Probing the Structure of Stringy Landscape by Large Scale CMB Experiments Amjad Ashoorioon

in collaboration with

Ulf H. Danielsson

Based on a work in progress

24 th Nordic Conference Dec. 4 th , 2009

Introduction to Chain Inflation

• In the original picture of inflation proposed by A. Guth (1981), the universe was trapped in a metastable vacuum. This would lead to a quasi-exponential expansion of the space-time.

• However in order to exit from inflationary phase, the nucleation rate from the false minimum to the true one should be substantial. This requirement has clashes with the other one coming from having enough number of e-foldings needed to solve the problems of SBB.

• Chain inflation is an incarnation of the old idea of old inflation , where instead of having one vacuum, one has a series of metastable minima. The universe tunnels rapidly through a series of first order phase transitions. During the time spent in any one of these minima, the universe inflates by a fraction of an e-fold.

K. Freese & D. Spolyar (2005) • At each stage, the phase transition is rapid enough that bubbles of true vacuum intersect one another and percolation is complete.

• Recalling that we have a huge number of vacua in string theory, one may take this approach seriously and try to realize it within stringy agents.

Introduction to Chain Inflation

• Danielsson & Chialva (2008), instead of the above sequential approach to chain inflation, assumed that during the course of inflaiton the universe is divided to patches, each in a phase, which is segregated from its neighbors by domain walls. Taking this ensemble approach to chain inflation, they studied the mechanism of generation of density perturbations in chain inflation.

• They also tried to realize chain inflation in the context of flux-compactified string theory, using complex structure moduli as the agents.

• Motivated by these studies, they considered two landscape structures; in one the energy of  n 2 m f 4  /2  n m amplitude of density perturbations and spectral index. Nonetheless, they did investigate the Implications of WMAP observations for the fundamental parameters of the model.

• Hereby we investigate this issue further and find out interesting bounds on the vacua energy gap and nucleation rates in each of these two models.

Outline

• Review of the previous results • Matching the models with observations • Distinguishing Chain inflation from its slow-roll counterparts • Conclusion

Review of the previous results

• The main contributions to the energy density of the universe during chain inflation come from the cosmological constant within each region, and also the energy stored in bubble the walls, .

Collision of the bubble walls will transform this vacuum energy to radiation: : the fraction of volume occupied by the

m

-th vacuum : the energy weighted fraction stored in uncollided bubble walls of the

m-1

th phase : nucleation rate per unit four volume : the probability that a wall generated at time

t

uncollided at time

t’

is still

Review of the previous results

We assume the total number of vacua is

M+1

and the nucleation rate per unit time, to be constant over time and independent of

m

, we have to solve the following coupled set of differential equations to find

Review of the previous results

Motivated by some studies of stringy landscape, two models where the energy density in each stage has the following functional forms have been suggested: One can define the equivalent of first slow-roll parameters in these two cases: Recall that for slow-roll inflation, it is

Matching the Models with Observation

Latest WMAP experiment have measured the amplitude of scalar perturbations and its corresponding spectral index to be  ( 2 .

445  0 .

096 )  10  9 To match the models with observation, we have to impose these constraints 60 e-foldings before the end of inflation. As in slow-roll case, the end of inflation is designated by .

We focus on the case where  60 In order to produce the right amount of perturbations at horizon scale, nucleation rate should be given as such in terms of the energy gap.

Matching the Models with Observation

N e

 60

M

min  1 Therefore, it is not possible to lower the energy scale of inflation by arbitrarily lowering the energy of the gap.

r

60   2

T

 2

R t

6 0  0 .

0858

CMBPOl should be able to see the signature at large scales.

m

n s

(

t

60 )  1  5  (

t

60 )  0.972375

results.

 Even though the nucleation time has been fixed in terms of the energy gap it does not mean that the overall shape of the potential (ignoring the wiggles) is fixed.

m

4

f

same nucleation rate between two minima Overall shape of the potential which realizes chain inflation could be far from flat

Matching the Models with Observation

Requiring thermalization at each step puts a much more stringent constraint on the energy gap.

Assuming inflation started at Planckian epoch

On the other hand, if one assumes that number of vacua has been right enough to get 60 e-folds, this constraint weakens to

Matching the Models with Observation

Imposing the constraint on the amplitude of density perturbations 60 e-folds before the end of inflation yields:

m

• Running is still small : = =

k



k

60

k



k

 • Thermalization condition leads to the following bound on the gap mass scale, if inflation has started from Planckian epochs:

Distinguishing Chain inflation from its slow-roll counterpart

• Of course aside from tiny differences in scalar spectral index! • Violation of consistency relation between tensor and scalar spectra:

r

  2

T

 2

R

  8

n T

Stewart & Lyth (1993)

r

  2

T

 2

R

  8

n T

3

Conclusion

• We used observation to constraint the free parameters of chain inflation.

• Constraining the amplitude of density perturbations, fixes the nucleation rate during chain inflation in terms of energy gap mass scale. The functionality depends on the underlying structure of the vacua. • Chain inflation, depending on the structure of underlying landscape, has specific predictions for the value of spectral index. Precise measurements of spectral index at large CMB scales can distinguish between these models.

• Chain inflation can be distinguished from its slow-roll counterparts by the violation of consistency relation.