dominated
by the uncertainty in the distance to the LMC and the Cepheid
period -- luminosity relation.]  Moreover, the expansion age
derived from this consensus Hubble constant,
which depends upon the composition of the
Universe, is consistent with the previous two age
determinations.

The poster child for precision cosmology continues to be the present
temperature of the CMB.  It was determined by the FIRAS instrument on
COBE to be:  $T_0 = 2.725\pm 0.001\,$K \cite{firas}.  Further,
any deviations from a black body spectrum are smaller than
50 parts per million.  Such a perfect Planckian spectrum has made
any noncosmological explanation untenable.

\subsection{Successes and Consistency Tests}

To sum up, we have determined the basic features of the Universe:
the cosmic matter/energy budget; a self consistent
set of cosmological parameters with realistic errors; and the global
curvature.  Two of the three key predictions of
inflation -- flatness and nearly scale-invariant,
adiabatic density perturbations -- have passed their first significant
tests.  Last but not least, the growing quantity of precision data are
now testing the consistency of the Friedmann-Robertson-Walker framework
and General Relativity itself.

In particular, the equality of the baryon densities determined from
BBN and CMB anisotropy is remarkable.  The first involves nuclear physics
when the Universe was seconds old, while the latter involves gravitational
and classical electrodynamics when the Universe was 400,000 years old.

The entire framework has been tested by the existence of the aforementioned
acoustic peaks in the CMB angular power spectrum.  They reveal large-scale
motions that have remained coherent over hundreds of thousands of years,
through a delicate interplay of gravitational and electromagnetic interactions.

Another test of the basic framework is the accounting of the density of
matter and energy in the Universe.  The CMB measurement of spatial flatness
implies that the matter and energy densities must sum to the critical density.
Measurements of the matter density indicate $\Omega_M = 0.33\pm 0.04$;
and measurements of the acceleration of the Universe from supernovae
indicate the existence of a smooth dark energy component that accounts
for $\Omega_X \sim 0.67$.  [The amount of dark energy inferred from the
supernova measurements depends its equation of state; for a cosmological
constant, $\Omega_\Lambda = 0.8 \pm 0.16$.]

Finally, while cosmology has in the past been plagued by ``age crises'' -- time
back to the big bang (expansion age) apparently less than the ages of the
oldest objects within the Universe -- today the ages determined by very different
and completely independent techniques point to a consistent age of 14\,Gyr.


\section{Mysteries}

Cosmological observations over the next decade
will test -- and probably refine -- the New Cosmology \cite{pasp_essay}.
If we are fortunate, they
will also help us to make better sense of it.  At the moment, the
New Cosmology has presented us with a number of cosmic
mysteries -- opportunities for surprises and
new insights.  Here I will quickly go through my list, and save the
most intriguing to me -- dark energy -- for its own section.

\subsection{Dark Matter}

By now, the conservative hypothesis is that the dark matter consists of a
new form of matter, with the axion and neutralino as the leading
candidates. That most of the matter in the Universe exists in a new
form of matter -- yet to be detected in the laboratory -- is a bold
and untested assertion.

Experiments to directly detect the neutralinos or axions holding our own galaxy
together have now reached sufficient sensitivity to probe the regions
of parameter space preferred by theory.  In addition, the neutralino can
be created by upcoming collider experiments (at the Tevatron or the LHC),
or detected by its annihilation signatures -- high-energy neutrinos from
the sun, narrow positron lines in the cosmic rays, and gamma-ray
line radiation \cite{dm_review}.

While the CDM scenario is very successful there are some nagging problems.
They may point to a fundamental difficulty or may be explained by messy
astrophysics \cite{kosowsky}.  The most well known of these problems are
the prediction of cuspy dark-matter halos (density profile $\rho_{\rm DM}
\rightarrow 1/r^n$ as $r\rightarrow 0$, with $n\simeq 1 - 1.5$)
and the apparent prediction of too much substructure.  While there are plausible
astrophysical explanations for both problems \cite{cusp_clump}, they could indicate an
unexpected property of the dark-matter particle (e.g., large self-interaction
cross section \cite{pjsdns}, large annihilation cross section \cite{kkt},
or mass of around 1\,keV).  While I believe it is unlikely, these problems
could indicate a failure of the particle dark-matter paradigm
and have their explanation in a radical modification of gravity theory \cite{kosowsky}.

