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String Cosmology: A
Brief Overview
Bin Chen
Dep. of Phys., Peking Univ.
28th. June, 2008
Questions with cosmology SM:
What happens at a cosmological singularity?
Does time begin?
What is the quantum vacuum for gravitational
Is there a future asym. vacuum state?
Why are there three large spatial coor.?
What is dark energy?
What is dark matter?
Need a quantum theory of gravity!
What is string/M theory?
A theory of quantum gravity. The most
promising candidate to unify all the
elementary particles and forces in nature
including gravity.
Elementary particles:
strings at Planckian scale. All
usual particles emerge as the excitations of the string.
Einstein’s dream:
all the forces and particles
emerge in an elegant geometrical way;
Incredible rich structure;
Achievements: blackhole entropy, AdS/CFT
correspondence, new ideas;
What is string theory?
its basic principle,its
structure, SFT,nonperturbative description,…
Experimental evidence?
Lab. experiment
impossible; very early universe is the best and
only lab.;
String Cosmology
Intersection between string/M and
cosmology: cosmology can be the key to
the verification of string theory, and
string theory can be what we need to
solve some deep puzzles in cosmology.
(String cosmology 2003, KITP)
Nature of the Big bang singularity;
Models of inflation based on string theory moduli;
Cosmology from Big crunch to Big bang;
Cosmology and holographic principle;
Quantum theory of Asym. de Sitter univ.
Possible imprints of string physics on
observational cosmology;
1. Cosmological Singularity
In principle, there is no singularity in
string theory due to the existence of
the minimal string scale;
In GR, the singularity in terms of
geodesic incompleteness; (in the sense of point
In string theory, strings see the
spacetime only through the sigma
Spacetime in string theory
Nonconventional;(string as probe)
The fuzziness of the event;
Stringy geometry: the singularities
(orbifolds, conifold) resolved; mirror
symmetry, topology transition …;
Quantum foam;
Emergent spacetime;
T-duality: R~1/R;
Resolution of the singularities: new
degrees of freedom;
Static singularities: orbifold and conifold;
Time-dependent singularities?
Provide the initial state;
Difficulties: (perturbatively)
Short of workable models;
Trouble with the vacuum; (same as QFTs in
the curved spacetime)
Large backreaction;
Perturbation theory could break down;
String theory in the time-dependent
backgrounds; (Rolling tachyon, Null orbifolds, …)
Nonperturbative string theory;(Matrix model, SFT,
Matrix cosmology,…)
Blackhole singularities; (AdS/CFT, …)
Holographic principle; (Holographic cosmology, …)
New idea or concept to have a better
understanding of the string theory !
Emergent spacetime
AdS/CFT correspondence:
gravity in 5-dim
Anti-de-Sitter spacetime is equivalent to a 4-dim.
gauge theory; (J. Maldacena, …)
Lesson: the usual concept of spacetime in terms of
metric could be broken down near cosmological
Is time emergent?
Space being emergent has
been shown in many examples; no concrete example
for emergent time;
2. Inflation or something else
How we get inflation in string theory?
From compactification 10D4D, there are large number of
moduli (scalars): very flat potential and moduli fixing; (KKLMMT
model, …)
Brane world; (Dvali, H. Tye,….)
warp geometry: TeV string scale;
DBI inflation: large non-Gaussianity and tensor mode,
cosmic string production,……;
Alternative to inflation:
Ekpyrotic models; (P. J. Steinhardt,
String cosmology ( in a specific sense):
Pre-Big-bang scenario; (G. Veneziano
String gas model; (R. Brandenberger,
3. Stringy signature:
Transplanckian physics: Ripple at sub-Planckian
could leave imprint; (Brandenberger, Starobinsky, …)
modified dispersion relation, noncommutative inflation, alphavacuum, ……
Cosmic superstrings: produced after inflation;
(Polchinski, Dvali, … 2003)
different from cosmic string in QFT
Extra dimensions; (RS, …)
Particular signatures from brane inflation;
Modern cosmology is becoming an
exact science with a fruitful and rapid
intersection between observation and
Fundamental issues require a quantum
theory of gravity;
String cosmology is promising!
Challenges to string theory;
Thank you