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On string cosmology. Renata Kallosh Stanford and YITP, Kyoto. SUSY 2008, June 19, Seoul. Outline. Dark Energy and the Landscape of String Theory : Type IIA, Type IIB, Heterotic string theories Brane Inflation and Modular inflation

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on string cosmology
On string cosmology

Renata Kallosh

Stanford and YITP, Kyoto

SUSY 2008, June 19, Seoul

  • Dark Energy and the Landscape of String Theory : Type IIA, Type IIB, Heterotic string theories
  • Brane Inflation and Modular inflation
  • What can fundamental physics learn from future detection or non-detection of

B-modes from inflation

Cosmic strings

  • LHC: Tension between string cosmology and a TeV and/or very light (LSP) gravitino, particularly if B-modes from inflation will be detected.
standard cosmological concordance model is emerging during the last 10 years
Standard Cosmological Concordance Model is emerging during the last 10 years
  • String Theory and Particle Physics in general have to adapt to these changes
  • It is now 10 years after the discovery of the Universe acceleration and the first indications of the LCDM model

So far 6 (8) parameters are explaining all the data from the sky!

Equation of state:


The data are consistent

with the cosmological constant, CC

w= -1

The pressure p is equal

and opposite to the energy

density r : the only way to

achieve a unique energy

density that does not change

in time, as Einstein had

introduced in 1917. After

Hubble discovery in 1929

of the Universe expansion

Einstein abandonned CC

Now it is back again as DARK ENERGY


CC > 0

CC ~ 10-120

In Planck units

SUPERSTRING THEORY: many AdS vacua with CC < 0

and Minkowski vacua with CC = 0,

but no de Sitter vacua with CC > 0


At that time it became clear that the existence of dark energy is a real issue, supported not only by supernovae. It describes 70% of everything. Fundamental physics has to explain it.

First constructions of metastable de Sitter vacua in String Theory

It is possible to stabilize internal dimensions, and to obtain an accelerating universe. Eventually, our part of the universe will decay, but it will take a very long time

Vacuum stabilization can be achieved in about 10500different ways. This means that the value of CC ~ 10-120 in Planck units may not be impossible in the context of stringy landscape with anthropic reasoning

w = - 1, CC=const, is in agreement with the data so far

V is the potential as a function of the volume of extra dimensions, described by s

Metastable dS minimum

what if cc const will be ruled out observationally as the explanation of dark energy
What if CC = const will be ruled out observationally as the explanation of Dark Energy?

Most likely, it will not happen earlier than in 10 years from now (???)

It is difficult to explain non-CC dark energy, as we will have to fine tune not only the height of the potential 10-120but also the slope ~ 10-120

At present w = -1 with 10% accuracy

Expectation: 10 years from now accuracy may be about 3% but it may still be very difficult to

rule out CC

string cosmology as a link between fundamental physics and the data from lhc and from cosmology
String Cosmology as a link between fundamental physics and the data from LHC and from cosmology
  • If we use string theory landscape to understand dark energy, we should also try to explain the rest of cosmology, including inflation
  • This is how it worked for Standard Model in particle physics: the underlying principle was spontaneously broken gauge theory. A particular model, SU(3)xSU(2)xU(1) with particular field content was able to explain all data in particle physics below certain energies.
  • The current goal of string cosmology is to construct/select models based on string theory capable of explaining current and future cosmological observations and compatible with future data from LHC
data in cosmology and lhc string cosmology fundamental physics
Data in cosmology and LHC string cosmologyfundamental physics
  • After 2003 when string cosmology with flux compactification and moduli stabilization was developed, we are looking for early universe inflation models derived from string theory. There is a list of such models compatible with available data.
  • We are also checking alternatives: ekpyrotics, new ekpyrotics etc. So far no consistent models.
  • We are analyzing the impact of future (soon to come) data and trying to work more on diverse string inflation models which may be later more suitable if certain crucial discoveries will be made: for example
  • B-modes detection:
  • may be of crucial importance
  • Cosmic strings detection:
  • very interesting for string theory and cosmology (stringy version of hybrid D-term inflation may fit the data)
  • Non-gaussianity detection:
  • a selection principle of cosmological models
Important new cosmological data expected soonPlanck, B-mode polarization experiments,SPT, ACT (telescopes),…
  • Spectral Index, ns
  • Non-gaussianity, fNLrecent discovery/non-discovery ???
  • B-modes, r=T/S, main news in May-June 2008: prospects for detection of B-modes from inflationin the range above r = 0.01 are excellent
  • Cosmic strings, if below10% may explain the data, requires ns=1

