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]

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.

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:0810.4660 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)

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

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)

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)

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

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.

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,

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

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:

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:

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:

Curvature and Isocurvature Perturbations in Two-fields Models

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

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

Curvature & Isocurvature Spectra

Curvature & Isocurvature Spectra

Tensor Spectrum

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.

Thank You!