I leave for the ``astrophysics to do list'' an accounting of the dark
baryons.  Since $\Omega_B \simeq 0.04$ and $\Omega_* \simeq 0.005$,
the bulk of the baryons are optically dark.  In clusters, the dark
baryons have been identified:  they exists as hot, x-ray emitting
gas.  Elsewhere, the dark baryons have not yet been identified.  According
to CDM, the bulk of the dark baryons are likely to exist as hot/warm gas
associated with galaxies, but this gas has not been detected.  [Since
clusters account for only about 5 percent of the total mass, the bulk
of the dark baryons are still not accounted for.]


\subsection{Baryogenesis}

The origin of quark-based matter is not yet fully understood.  We do
know that the origin of ordinary matter requires a small excess of
quarks over antiquarks (about a part in $10^9$)
at a time at least as early as $10^{-6}\,$sec,
to avoid the annihilation catastrophe associated with a baryon symmetric
Universe \cite{hbb_std}.  If the Universe underwent inflation, the baryon asymmetry cannot
be primeval, it must be produced dynamically (``baryogenesis'')
after inflation since
any pre-inflation baryon asymmetry is diluted away by the enormous entropy
production associated with reheating.

Because we also now know that electroweak processes
violate $B+L$ at a very rapid rate at temperatures
above $100\,$GeV or so, baryogenesis is more constrained than when the idea
was introduced more than twenty years ago.  Today there are three
possibilities:  1) produce the baryon asymmetry by GUT-scale physics with $B-L
\not= 0$ (to prevent it being subsequently washed away by $B+L$ violation);
2) produce a lepton asymmetry ($L \not= 0$), which is then transmuted
into the baryon asymmetry by electroweak $B+L$ violation \cite{leptogenesis}; or
3) produce the baryon asymmetry during
the electroweak phase transition using electroweak $B$ violation \cite{electroweak}.

While none of the three possibilities can be ruled out, the second possibility
looks most promising, and it adds a new twist to the origin of quark-based matter:
We are here because neutrinos have mass.  [In the lepton asymmetry first
scenario, Majorana neutrino mass provides the requisite lepton number violation.]
The drawback of the first possibility is the necessity of a high reheat temperature
after inflation, $T_{\rm RH} \gg 10^{5}\,$GeV, which is difficult to
achieve in most models of inflation.  The last possibility, while
very attractive because all the input physics might be measurable at
accelerator, requires new sources of $CP$ violation at TeV energies as well
as a strongly first-order electroweak phase transition (which is currently
disfavored by the high mass of the Higgs) \cite{electroweak}.

\subsection{Inflation}


There are still many questions to be answered about inflation, including the
most fundamental:  did inflation (or something similar) actually take place!

A powerful program is in place to test the inflationary framework.  Testing
framework involves testing its three robust predictions:
spatially flat Universe; nearly-scale
invariant, nearly power-law spectrum of Gaussian
adiabatic, density perturbations; and a spectrum of
nearly scale-invariant gravitational waves.

The first two predictions are being probed today and
will be probed much more sharply over the next decade.  The value of
$\Omega_0$ should be determined to much better than 1 percent.
The spectral index $n$ that characterizes the density
perturbations should be measured to percent accuracy.

Generically, inflation predicts $|n-1| \sim
{\cal O}(0.1)$, where $n=1$ corresponds to exact scale invariance.
Likewise, the deviations from an exact power-law predicted by
inflation \cite{kosowskymst}, $|dn /d\ln k| \sim 10^{-4} - 10^{-2}$
will be tested.  The CMB and the abundance of rare objects such
as clusters of galaxies will allow Gaussianity to be tested.