A. Lange, K. Ganga

Cosmological data as a test and selection principle for string theory

calendar for b mode detection
Holy grail of observational cosmologyCalendar for B-mode detection





NASA Beyond Einstein

















ESA Cosmic Vision


Many proposals are already funded

which may measure r = T/S in the interval









space of m string theory vacua
Space of M/String Theory vacua

Moduli Stabilization by fluxes and non-perturbative corrections in non-critical and type IIB superstring theory de Sitter vacua, models of inflation

Until recently problems in type IIA superstring theory

Heterotic string theory?

type iia string theory
Type IIA string theory
  • Stabilization of all moduli is possibble in a class of models in massive IIA. In these models there is an infinite number of AdS vacua, L < 0 DeWolfe, Giryavets, Kachru,Taylor, 2005
  • Cannot be uplifted to de Sitter vacua, L > 0, no-go theorem

RK, M. Soroush, 2006

  • In these models inflation is impossible, no-go theorem

Hertzberg, Kachru, Taylor, Tegmark, 2007

  • New type IIA models: extra dimensions with negative curvature, chaotic inflation with gravity waves, Silverstein, Westphal, 2008
  • Cosmology as a selection principle?
d brane inflation in string theory
D-Brane Inflation in string theory

KKLMMT brane-anti-brane inflation

Two-throat model

Dirac-Born-Infeld inflation

Nil manifold D4 brane inflation

With gravity waves!

Hybrid D3/D7 brane inflation

(Stringy D-term inflation)

modular inflation models
Modular Inflation models

Racetrack inflation


Kahler modular inflation

Roulette inflation

Stringy inflation models

on WMAP5


+D4 branes

String Inflation Models to be constructed…

Bevis, Hindmarsh, Kunz, Urrestilla

January 2008

Battye, Garbrecht,

Moss, 2006


10% of cosmic strings

versus usual fit

For this model cosmic strings have to be detected!

Pogosian, Tye, Wasserman, Wyman, 0804.0810

Cosmic strings with tensions near the observational bounds could generate enough power to account for the excess over inflation suggested by ACBAR data at l>2000

Need more data on very large l

Expected soon!

Racetrack Inflation, KKLT

the first simple working model of themoduli inflation

Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, Kallosh, Linde, Quevedo


Kähler potential:

KKLT Uplifting term:

“working” means: fit the data known today

No cosmic strings

Racetrack Inflation


Spectral index as a function of the number of e-foldings

(minus the total number of e-foldings)

No grav. waves

recent new results in string inflation model bulding
Recent new results in string inflation model bulding
  • Update of KKLMMT model of D3-anti-D3 inflation in the warped throat geometry
  • Update of the D3/D7 stringy version of D-term inflation
  • Chaotic inflation in string theory, predicting a detectable level of B-modes
  • Better understanding of the light gravitino problem in the context of string inflation
update on kklmmt brane inflation model recent detailed studies of quantum corrections
Update on KKLMMT brane inflation model:recent detailed studies of quantum corrections


Carefully computed stringy corrections do not remove terms as expected a while ago, but add other terms to the potential. With fine-tuning one can find an inflection point and slow-roll inflation

Cosmic strings, no GW

Princeton group

Baumann, Dymarsky, Klebanov, Maldacena, McAllister… 2007


Inflection point

Accidental Inflation: Linde, Westphal

Update on D3/D7brane inflation

Haack, RK, Krause, Linde, Luest, Zagermann, 2008

The model is controlled by special geometry of N=2 supergravity and string compactification on K3 x

The reason for the recent update was the observation by Hindmarsh et al

than one can fit the data with ns=1 assuming the presence of light cosmic strings.

