Accelerating Cosmological Expansion from Shear and Bulk Viscosity

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Accelerating Cosmological Expansion from Shear
and Bulk Viscosity
Urs Achim Wiedemann CERN PH-TH
S. Floerchinger, N. Tetradis, U.A. Wiedemann
Rencontres de Moriond, La Thuile, 26 March 2015
Based on S. Flörchinger, N. Tetradis, U.A.
Wiedemann, arXiv1411.3280
Phys. Rev. Lett. N. Brouzakis, S.
Flörchinger, N. Tetradis, U.A. Wiedemann,
arXiv1411.2912
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The averaging problem
Cosmological perturbation theory starts from
background fluctuation splitting


What is evolution equation of the background
fields ?
Einstein equations are valid on most
inhomogeneous scale. They are non-linear, so
averaging is non-trivial, e.g.
Formally
Back reaction effects non-vanishing spatial
averages of
products of fluctuations.
If back reaction non-negligible, then
background fields do not satisfy standard
Friedmann equations.
(G.F.R. Ellis, 1984)
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Back reaction effects
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Standard homogeneous solution for cosmological
fluid
Assume isotropy and homogeneity (neglect
curvature cosmological constant)
00 component of Einstein field equations gives
1st Friedmann equation
ij component of Einstein field equations gives
2nd Friedmann equation whose only
additional information is energy conservation
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Energy momentum tensor for a dissipative fluid
Tensor decomposition of w.r.t. flow
field and defined by (Landau frame)

shear and bulk viscosities
Metric perturbations enter evolution equations
via
For instance
For regime of structure formation
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Back reaction on matter side
0-component of yields to
leading
The spatial average is
Dissipation affects time evolution of homogeneous
background solution

• Backreaction D acts like a negative pressure
• Average energy density increases due to
• Shear viscous dissipation
• Bulk viscous dissipation
• Work done against pressure gradients

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Effect on cosmological expansion
To study acceleration parameter
supplement
with equation for scale parameter.
yields
For
Accelerating expansion (qgt0) occurs in this case
for
In general, ac/deceleration depends on e.o.s. and
size of dissipative effects.
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Material properties of dark sector affect q

• Bulk viscosity for D0, large known to lead
  to accelerated expansion.
• But bulk visocity
  needs to be very large
• Realistic? Issues
  about thermodynamic stability?
• for D gt 0,
  accelerated expansion can occur
• for smaller and
  for .

See e.g. J. Gagnon, J. Lesgourgues, JCAP 1109
(2011) 026

• Shear viscosity For qgt0, need
  . Feasible?
• For weakly interacting relativistic
  particle, .

S. Weinberg 1971
Speculation
Curiously, mean free time e.g. of gravitons
is One obtains qgt0, for
S. Hawking 1966
Could (instead of in ) some
(dark) radiation field coupled to CDM account for
accelerated cosmological expansion?
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Dissipation affects growth of large scale
structure
To first order in fluctuations, Einstein
equations for density contrast
and velocity potential read in Fourier space
Case
Closed by Poisson- like constraint

• Shear viscosity
• limits growth of velocity fluctuations on short
  scales
• enters evolution of density contrast only via
  velocity dependence

Work in progress We currently study the growth
of large scale structure in presence of
dissipation (both analytically and with modern
codes)
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Time-RG Flow approach
M. Pietroni, JCAP 0810 (2008) 036

• Evolution equations of spectra on top of
  homogeneous background

can be written and solved directly for

• By applying this technique to a problem in heavy
  ion collisions, we found a back reaction effect
  at order

N. Brouzakis, S. Flörchinger, N. Tetradis, U.A.
Wiedemann, arXiv1411.2912,

• The dissipative term in cosmology can be written
  in terms of spectra and should be calculable with
  the time-RG approach

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Cosmology and heavy ion collisions
discuss the largest (smallest) physical systems
for which an analysis of fluctuations informs us
about material properties. What
can we learn from this analogy?
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Conclusions
S. Flörchinger, N. Tetradis, U.A. Wiedemann,
Phys.Rev.Lett. 114, 091301 (2015)

• Dissipation of velocity perturbations affects
  time evolution of fluid dynamic fields and
  cosmological solution of Einsteins equations.
• If sufficiently large, this back reaction could
  account for the
• accelerated cosmological expansion.
• Size of the back reaction is calculable from the
  perturbative growth of velocity fluctuations if
  viscous properties of dark sector are known.
• (Viscosities are calculable from 1st
  principles for the lagrangian of any field
  theory).
• Vice-versa, material properties and thus
  fundamental constituents of the dark sector can
  be constrained by constraining viscosities.
• (This motivates studies of structure growth
  in presence of dissipation)
• In scenarios in which viscous back reaction is
  too small to account for
• accelerated cosmological expansion, it may
  still be relevant for finer
• details of structure growth (e.g. in the BAO
  range).

We are excited about a possible fruitful
interplay between the fields of heavy ion physics
and cosmology.