Inflationary theory has given little guidance as to the amplitude
of the gravitational waves produced during inflation.  If detected,
they are a smokin' gun prediction.  Their amplitude is directly
related to the scale of inflation, $h_{\rm GW} \simeq H_{\rm inflation}/\mpl$.
Together measurements of $n-1$ and $dn/ \ln k$, they can reveal much
about the underlying scalar potential driving inflation.  Measuring their
spectral index -- a most difficult task -- provides a consistency test
of the single scalar-field model of inflation \cite{reconstruct}.

\subsection{The Dimensionality of Space-time}

Are there additional spatial dimensions beyond the three for which
we have very firm evidence?  I cannot think of a deeper question
in physics today.  If there are new dimensions, they are likely
to be relevant for cosmology, or at least raise new questions in
cosmology (e.g., why are only three dimensions large?  what is going
on in the bulk? and so on).  Further, cosmology may well be
the best means for establishing the existence of extra dimensions.


\subsection{Before Inflation, Other Big-bang Debris, and Surprises}

Only knowing everything there is to know about the Universe
would be worse than knowing all the questions to ask about it.
Without doubt, as our understanding deepens, new questions and
new surprises will spring forth.

The cosmological attraction of inflation
is its ability to make the present state of the Universe insensitive
to its initial state.  However, should we establish inflation as part of
cosmic history, I am certain that cosmologists will begin asking
what happened before inflation.

Progress in cosmology depends upon studying relics.  We have made
much of the handful we have -- the light elements, the baryon asymmetry,
dark matter, and the CMB.  The significance of a new relic cannot
be overstated.  For example, detection of the cosmic sea of neutrinos would
reveal the Universe at 1 second.

Identifying the neutralino
as the dark matter particle and determining its properties at an accelerator
laboratory would open a window on the Universe at $10^{-8}\,$sec.
By comparing its relic abundance as derived from its mass and cross section
with its actual abundance measured in the Universe, one could test
cosmology at the time the neutralino abundance was determined.

And then there may be the unexpected.  Recently, a group reported evidence
for a part in $10^5$ difference in the fine-structure constant at redshifts
of order a few from its value today \cite{varying_alpha}.  I remain skeptical,
given possible astrophysical explanations, other much tighter constraints
to the variation of $\alpha$ (albeit at more recent times), and the absence
of a reasonable theoretical model.  For reference, I was also skeptical
about the atmospheric neutrino problem because of the need for large-mixing
angles.

\section{Dark Energy:  Seven Things We Know}

The dark energy accounts for 2/3 of the stuff in
the Universe and determines its destiny.  That puts it high
on the list of outstanding problems in cosmology.
Its deep connections to fundamental physics -- a new
form of energy with repulsive gravity and possible implications for
the divergences of quantum theory and supersymmetry breaking --
put it very high on the list of outstanding problems
in particle physics \cite{weinberg,carroll}.

What then is dark energy?  Dark energy is my term for the
causative agent for the current
epoch of accelerated expansion.  According to the second
Friedmann equation,
\begin{equation}
{\ddot R \over R} = -{4\pi G \over 3}\left( \rho + 3 p \right)
\label{eq:acc-eq}
\end{equation}
this stuff must have negative pressure, with magnitude
comparable to its energy density, in order to produce accelerated
expansion [recall $q = -(\ddot R/R)/H^2$; $R$ is the
cosmic scale factor].  Further, since
this mysterious stuff does not show its presence in galaxies
and clusters of galaxies, it must be relatively smoothly distributed.

That being said, dark energy has the following defining properties:
(1) it emits/absorbs no light; (2) it has large, negative pressure,
$p_X \sim -\rho_X$; (3) it is approximately
homogeneous (more precisely, does not
cluster significantly with matter on scales at least as large as clusters
of galaxies); and (4) it is very mysterious.
Because its pressure is comparable in magnitude
to its energy density, it is more ``energy-like'' than ``matter-like''
(matter being characterized by $p\ll \rho$).
Dark energy is qualitatively very different from dark matter, and is
certainly not a replacement for it.

