Download 幻灯片 1 - 中国科学院理论物理研究所

超弦理论与宇宙学
李淼
中国科学院理论物理研究所
String Theory and Cosmology
Miao Li
Institute of Theoretical Physics
Chinese Academy of Sciences
String theory is widely
believed to be a
theory of quantum
gravity.
As such, it is usually
formulated in a fixed
background using the
definition of
scattering amplitudes
More precisely, we can study string
theory in a time-independent background
that has asymptotic geometry of either
(a) Minkowski
or
(b) Anti-de Sitter
String theory used to have
many different guises:
Open String, Closed String,
Heterotic String, Different
compactifications.
It is now understood
that they are manifestations
of a single grand theory,
M theory
Different string theories
are connected by duality
relations, the prototype
of this transformations is
the relation between a
electric charge and a
magnetic charge:
For example, in type IIB
theory, a string is
mapped to a D-string,
the new theory is Dstrings is again a type
IIB theory:
However, it has proven very difficult to study string theory in
a time-varying background.
A universe with a starting
point in time
De Sitter space with a bounce
The most used approach to cosmology in string theory is to
use adiabatic approximation. In such an approach, one uses
a collection of fields {F(t)} to describe the background at any
given time t, F(t) can be a scalar field, or the geometry
parameter. By adiabaticity, we mean that the physics of {F(t)}
is simply that of a fixed background with the same values of
these fields for all times.
However, this conservative, poor man’s approach
must miss some of most important ingredients of a
theory of quantum gravity.
One such ingredient is the so-called holography,
motivated by quantum physics of black holes.
A quantitative statement is that the entropy in a
region is bounded by the area of the surface
surrounding this region.
Bekenstein-Hawking formula:
This formula implies that, the physics of quantum gravity can
be utterly non-local and even a-causal.
In the context of cosmology, several people (Fischler,
Susskind, Bousso) proposed principle of
cosmological holography. Bousso’s covariant entropy
Bound:
So far, string theorists are faced with this
very challenging problems:
(a) To formulate string theory on a timevarying background.
(b) To find a formalism reflecting directly
the holographic principle.
Two major developments in
observational cosmology.
(1)Discovery of accelerating
expansion.
(2) Detailed map of primordial
perturbation constructed from the
power spectrum of CMB
(cosmic microwave background)
(1) Dark energy
Reconstructed from data about
supernovae type Ia
This results implies that there is dark energy in
our universe, or simply a cosmological constant.
According to these obsevations, our universe is
filled with relativistic matter and dark energy, the
latter is characterized by the equation of state
Furthermore, the dark energy density is very small
It is very important to determine the nature of the dark
energy through determining parameter w. For a cosmological
constant, w=-1.
Some of the most recent results are:
From astro-ph/0204512
The nonvanishing and a very small dark energy
density poses a serious challenge to string theory.
Since in string theory, as in a quantum field theory,
dark energy is understood as vacuum energy
generated by quantum fluctuations.
As such, the vacuum energy is always determined by
a characteristic energy scale.
The most natural scale is the Planck scale, at which a
particle will dress itself by a gravitational horizon:
So the largest theoretical dark energy value is
The ratio of the observed value to this theoretical
value is absurdly small
People have tried for several decades to understand
this problem and invented numerous ideas, by far not
a single idea is widely accepted as hopeful.
In the researcg community, one of the most popular
idea is the so-called quintessence model. In this
model, the dark energy comes from a scalar field Q,
a spatially homogeneous scalar field has the energy
density and pressure:
Thus
if
The quintessence model is at best a phenomenological
model, since, it is not yet possible to realize such a
model in string theory or a quantum field.
The essential difficulty is that in string theory, one
usually has super-symmetry, a kind of symmetry
relating bosons to fermions, and usually badly broken
in nature. When it is broken, we usually have a relation
The mass difference is too small to be consistent with
experiments.
Although string theory has not been able to resolve
this deep puzzle, string theory does hold the key to
understanding it. For instance, holography may imply
that dark energy related to the cosmic horizon. It has
been conjectured that in a holographic universe, dark
energy is given by
Where L is an infrared cut-off set by our universe.
More recently, it was argued that if L is the size of the
event horizon, then the present observational data
can be explained.
(2) Primordial perturbations.
A series of CMB experiments, in particular, the
Wilkinson Microwave Anisotropy Probe (WMAP)
experiment, has collected enough data to give a very
detailed map on the primordial perturbations generated
prior Big Bang. These perturbations are seeds of the
structure (galaxies, clusters of galaxies, filaments,
voids).
From the data, many important cosmic parameters
(age of universe, densities, Hubble constant…) are
inferred.
The map of cosmic microwave background
fluctuations
Some of the cosmic parameters
Age of the universe 13.7 billion years old
Dark energy 73%, dark matter 23%, atoms 4%.
The Hubble constant was 71 +4/-3 km/s/Mpc .
The universe is flat.
……
More detailed data
More detailed results
Detailed results continued
Consistency with other experiments
These observations confirm the predictions of the
inflation scenario: prior big bang, there exists a very
short period during which the universe expands very
fast, and density perturbations are generated by
quantum fluctuations of the inflaton-a scalar field
driving inflation.
Inflation explores fundamental physics in at least two ways.
First, the inflaton potential is supposed to be very flat,
this is often referred to as a fine-tuning problem.
There is no natural way to construct such a potential
in a fundamental theory such as string theory.
Second, inflation greatly amplifies space. For
instance, the largest cosmic scale just entered our
horizon originated 60 e-foldings before the end of
inflation, thus, the ratio of amplification is
The Planck scale ended up to be about
larger than the size of atom.
Indeed, WMAP results indicate that the traditional
slow-roll inflation may not be good enough to explain
everything.
For example, the unexpected suppression of power
of low multi-pole correlation (if not due to systematic
error) certainly indicates that something unusual
happened 60 e-foldings before the end of inflation.
The running of spectral index of the primordial power
spectrum can not be explained by the usual inflation
too, it may not be to crazy to speculate that this is
really due to new effects in string theory, for instance,
non-commutative space-time.
Conclusions:
(1) We are in an exciting era of precision
cosmological observation. Once in a while, new
flux of experimental data comes to sight.
(2) A few serious challenges are awaiting
fundamental theory such as string theory to meet.
(3) Many researchers in string theory are for the first
time facing experiments, not just theoretic artifice.