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, alpha- vacuum, …… 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