\subsection{Two Lines of Evidence for an Accelerating Universe}

Two independent lines of reasoning point to an accelerating Universe.  The first
is the direct evidence based upon measurements of type Ia supernovae
carried out by two groups, the Supernova Cosmology Project \cite{perlmutter} and
the High-$z$ Supernova Team \cite{riess}.  These two teams used different
analysis techniques and different samples of high-$z$ supernovae
and came to the same conclusion:  the expansion of the Universe is speeding
up, not slowing down.

The recent serendipitous discovery of a supernovae at $z=1.76$
bolsters the case significantly \cite{riess2001} and provides the first evidence for
an early epoch of decelerated expansion\cite{turner_riess}.
SN 1997ff falls right on the accelerating Universe curve
on the magnitude -- redshift diagram,
and is a magnitude brighter than expected in a dusty open Universe
or an open Universe in which type Ia supernovae are systematically
fainter at high-$z$.

The second, independent line of reasoning for accelerated expansion
comes from measurements of the composition of the Universe, which
point to a missing energy component with negative pressure.  The argument
goes like this:  CMB anisotropy measurements indicate that
the Universe is nearly flat, with density parameter, $\Omega_0=1.0\pm 0.04$.
In a flat Universe, the matter density and energy density
must sum to the critical density.  However,
matter only contributes about 1/3
of the critical density, $\Omega_M = 0.33\pm 0.04$.
(This is based upon measurements of CMB anisotropy,
of bulk flows, and of the baryonic fraction in clusters.)  Thus,
two thirds of the critical density is missing!  Doing the bookkeeping
more precisely, $\Omega_X = 0.67\pm 0.06$ \cite{turner2001}.

In order to have escaped detection, this missing energy
must be smoothly distributed.
In order not to interfere with the formation of structure (by
inhibiting the growth of density perturbations),
the energy density in this component must change
more slowly than matter (so that it was subdominant in the past).
For example, if the missing 2/3 of critical density were smoothly
distributed matter ($p=0$), then linear density
perturbations would grow as $R^{1/2}$ rather than as $R$.  The shortfall
in growth since last scattering ($z\simeq 1100$) would be a factor of 30,
far too little growth to produce the structure seen today.

The pressure associated with the missing energy component determines
how it evolves:
\begin{eqnarray}
\rho_X & \propto& R^{-3(1+w)} \nonumber\\
\Rightarrow \rho_X /\rho_M &\propto& (1+z)^{3w}
\end{eqnarray}
where $w$ is the ratio of the pressure of the missing energy component
to its energy density (here assumed to be constant).
Note, the more negative $w$, the faster the ratio of missing energy
to matter decreases to zero in the past.  In order to grow the
structure observed today from the density perturbations indicated by CMB anisotropy
measurements, $w$ must be more negative than about $-{1\over 2}$ \cite{turnerwhite}.

For a flat Universe the deceleration parameter today is
$$q_0 = {1\over 2} + {3\over 2}w\Omega_X \sim {1\over 2} + w$$
Therefore, knowing $w<-{1\over 2}$ implies $q_0<0$ and accelerated expansion.
This independent argument for accelerated expansion and dark energy makes
the supernova case all the more compelling.

\subsection{Gravity Can Be Repulsive in Einstein's Theory, But ...}

In Newton's theory, mass is the source of the gravitational
field and gravity is always attractive.  In General Relativity,
both energy and pressure source the gravitational field:
$\ddot R/R \propto -(\rho + 3p)$, cf.,
Eq. \ref{eq:acc-eq}.  Sufficiently large
negative pressure leads to repulsive gravity.

While accelerated expansion can be accommodated within Einstein's theory,
that does not preclude that the ultimate explanation
lies in a fundamental modification of Einstein's theory.
Lacking any good ideas for such a modification, I will discuss
how accelerated expansion fits in the context of General Relativity.
If the explanation for the accelerating
Universe ultimately fits within the Einsteinian framework,
it will be a stunning new triumph for General Relativity.

\subsection{The Biggest Embarrassment in all of Theoretical Physics}

Einstein introduced the cosmological constant to balance the attractive
gravity of matter.  He quickly discarded the
cosmological constant after the discovery of the expansion
of the Universe.

