Reheating the Universe afterString Theory Inflations

PILJIN YINTU, 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 Kofmanhep-th/0507257

With Gibbons, Hori, Hashimoto, O-Kab Kwonhep-th/0009061, hep-th/0209034, hep-th/0305229

With Ho-Ung Yee, M. Gutperlehep-th/0402027, hep-th/0409050

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 NutshellCalabi-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 ThroatKlebanov+Strassler, 2000

HierarchyGiddings+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’santi 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/9805170

Annihilation

D3D3 Anti-D3Anti-D3

PY hep-th/9901159

tachyontachyon

V(T)

T

conserved electric flux = fundamental string charge

Unstable D-Brane System: Effective Field Theory SenGarousiKlusonBergshoeff et.al 1999

Minimal Case:

Tachyon MatterA. 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 InteractionGoverned by a Deformed Light-Cone

Usual Light-Cone in p+1 Dimension

Deformed 1+1 Dimensional Light-ConeAlong the Length of the Flux Lines:

Free propagation of signalsalong the flux lines withreduced speed of light:

Static solutions are all homogeneous along the flux lineand 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 stringswith oscillators excited

Decaying Boundary State

SenSen+MukhopadhayRey+Sugimoto2002

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 producedclosed 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 sectorafter 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’sleftover

Cascade to Localized KK Modes

D3’s or anti-D3’sleftover

Localized KK Modes

Bulk Modes Localized KK ModesLocalized String Modes

Initial Energy Deposit Cascades 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 2nd throat

- large decay width in the 2nd 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 2nd throatan advantage for the reheating into the 2nd throat ?

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

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

mixing further suppressed by the decay width (= imaginary mass)

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

mixing further suppressed by the decay width (= imaginary mass)

One must also take account tunneling to other nearby states in the 2nd throatwith larger mass differences and the further suppression of tunneling thereof:

Then the total effective width of the (stable) KK modes of the 1st 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 2nd 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-SundrumDimopoulos+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 ModelD-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 inflationwith 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?