Reheating the Universe after String Theory Inflations PILJIN YI NTU, 2005

Brane Inflation / Brane World: Prototype Brane World / Standard Model + Dvali+Tye, 1998

String Theory Inflation (KKLMMT) Unstable D-Branes and Decay Products Reheating Hierarchical Brane Worlds Heavy Relic Problems

Content Issues Brane Inflation (KKLMMT) in a Nutshell Unstable D-Brane Systems and Decay Products Reheating Summary and Outlook With Lev Kofman hep-th/ With Gibbons, Hori, Hashimoto, O-Kab Kwon hep-th/ , hep-th/ , hep-th/ With Ho-Ung Yee, M. Gutperle hep-th/ , hep-th/

Usual Issues with Cosmology Inflation Era: –Origin of Inflaton –Sufficient e-folding: Fine Tuning –Density Perturbation Post-Inflation: –Reheating –Baryogenesis –Nucleosynthesis Structure Formation and Dark Matter

Cosmology on Branes: mixing of closed string physics and open string physics Inflation Era: –Simple Identification of Inflaton –Sufficient e-folding: Fine Tuning Still Necessary? –Density Perturbation: Largely Unaffected Post-Inflation: –Reheating: Closed to Open –Baryogenesis –Nucleosynthesis Structure Formation and Dark Matter How is the Standard Model embedded?

Repopulating a Brane World Is there a viable standard model or GUT world? Is there a viable baryogenesis? Is there a viable nucleosynthesis? Can the standard model sector drive the expansion of the universe at the time of nucleosynthesis? Cold dark matter today?

Brane Inflation in a Nutshell Calabi-Yau Standard Model + ……

How to make the inflation scale much lower than the Planck scale / the string scale?

Flux Compactification with a Hierarchy: Warped Calabi-Yau with a Klebanov-Strassler Throat 3+1 dimensional world internal geometry

Klebanov-Strassler Throat Klebanov+Strassler, 2000

Hierarchy Giddings+Kachru+Polchinski, 2001

KS Throat Attached to a Compact Calabi-Yau is a Randall-Sundrum Scenario (I) Realized as a String Theory Solution

Hierarchy and Inflation (KKLMMT) D3’s anti D3’s Kachru+Kallosh+Linde+Maldacena+McAllister+Trivedi, 2003

What happens after the branes meet and annihilate?

states can be GSO truncated from all strings except for A coincident pair of D-brane / anti D-brane will annihilate via Tachyon Condensation Unstable D-Brane System A.Sen hep-th/

Annihilation D3Anti-D3 PY hep-th/

tachyon V(T) T conserved electric flux = fundamental string charge Unstable D-Brane System: Effective Field Theory Sen Garousi Kluson Bergshoeff et.al 1999

Minimal Case:

Tachyon Matter A. Sen 2002 Ideal Fluid of Massive Particles (Tachyon Matter)

With Net Fundamental String Fluxes: Fundamental string charge Ideal Fluid of Massive Particles (Tachyon Matter) + Ideal Fluid of Relativistic Flux Lines (String Fluid) With Mutual Interaction Conserved momentum Gibbons+Hori+PY, 2000

Ideal Fluid of Massive Particles (Tachyon Matter) + Ideal Fluid of Relativistic Flux Lines (String Fluid)

With 1+1 Dimensional Mutual Interaction Governed by a Deformed Light-Cone Usual Light-Cone in p+1 Dimension Deformed 1+1 Dimensional Light-Cone Along the Length of the Flux Lines: Free propagation of signals along the flux lines with reduced speed of light: Static solutions are all homogeneous along the flux line and arbitrary in other directions. Gibbons+Hashimoto+PY 2002

Fluids in Open String Picture Closed String Interpretation

Fluids in Open String Picture Closed String Interpretation A. Sen 2003

Fluids in Open String Picture Closed String Interpretation H-U Yee+PY, 2004

How to see this ?

Take a limit of no string fluid = no fundamental string charge Tachyon matter only = String oscillator modes only Collection of heavy closed strings with oscillators excited

Decaying Boundary State Sen Sen+Mukhopadhay Rey+Sugimoto 2002

Spectroscopy (I) of the Decaying D-Brane Lambert+Liu+Maldacena, 2003 cf) Chen+Li+Lin 2002

Spectroscopy (II) Exponential suppression on (transverse) momenta: Small width on velocity dispersion This feature translates to boundary state proof of Gutperle+PY, 2004

Lessons: Unstable D-Brane (or D-anti-D) decays to highly excited closed strings of level instead of “radiating away.” Once we take account string coupling, the produced closed strings will further decay to lighter string states. Tree level Open String Theory knows about classical Closed Strings: Why? Closed Strings as coherent states of Open Strings? Open Strings as a fundamental building block?

Reheating

Brane inflation has a very effective reheating mechanism as far as quickly producing a lot of matter energy goes, but… Can we deposit energy predominantly to the standard model sector after the end of a brane inflation? Is there a viable nucleosynthesis? Can the standard model sector drive the expansion of the universe at the time of nucleosynthesis? How much energy is deposited in the form of massless gravitons and semi-stable dark matter?