The advent of quantum field theory made consideration of
the cosmological constant obligatory, not optional:  The only
possible covariant form for the energy of the (quantum) vacuum,
$$ T_{\rm VAC}^{\mu\nu} = \rho_{\rm VAC}g^{\mu\nu},$$
is mathematically equivalent to the cosmological constant.
It takes the form for a perfect
fluid with energy density $\rho_{\rm VAC}$ and isotropic
pressure $p_{\rm VAC} = - \rho_{\rm VAC}$ (i.e., $w=-1$)
and is precisely spatially uniform.  Vacuum energy is almost
the {\em perfect} candidate for dark energy.

Here is the rub: the quantum zero-point contributions arising from
well-understood physics (the known particles, integrating
up to $100\,$GeV) sum to $10^{55}$
times the present critical density.
(Put another way, if this were so, the Hubble time would
be $10^{-10}\,$sec, and the associated event horizon
would be 3\,cm!)  This is the well known cosmological-constant
problem \cite{weinberg,carroll}.

While string theory currently offers the best hope for
marrying gravity to quantum mechanics, it has shed precious little
light on the cosmological constant problem, other than to speak
to its importance. Thomas has
suggested that using the holographic principle to count
the available number of states in our Hubble volume
leads to an upper bound
on the vacuum energy that is comparable to the energy
density in matter + radiation \cite{sthomas}.  While this
reduces the magnitude of the cosmological-constant
problem very significantly, it does not solve the dark
energy problem:  a vacuum energy that is always comparable
to the matter + radiation energy density would strongly
suppress the growth of structure.

The deSitter space associated with the accelerating Universe may pose
serious problems for the formulation of string theory \cite{witten}.
Banks and Dine argue that all explanations
for dark energy suggested thus far are incompatible with
perturbative string theory \cite{dine_banks}.  At the very
least there is high tension between accelerated expansion
and string theory.

The cosmological constant problem leads to a fork in the
dark-energy road:  one path is to wait for theorists to get the
``right answer'' (i.e., $\Omega_X = 2/3$); the other path is to assume that
even quantum nothingness weighs nothing and something else
with negative pressure must be causing the Universe to speed up.
Of course, theorists follow the advice of Yogi Berra:
``When you see a fork in the road, take it.''

\subsection{Parameterizing Dark Energy:  For Now, It's $w$}

Theorists have been very busy suggesting all kinds of interesting
possibilities for the dark energy:  networks of topological defects,
rolling or spinning scalar fields (quintessence and spintessence),
influence of ``the bulk'', and the breakdown
of the Friedmann equations \cite{carroll,turner2000}.
An intriguing recent paper suggests
dark matter and dark energy are connected through axion
physics \cite{barr_seckel}.

In the absence of compelling theoretical guidance,
there is a simple way to parameterize dark energy,
by its equation-of-state $w$ \cite{turnerwhite}.

The uniformity of the CMB testifies to the near isotropy
and homogeneity of the Universe.  This implies that the
stress-energy tensor for the Universe must take the perfect
fluid form \cite{hbb_std}.  Since dark energy dominates
the energy budget, its stress-energy tensor must, to a
good approximation, take the form
\begin{equation}
{T_{X}}^\mu_\nu \approx {\rm diag}[\rho_X,-p_X,-p_X,-p_X]
\end{equation}
where $p_X$ is the isotropic pressure and the desired dark
energy density is
$$\rho_X = 2.7\times 10^{-47}\,{\rm GeV}^4$$
(for $h=0.72$ and $\Omega_X = 0.66$).  This corresponds to
a tiny energy scale, $\rho_X^{1/4} = 2.3\times 10^{-3}\,$eV.

The pressure can be characterized by its ratio to the
energy density (or equation-of-state):
$$w\equiv p_X/\rho_X$$
Note, $w$ need not be constant; e.g., it could be a function of $\rho_X$
or an explicit function of time or redshift.  ($w$ can always
be rewritten as an implicit function of redshift.)

