Energy Transfer in Multifield Inflation and Cosmological Signatures

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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/0607001 0810.4660
hep-th
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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.

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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 inflatons 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,
arXiv0810.4660

• 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)

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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

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Cascade Inflation
Starting point M-theory in the presence of N
parallel M5-branes distributed along the orbifold
and compactified on a CY3 preserving N1
supersymmetry in 4D. Each M5-brane has wrapped
the same 2-cycle S2 on the CY3 only once and fill
the 4D space-time.
K. Becker, M. Becker and A. Krause (2005)
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Cascade Inflation
Ashoorioon Krause (2006)
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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
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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 dofs in the
heterotic
M-theory description.
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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,
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Two Field Model

• The potential for our two scalar field model is

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Two Field Model

• We will concentrate mostly on the case that
  inflatons energy is transformed to
• radiation,

• We choose the following values for the
  parameters

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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
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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
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Curvature and Isocurvature Perturbations in
Two-fields Models
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Evolution of Curvature and Isocurvature
Perturbations
and
To obtain
,
and
To obtain
,
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Evolution of Curvature and Isocurvature
Perturbations
Starobinsky Yokoyama (1995)
Gordon, Wands, Bassett Maartens (2001)
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Curvature Isocurvature Spectra
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Curvature Isocurvature Spectra
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Tensor Spectrum
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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/0606452, 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.

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Thank You!