Transcript Coordinate Noncommutativity, Quantum Groups and String

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
fields?
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;
Challenges:
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.
Topics:
(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;
……
Landscape;
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
particle)
In string theory, strings see the
spacetime only through the sigma
model;
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;
(nonperturbative)
Remarks:
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;
Suggestions:
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
singularity;
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, et.al….)
warp geometry: TeV string scale;
DBI inflation: large non-Gaussianity and tensor mode,
cosmic string production,……;
Alternative to inflation:
Ekpyrotic models; (P. J. Steinhardt, et.al.)
String cosmology ( in a specific sense):
Pre-Big-bang scenario; (G. Veneziano et.al.)
String gas model; (R. Brandenberger, et.al.)
……
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;
Conclusion
Modern cosmology is becoming an
exact science with a fruitful and rapid
intersection between observation and
theory;
Fundamental issues require a quantum
theory of gravity;
String cosmology is promising!
Challenges to string theory;
Thank you