For vacuum energy $w=-1$; for a network of topological defects
$w=-N/3$ where $N$ is the dimensionality of the defects (1 for
strings, 2 for walls, etc.).  For a minimally coupled, rolling scalar field,
\begin{equation}
w = {{1\over 2} \dot\phi^2 - V(\phi ) \over {1\over 2} \dot\phi^2 + V(\phi )}
\end{equation}
which is time dependent and can vary between $-1$ (when potential energy
dominates) and $+1$ (when kinetic energy dominates).  Here $V(\phi )$ is
the potential for the scalar field.

\subsection{The Universe:  The Lab for Studying Dark Energy}

Dark energy by its very nature is diffuse and a low-energy
phenomenon.  It probably cannot be produced at accelerators;
it isn't found in galaxies or even clusters of galaxies.
The Universe itself is the natural lab -- perhaps the only
lab -- in which to study it.

The primary effect of dark energy on the Universe
is determining the expansion rate.  In turn, the expansion
rate affects the distance to an object at a given
redshift $z$ [$\equiv r(z)$]
and the growth of linear density perturbations.
The governing equations are:
\begin{eqnarray}
H^2(z) & = & H_0^2(1+z)^3 \left[ \Omega_M + \Omega_X(1+z)^{3w} \right] \nonumber\\
r(z) & = & \int_0^z du/H(u) \nonumber \\
0 & = & {\ddot \delta}_k + 2H{\dot\delta}_k -4\pi G\rho_M\delta_k
\end{eqnarray}
where for simplicity $w$ is assumed to be constant
and $\delta_k$ is the Fourier component of comoving
wavenumber $k$ and overdot indicates $d/dt$.

The various cosmological approaches to ferreting
out the nature of the dark energy -- all of which
depend upon how the dark energy affects the expansion
rate -- have been studied \cite{yellowbook}.
Based largely upon my work with Dragan Huterer \cite{ht},
I summarize what we now know about the efficacy of
the cosmological probes of dark energy:

\begin{itemize}

\item Present cosmological observations prefer $w=-1$,
with a 95\% confidence limit $w < -0.6$ \cite{perlmutteretal}.

\item Because dark energy was less important in the past,
$\rho_X/\rho_M \propto (1+z)^{3w}\rightarrow 0$ as $z
\rightarrow \infty$, and the Hubble
flow at low redshift is insensitive to the composition of
the Universe, the most sensitive
redshift interval for probing dark energy is $z=0.2 - 2$ \cite{ht}.

\item The CMB has limited power to probe $w$ (e.g.,
the projected precision for Planck is $\sigma_w = 0.25$)
and no power to probe its time variation \cite{ht}.

\item A high-quality sample of 2000 SNe distributed from
$z=0.2$ to $z=1.7$ could measure $w$ to a precision $\sigma_w
=0.05$ (assuming an irreducible systematic error of 0.14 mag).
If $\Omega_M$ is known independently to better
than $\sigma_{\Omega_M} = 0.03$, $\sigma_w$ improves by
a factor of three and the rate of change of $w^\prime =
dw/dz$ can be measured to precision $\sigma_{w^\prime} = 0.16$ \cite{ht}.

\item Counts of galaxies and of clusters of galaxies may have
the same potential to probe $w$ as SNe Ia.  The
critical issue is systematics (including the evolution of
the intrinsic comoving number density, and the ability to identify
galaxies or clusters of a fixed mass) \cite{count}.

\item Measuring weak gravitational lensing by large-scale
structure over a field of 1000 square degrees (or more)
could have comparable sensitivity to $w$ as type Ia supernovae.
However, weak gravitational lensing does not appear to be a good
method to probe the time variation of $w$ \cite{dragan}.  The systematics
associated with weak gravitational lensing have not yet been studied
carefully and could limit its potential.

\end{itemize}

With the exception of vacuum energy, all the other possibilities
for the dark energy cluster to some small extent on the largest
scales \cite{friemanetal}.  Measuring this clustering, while
extremely challenging, could rule out vacuum or help to elucidate
the nature of the dark energy.  Hu and Okamoto have recently
suggested how the CMB might be used to get at this clustering \cite{okamoto}.

