3 Perturbative UV Backreaction:

1
Cosmological Backreaction The Mystery and The
Myth Niayesh Afshordi Institute for Theory and
Computation, Harvard-Smithsonian Center for
Astrophysics Ghazal Geshnizjani, Daniel J.H.
Chung Department of Physics, University of
Wisconsin-Madison
Prelude In this poster, I discuss how
back-reaction of large amplitude inhomogeneities
can affect the local cosmological observables. I
first argue that the possibility of a significant
UV backreaction (due to general relativistic
corrections on scales smaller than Hubble radius)
is ruled out at the perturbative level. However,
such corrections (although unlikely) are not
ruled out at the non-perturbative level, and thus
could become significant. The backreaction of IR
modes (scales larger than Hubble radius) to
Friedmann cosmology is severely constrained by
current cosmological observations. Nevertheless
they can play an important role during inflation.
NEW VIEWS OF THE UNIVERSE Chicago, IL, 8-13
December, 2005

• Why Backreaction?

2) Perturbative UV Backreaction Failure of
Comoving Gauge at Shell Crossing

• General Relativity is a non-linear theory. Thus
• Perturbations can affect the background evolution
• Example gravity waves have an effective energy
  momentum tensor
• Motivations for study of Cosmological
  Backreaction
• May naturally end Inflation (Graceful Exit
  Problem)
• May naturally cause cosmic acceleration
• (Cosmological Constant Problem)
• Gauge Ambiguities have always plagued the
  interpretation

A covariant way of defining cosmological
backreaction is through considering the volume of
comoving hypersurfaces. Within this framework,
Kolb, Matarrese, Riotto 2005 argue that the
volume of the gradient expansion of backreaction
contains post-Newtonian terms of the form
h(H-1r?)2(H-2r2?)2i which can become large today.
However, it is easy to see that comoving gauge
becomes ill-defined upon shell crossing, when
H-2r2?1, which is long before the backreaction
proposed by Kolb, et al. becomes important The
lower figure on the right shows how comoving
hypersurfaces become singular at shell crossing
(dotted curve).
velocity
x
Time
e.g. this is spatial average of a tensor not
well defined in General Relativity
x

• 4) Non-Perturbative UV Backreaction

3) Perturbative UV Backreaction Longitudinal/Newt
onian Gauge

• ?q H-2h(r?)2i H-2s dk P(k)
  may have a UV divergence
  that cannot be extrapolated from CDM simulations.
• require nNL gt -1 from simulations -2lt nNLlt-3
• Can astrophysical black holes cause a
  significant backreaction?
• Their density is probably too small
• How about primordial BHs ?
• Naïve expectation is that BH merger leads to
  gravity wave emission ? w gt 0

Unlike the comoving gauge, the Longitudinal/Newton
ian gauge ds2
(12?)dt2-(1-2?)?ij dxi dxj remains well-defined
through shell crossing. The level of general
relativistic non-linear correction to the
deceleration parameter in this gauge is ?q H-2
h(r?)2i 10-5 for ?CDM cosmology and linear
perturbations.

• 5) IR Backreaction Cannot Mimic Dark Energy
• Raychadhury equation requires substantial
  horizon-scale shear/rotation for significant
  backreaction on cosmic acceleration, which is
  inconsistent with small Cosmic Microwave
  Background anisotropies (10-5)
• Einstein equations are local ? IR (scalar) modes
  locally look homogenous, and thus their impact
  (within a Hubble time) is degenerate with the
  initial conditions of the homogeneous universe.
  This rules out the claim by Martineau
  Brandenberger 2005.
• Corrections of the form ?q H-2?r2? (proposed by
  Barausse, Matarrese, Riotto 2005, and Kolb,
  Matattese, Notari, Riotto 2005) are equivalent to
  renormalizing spatial curvature, which is . 0.02
  based on Cosmic Microwave Background (WMAP)
  observations. Consideration of anisotropy, or
  extrapolation to small scales, limits this effect
  to . 10-5 (Geshnizjani, Chung, Afshordi 2005,
  Hirata Seljak 2005, Flanagan 2005)

6) IR Backreaction and Inflation

• Inflation may create a large phase-space of IR (k
  lt aH) modes, so that
• Cannot end inflation at 2nd order, only alters
  its history
• (for single field models
  Afshordi Brandenberger 2001)
• Can alter inflationary predictions for multiple
  fields/ non-smooth potentials
• Finelli Brandenberger 2000, Geshnizjani
  Afshordi 2005
• At higher orders, large logarithms (many
  e-foldings) can potentially end inflation ?
  Graceful Exit
• e.g. Tsamis Woodard 1996

Mukhanov, Abramo Brandenberger 1996
References This work is based on Afshordi, N.,
Chung, D.J.H. Geshnizjani, G. 2005, in
preparation Afshordi, N., and Brandenberger, R.
2001, PRD 63, 123505 Barausse, E., Matarrese, S.,
and Riotto, A. 2005, PRD 71, 063537 Finelli, F.,
and Brandenberger, R. 2000, PRD 62,
083502 Flanagan, E.E. 2005, PRD 71, 103521
Geshnizjani, G., and Afshordi, N. 2005, JCAP
0501, 011 Geshnizjani, G., Chung, D.J.H., and
Afshordi, N. 2005, PRD 72, 023517 Hirata, C.,
and Seljak 2005, PRD 72, 083501 Kolb, E.W.,
Matarrese, S., Notari, A., and Riotto, A. 2005,
hep-th/0503117 Kolb, E.W., Matarrese, S., and
Riotto, A. 2005, astro-ph/0506534 Martineau, P.,
and Brandenberger, R. 2005, astro-ph/0510523
Mukhanov, V.F., Abramo, L.R., and Brandenberger,
R. 1997, PRL 78, 1624 Tsamis, N.C., and Woodard,
R. 1996, NPB 474, 235

• 8) The Moral
• Many Analyses of Cosmological Backreaction are
  plagued by gauge ambiguities/artifacts
• IR backreaction can potentially affect the
  dynamics of early universe, but its impact today
  is severely constrained by cosmological
  observations (lt 10-5)
• Perturbative UV backreaction is also severely
  constrained (lt 10-5)
• Non-perturbative UV backreaction is not ruled
  out, but sounds unlikely