(P)Reheating from the Decaying D-Brane Energy is deposited to massive particles with little kinetic energy, almost evenly in each mass range, up to

D-Brane Decay and (P)Reheating D3’s or anti-D3’s leftover

Cascade to Localized KK Modes D3’s or anti-D3’s leftover Localized KK Modes

Bulk ModesLocalized KK ModesLocalized String Modes Initial Energy DepositCascades to Lighter KK Modes

Reheating for a single throat scenario Calabi-Yau with a single warped throat Kofman+PY, 2005

Triple Stage Reheating for a Single Throat: 1)Preheating: Production of Heavy Closed Strings 2)Decay to Local KK Modes and Thermalization 3)Decay to Open String Sector and Thermalization

(assuming wide throat)

Standard Model Throat Inflation Throat Energy transfer via Tunneling Multi-Throat Cases? Classical processes cannot do the job right, for it leave behind to much gravitational energy

Quadruple Stage Reheating for Multi-Throat: 1)Preheating: Production of Heavy Closed Strings 2)Decay to Local KK Modes and Thermalization 3)Tunneling to a Longer “Standard Model” Throat and Thermalization of Local KK Modes in that Throat 4)Decay to the Standard Model Sector and Thermalization

Inflation Throat Standard Model Throat Mix and Decay Issues: - mixing mass matrix between KK modes - larger number of states in the 2 nd throat - large decay width in the 2 nd throat - oscillation and decay

Basics of Two-Level Oscillation Small mass difference induces large mixing at the cost of slow time dependence; Large mass difference suppresses mixing

Basic Facts about localized and free KK modes in a KS Throat Mass Gap Naïve Number of States m < M Probably not, but longer throat should have more KK modes

Is the larger number of states in the 2 nd throat an advantage for the reheating into the 2 nd throat ?

Is the larger number of states in the 2 nd throat an advantage for the reheating into the 2 nd throat ?

Is the larger number of states in the 2 nd throat an advantage for the reheating into the 2 nd throat ? mixing further suppressed by the decay width (= imaginary mass)

Is the larger number of states in the 2 nd throat an advantage for the reheating into the 2 nd throat ? mixing further suppressed by the decay width (= imaginary mass)

One must also take account tunneling to other nearby states in the 2 nd throat with larger mass differences and the further suppression of tunneling thereof: Then the total effective width of the (stable) KK modes of the 1 st throat is Decay width of stable state 1 due to mixing with unstable state 2:

At best, effect of having more KK degrees of freedom in the 2 nd throat washes out. (No thermal equilibrium between throats or between a throat and the bulk.) Open string degrees of freedom contributes to the width in the 2nd throat but not to the mixing, hampering decay of the state 1 into throat 2

A simple tunneling problem in continuum?:

Toy Computation: “Double” Randall-Sundrum Dimopoulos+Kachru+Kaloper+Lawrence+Silverstein, 2001 Estimated tunneling rate: = Effective decay width

suppression for leaking KK modes 1 into bulk suppression for leaking KK modes 2 into bulk Consistent with the most optimistic estimate for the mixing mass matrix element: Does this hold for more general KK modes? Decay via dimension 6 mixing of operators

Lifetime of KK modes in throat 1 should be much shorter than the age of universe at the nucleosynthesis Decay of KK mode into massless gravitons is also a dimension-6 operation. Order one numbers matter Main Issues in multi-throat scenarios: Heavy KK modes dilute much slower than light KK modes or gravitons. Will they swamp the universe into matter dominated universe? Medium length spectator throat will also cause serious trouble. Depositing energy into these is as effective as into the standard model throat, but getting it out is much more difficult due to somewhat deeper depth of the throat.

Inflation throat Standard Model throat 3rd throat Heavy Relics Unstable D-branes Standard Model D-Branes much more suppressed 4D Graviton, Gravitino Operators mixing different sectors are at least dimension 6 or higher

Main Model Building Issues from the Reheating Can a single throat give a viable brane world? Low scale of inflation or a secondary hierarchy generation via SUSY? Multi-throat case: How fast is the tunnelling? What are real spectra of localized KK modes? What if other light moduli in the bulk? Their decay characterstics? e.g., Kaehler moduli in large volume KKLT. Can we control massive dark matter deposit in a medium length throat elsewhere? Heavy relic problems. Very Difficult. D-term inflation and D3/D7? D3/D7 in the presence of throat(s)? Need an explicit model with D-term scale well below D-brane tension scale.

Summary and Questions Universal initial condition of reheating from unstable D-brane inflation with many heavy string states excited. Single throat scenario is simple for both inflation and reheating. Weakly coupled supersymmetric GUT in the inflation throat? Multi-throat scenarios may work with large enough inflation scale. How to make it safe from graviton/gravitino/moduli overproduction? What if the volume of internal manifold is large? Similar issues in IIA and Heterotic? No usable background yet. D3/D7 needs more attention: A simple low energy D-term inflation?