While the Universe is likely the lab
where dark energy can best be attacked,
one should not rule other approaches.  For example,
if the dark energy involves a ultra-light
scalar field, then there should be a new
long-range force \cite{carroll2}.


\subsection{The Nancy Kerrigan Problem}

A critical constraint on dark energy is that it not interfere
with the formation of structure in the Universe.  This means
that dark energy must have been relatively unimportant in the
past (at least back to the time of last scattering, $z\sim 1100$).
{If} dark energy is characterized by constant $w$, not
interfering with structure formation can be quantified as:
$w\la -{1\over 2}$ \cite{turnerwhite}.  This means
that the dark-energy density evolves more slowly than
$R^{-3/2}$ (compared to $R^{-3}$ for matter) and implies
\begin{eqnarray*}
\rho_X/\rho_M & \rightarrow & 0\qquad{\ \,\rm for\ }t\rightarrow 0 \\
\rho_X/\rho_M & \rightarrow & \infty \qquad{\rm for\ }t\rightarrow \infty \\
\end{eqnarray*}

That is, in the past dark energy was unimportant and in the
future it will be dominant!  We just happen to live at the
time when dark matter and dark energy have comparable densities.
In the words of Olympic skater Nancy Kerrigan, ``Why me?  Why now?''

Perhaps this fact is an important clue to unraveling the nature
of the dark energy.  Perhaps not.  I shudder to say this, but
it could be at the root of an anthropic explanation for the size
of the cosmological constant:  The cosmological constant is
as large as it can be and still allow the formation of structures
that can support life \cite{weinberg2}.

\subsection{Dark Energy and Destiny}

Almost everyone is aware of the connection between the shape
of the Universe and its destiny:  positively curved recollapses,
flat; negatively curved expand forever.  The link between
geometry and destiny depends upon a critical assumption: that
matter dominates the energy budget (more precisely, that all components
of matter/energy have equation of state $w> -{1\over 3}$).
Dark energy does not satisfy this condition.

In a Universe with dark energy the connection between geometry
and destiny is severed \cite{kraussturner}.  A flat Universe
(like ours) can continue expanding exponentially forever
with the number of visible galaxies diminishing to a few
hundred (e.g., if the dark energy is a true cosmological constant);
the expansion can slow to that of a matter-dominated
model (e.g., if the dark energy dissipates and becomes sub-dominant);
or, it is even possible for the Universe to recollapse
(e.g., if the dark energy decays revealing a negative cosmological constant).
Because string theory prefers anti-deSitter space, the third
possibility should not be forgotten.

Dark energy is the key to understanding our destiny.

\section{A Cosmic Perspective from Rovaniemi}

After attending an exciting, enjoyable, and very productive COSMO-01, 
here is my summary of the state of cosmology:

\begin{itemize}

\item We have discerned the basic features of the Universe, as embodied
in The New Cosmology.

\item We can say confidently that events that took place during earliest
moments have had a profound influence on the present state of Universe.

\item We have a impressive program in place to test inflation and the particle
dark-matter hypothesis, as well as their corollary, the Cold Dark Matter theory
of structure formation.

\item For some years, the front line in cosmology will continue to be phenomenology.

\item No doubt, there will be surprises and we will need new ideas
to replace (or supplement) those that are driving cosmology today.

\item Schramm's Razor -- given two equally interesting new ideas, pursue
the one that's more testable -- is more true than ever.

\end{itemize}


I am look forward to new results, new ideas and new (as well as old) faces
at COSMO-02 in Chicago.


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\end{document}




astro-ph0202005.extracted_bib
\begin{thebibliography}{99}

\bibitem{history}  See e.g., M.L. Humason, N.U. Mayall, and A.R. Sandage, Astrophys. J.
{\bf 61}, 97 (1956).

\bibitem{weinberg1}  S. Weinberg, {\em Gravitation
and Cosmology} (Wiley \& Sons, NY, 1972).