This is in amazing agreement with the prediction by RK, Linde and Endo, Kawasaki, Moroi (2001-2003)that in D-term inflation (Binetruy-Dvali-Halyo) one can have light cosmic strings for very small gauge couplings under condition that ns=1

In the usual regime D-term inflation starts far away from the bifurcation point, ns ~ 0.98. However, local BPS cosmic strings are violating the observational bound. Semilocal strings may be still possible.



term from fluxes on the brane

Pillow with 4 fixed points

We computed stringy corrections to the potentialtheydepend on the value of shape moduli, stabilized by fluxes

A stringy correction term can vanish,

can be small, not small, positive or negative. This depends on the choice of fluxes stabilizing

the complex structure modulus

t=Re t +i Im t

For Re t=0.26

small coupling
Small coupling

In this class of models cosmic string tension is proportional to the Fayet-Illiopoulos term

Usual regime of D-term


Cosmic strings are too heavy

Inflation starts close to the bifurcation point

since the potential is very flat.

This numerical example is compatible with Hindmarsh et al fit to CMB data with 10% of cosmic strings

flexibility with account of stringy corrections
Flexibility with account of stringy corrections

Allow to suppress the

cosmic strings tension

and have a spectral index

compatible with WMAP

Eternal Inflation possible due to the maximum

of the combined potential : the log f term as in D-term inflation and in addition aflexiblef2from stringy corrections.


RK, Linde 2004

The height of the KKLT barrier is smaller than |VAdS| =m23/2. The inflationary potential Vinfl cannot be much higher than the height of the barrier. Inflationary Hubble constant is given by H2 = Vinfl/3 < m23/2.


Modification of V at large H


Bound on the Hubble constant in this class of models:

H < m3/2

Related constraints on temperatureBuchmuller, Hamaguchi, Lebedev, Ratz 2004

monodromy in cmb gravity waves in string inflation
Monodromy in CMB Gravity Waves in String Inflation

E. Silverstein and A. Westphal

New mechanism of avoiding standard limits on the range of the inflaton field: despite the volume of the internal manifold is finite, the geometrical range of the D-brane in the compactified Nil 3-manifold is unlimited due to a monodromy. The moduli space of the brane lies in the subspace of the covering space of the the Nil 3-manifold

Internal space of negative curvature, very

different from the more familiar corner of string theory, Calabi-Yau spaces

The origin of the bound in Silverstein-Westphal model in type IIA string theory compactified on a Nil 3-manifold
  • The negative curvature term gives the only positive contribution to the potential
  • The scale of supersymmetry breaking is at or above of the curvature scale
large volume compactification models
Large volume compactification models

Conlon, RK, Linde, Quevedo, 2008

RK, Linde, 2007

For TeV gravitino

There is a problem!

An attempt to make gravitino mass during inflation many orders different from the observable one

a fine tuned class of models
A fine-tuned class of models

2004, KL model

Using racetrack superpotential with two exponents

one can obtain a supersymmetric Minkowski vacuum without any uplifting of the potential

Inflation in these models can occur at H >> m3/2

No correlation between the gravitino mass, the height of the barrier and the Hubble constant during inflation

Badziak, Olechowski, 2008

Triple gaugino condensation + corrections to Kähler potential

+ severe fine-tuning TeV gravitino

As in all modular racetrack-type inflation models in string theory, despite the fine-tuning, the B-modes are too small to be detected

tensor modes and gravitino
Tensor Modes and GRAVITINO
  • In models of moduli stabilization in string theory
  • Therefore
  • Detection of B-modes measurment of Hubble during inflation

and indirect bound on gravitino in these models

For one would expect undetectable GW

RK, Linde 2007

superheavy gravitino

With fine-tuning

gravitino string theory b modes and lhc
Gravitino, string theory, B-modes and LHC

In the well developed string theory models of inflation constructed so far based on

  • KKLT mechanism of moduli stabilization
  • large volume compactification models
  • models predicting gravity waves
  • B-modes and light gravitino are incompatible, unless an extremely severe fine-tuning is made.
  • Thus, at present there is no known way (with exception of extremely severe fine-tuning) to accommodate in string theory a future detection of B-modes and a possible future experimental identification of the gravitino as LSP or even TeV scale
  • Even if B-modes will not be detected, there is still a tension between string cosmology and light gravitino, particularly if it forms dark matter and is very light. Significant fine-tuning may save existing constructions or, better, new ideas should be suggested.
near future theory and data lhc and cosmology
Near future: theory and dataLHC and COSMOLOGY:
  • Supersymmetry?
  • Non-gaussianity
  • More on spectral index
  • Cosmic strings
  • L>2000 excess of power
  • B-modes ?
  • Mass of gravitino?
  • Test of superstring theory?

We are waiting for LHC, dark matter and B-mode experiments data