1. Energy Transfer in Multi-field Inflation and Cosmological Signatures
Amjad Ashoorioon
University of Michigan
December 17th, 2008
Miami 2008 Conference
In collaboration with
Axel Krause and
Krzysztof Turzynski,
Based on
hep-th/
[hep-th]

2. Multi-Brane Inflation
Initial efforts to realize inflation in string theory was focused on a single mobile brane
inflation.
KKLMMT (2003)
However, general compactifications with fluxes naturally possess several mobile
branes to satisfy constraints like tadpole cancellation
- In this class, the brane-brane interactions will steer the multi-brane system towards a dynamical attractor.
An example of this class, is multiple M5-brane inflation in which the non-perturbative
exponential interactions between the branes will lead to a dynamics in which the branes
move in a concerted way, a phenomenon which is know as assisted inflation.
K. Becker, M. Becker and A. Krause (2005)
- In multiple M5-brane inflation, a cascade evolution occurs.
A. Ashoorioon & A. Krause (2007)
in 4d effective theory picture, the process looks like energy transfer from the inflaton to the orbifold fixed plane.

3. Multi-Brane Inflation
The energy on the fixed orbifold plane could be modeled as a barotropic fluid
which couples to the inflaton and allows for the transfer of the inflaton’s energy
in discrete steps.
More adapt to the cosmological perturbations formalism is a field theory description
based on Lagnrangean. We model the barotropic fluid with a scalar field with suitable
steep exponential potential which can mimic various equations of state.
A. Ashoorioon, A. Krause & K. Turzynski, arXiv:
Explicit calculation of curvature and isocurvature perturbations in the above
two-filed model is our final goal.
Although we will focus on M-theory cascade inflation in this talk, our result is relevant
to any model in which part of the energy of inflaton transfers to some other
non-inflationary component.
Westphal &
E. Silveretein (2007)

4. Outline Cascade Inflation Instanton Transition in Heterotic M-theory
Two Field Model
Curvature and Isocurvature Perturbations in Two-fields Models
Evolution of Curvature and Isocurvature Perturbations
Curvature & Isocurvature Spectra
Tensor Spectrum
Conclusion

5. Cascade Inflation
Starting point: M-theory in the presence of N parallel M5-branes distributed along the orbifold and compactified on a CY3 preserving N=1 supersymmetry in 4D. Each M5-brane has wrapped the same 2-cycle Σ2 on the CY3 only once and fill the 4D space-time.
K. Becker, M. Becker and A. Krause (2005)

6. Cascade Inflation
Under neglect of energy transferred to the boundaries, we have a cascade of
power-law inflations during which the scale factor evolves as:
Where the continuity of the scale factor at transition times determines.
Ashoorioon & Krause
(2006)

7. Cascade Inflation
By inverting the exact power-law inflation solutions for
and noting that
, one obtains
Exit from inflation happens when at the
-th phase where

8. Instanton Transition in Heterotic M-theory
down to 4d, the small
In heterotic M-theory compactifications on
instantons are described by a torsion free sheaf, a singular bundle, which can be
smoothed out to a non-singular holomorphic vector boundle by moving in moduli
space.
Ovrut, Pantev and Park (2000)
To date, no clear fundamental M-theory description of these small instanton
transitions is available, which fully describe its dynamics, including the produced
tensionless strings.
In what follows, switching back to 4d analysis of the ensuing cosmology, we will
adopt a QFT description which models such a transition by coupling the inflaton,
to another scalar field,
, which would come from boundary dof’s in the heterotic
M-theory description.

9. Two Field Model
For simplicity, we will only consider one such instanton transition.
A scalar field with potential
leads to power-law evolution
of the scale factor, even when
Matarrese (1985)
Thus we can mimic variety of barotropic fluids,
, by choosing an
exponential with proper exponent,

10. Two Field Model
The potential for our two scalar field model is:

11. Two Field Model
We will concentrate mostly on the case that inflaton’s energy is transformed to
radiation,
We choose the following values for the parameters:

12. Curvature and Isocurvature Perturbations in Two-fields Models
A two-scalar-field system coupled to gravity is described by
To study the linear perturbations of the theory, we start with the longitudinal
gauge for the metric:
and we perturb the scalar fields around their homogeneous parts,
It is useful to introduce gauge-invariant Mukhanov-Sasaki variables:

13. Curvature and Isocurvature Perturbations in Two-fields Model
One can decompose the perturbations along (Curvature or Adiabatic perturbation) and
perpendicular to the trajectory (Isocurvature or Entropy perturbations) in the field
space:
where:

14. Curvature and Isocurvature Perturbations in Two-fields Models

15. Evolution of Curvature and Isocurvature Perturbations
To obtain ,
and
To obtain ,
and

16. Evolution of Curvature and Isocurvature Perturbations
Starobinsky & Yokoyama (1995)
Gordon, Wands, Bassett & Maartens (2001)

17. Curvature & Isocurvature Spectra

18. Curvature & Isocurvature Spectra

19. Tensor Spectrum

20. Conclusion
We demonstrated explicitly that energy transfer from the infaton to some other
scalar field causes modulated oscillations on the curvature spectrum
which damp away toward smaller scales.
Recently Covi, et. al. [astro-ph/ ], have tried to explain the measured
deviation of the WMAP3 from featureless power spectrum, using potentials with
step and found interesting constraints on the location and magnitude of possible
steps. One may be able to use the results of that paper to derive M-theory
parameters!
A. Ashoorioon & B. Powell, Work in preparation
The contribution of isocurvature perturbations decay toward the end of inflation.
However as decay, they induce curvatures ones on the scales that exit the horizon before the energy transfer. Thus the amplitude of curvature spectrum at small scales will be smaller than expected. This may be used to mitigate the problem of overprediction of dwarf galaxies, which could be caused using scale-invariant spectrum as an initial input for N-body simulations.

21. Thank You!