\bibitem{swogu} M.S. Turner, ``Grand Unification and the Fundamental
Problems of Classical Cosmology,'' in {\it Second Workshop on Grand Unification},
eds. J.P. Leveille, L.R. Sulak, and D.G. Unger (Birkh\"{a}user, Boston, 1981)

\bibitem{hbb_std} See e.g., P.J.E. Peebles, {\em Physical Cosmology}
(Princeton University Press, Princeton, NJ, 1971); or E.W. Kolb and
M.S. Turner, {\em The Early Universe} (Addison-Wesley, Redwood
City, CA, 1990).

\bibitem{flat}
P. de Bernardis et al, Nature {\bf 404}, 955 (2000);
S. Hanany et al, Astrophys. J. {\bf 545}, L5 (2000);
C.B. Netterfield et al, astro-ph/0104460; C. Pryke et al,
astro-ph/0104490

\bibitem{tytler}
D. Tytler et al, Physica Scripta {\bf T85}, 12 (2000);
J.M. O'Meara et al, Astrophys. J. {\bf 552}, 718 (2001)

\bibitem{baryon_density}
S. Burles et al, Phys. Rev. D {\bf 63}, 063512 (2001);
Astrophys. J. {\bf 552}, L1 (2001)

\bibitem{cmbratio} C.B. Netterfield et al, astro-ph/0104460; C. Pryke et al,
astro-ph/0104490

\bibitem{mohr} See e.g., J. Mohr et al, Astrophys. J. 517, 627 (1998)

\bibitem{turner2001}
M.S. Turner, astro-ph/0106035

\bibitem{powerspectrum} W.J. Percival et al (2dF), astro-ph/0105252; S. Dodelson et al
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\bibitem{bias} O. Lahav et al (2dF), astro-ph/0112162

\bibitem{superK}  Y. Fukuda et al, Phys. Rev. Lett. {\bf 81}, 1562 (1998)

\bibitem{cosmo_nulimit} R. Croft, W. Hu and R. Dave, Phys. Rev. Lett.
{\bf 83}, 1092 (1999)

\bibitem{krauss} L. Krauss and B. Chaboyer, astro-ph/0111597; I. Ferreres,
A. Melchiorri, and J. Silk, MNRAS {\bf 327}, L47 (2001)

\bibitem{knox}  L. Knox, N. Christensen, and C. Skordis, astro-ph/0109232

\bibitem{H0} W.L. Freedman et al, Astrophys. J. {\bf 553}, 47 (2001)

\bibitem{firas} J. Mather et al, Astrophys. J. {\bf 512}, 511 (1999)

\bibitem{pasp_essay}
M.S. Turner, PASP {\bf 113}, 653 (2001) (astro-ph/0102057)

\bibitem{dm_review} See e.g., B. Sadoulet, Rev. Mod. Phys. {\bf 71}, S197 (1999) or
K. Griest and M. Kamionkowski, Phys. Rep. {\bf 333-4}, 167 (2000)

\bibitem{kosowsky}  See e.g., J. Sellwood and A. Kosowsky, astro-ph/0009074

\bibitem{cusp_clump} See e.g., J. Bullock, A. Kravtsov and D. Weinberg, Astrophys.
J. {\bf 539}, 517 (2000); R.S. Somerville, astro-ph/0107507; A.J. Benson et al,
astro-ph/0108218; M.D. Weinberg and N. Katz, astro-ph/0110632;
A. Klypin, H.-S. Zhao, and R.S. Somerville, astro-ph/0110390;
D. Merritt and F. Cruz, Astrophys. J. {\bf 551}, L41 (2001); M. Milosavljevic
and D. Merritt, Astrophys. J. {\bf 563}, 34 (2001); M. Milosavljevic et al,
astro-ph/0110185

\bibitem{pjsdns} D.N. Spergel and P.J. Steinhardt, Phys. Rev. Lett. {\bf 84},
3760 (2000)

\bibitem{kkt} M. Kaplinghat, L. Knox and M.S. Turner, Phys. Rev. Lett. {\bf 85} 3335 (2000)

\bibitem{leptogenesis}  W. Buchmuller, hep-ph/0107153

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