Relic Gravitational Waves as a Test of the Early Universe

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Relic Gravitational Wavesas a Test of the Early
Universe

• Tina Kahniashvili
• CCPP, New York University
• Collaboration
• Giga Gogoberidze (AAO, Georgia)
• Arthur Kosowsky (Pittsburgh, USA)
• arXiv0705.1733 astro-ph
• McMaster University Origins Institute
• 17 May 2007

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Outline

• Relic gravitational waves sources
• Inflation
• quantum fluctuations
• Inflationary generated magnetic fields
• during phase transitions
• Bubble collisions
• Topological defects (strings)
• Primordial turbulence
• Magnetic field
• Gravitational waves (by helicity) imprints on CMB
• Polarization anisotropies
• Parity odd cross correlation spectra
• Analogy with acoustic waves
• Characteristic frequency and spectrum slop
• Future prospects for gravitational waves direct
  detection

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Motivations

• Precise cosmological observations allow to
  understand the physical processes in the
  very early Universe

• Any self-consistent cosmological model claiming
• to explain today picture of the Universe, should
  be
• in an agreement with currently available and
  nearest
• future observations, which keep traces of the
  early
• epochs
• Baryongenesis light element abundance
• Large-Scale structure formation
• Linear stage of perturbations (CMB)
• Universe geometry
• Gravitational waves
• Cosmological neutrinos

• Since GWs propagate freely after being generate,
  they keep the information on their source
• Detection of GWs could open a window into new
  physics (parity symmetry violation, quantum
  gravity models, physics of phase transitions).
• If relic GWs will be detected how it would be
  possible to identify their source?
• Characteristic frequency spectrum shape
• Importance connect GWs characteristics with
  theoretical models of the early Universe
• and physics of the source.

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Invisible epochs of the universe expansion

• The apparent inverse horizon size at a scale a,
  or Hubble frequency is shifted to a lower
  frequency, da/dtHa.
• DE log(da/dt)log(a),
• RD log(da/dt)- log(a),
• MD log(da/dt)-log(a)/2
  

From C. Hogan 2006
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Tensor Perturbations Cosmological Gravitational
Waves

• Cosmological GWs linear tensor perturbations
  with respect to Friedman-Lemaitre-Robertson-Walker
  metric
• gika2(?ik hik)
• GWs are gauge-invariant perturbations governed by
  Einstein equations
• Gik8? GTik

• Tensor mode of perturbations
• h?? ?g??
• no analogy under Newtonian gravity
• gauge-invariant
• transverse, traceless h??
• symmetric h?? h??
• gauge choice ! h0i h0i 0 h00 ! 9 degrees
• hij hji ! 6 degrees
• ? hii 0 ! 5 degrees
• hij kj0 ! 2 degrees
• Two degrees of freedom represent two degree of
  GWs polarization

Mukhanov, Feldman, and Brandenberger 1992
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Relic Gravitational wave background
From C. Hogan 2006
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GWs detection missions
from S. Chongchiman and G. Efstathiou, 2006
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Relic GWs vs. CMB
GWs have imprints on CMB temperature and
polarization anisotropies

• Polnarev 1985

Polnarev 1985
WMAP- 3year data
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Relic GWs vs. CMB temperature anisotropies

• ? T/T depends on the tensor perturbations
  amplitude and thus put the upper limit on GUTs
  scale
• Rubakov, Sazhin, and Veryaskin, 1982,
• Abbott and Wise, 1984

Pritchard and Kamionkowsky 2004
Relic GWs vs. CMB polarization anisotropies

• B-polarization signal the peak position insures
  to distinguish the source of B-polarization
  signal.
• Zaldariagga and Seljak, 1997
• Kamionkowsky, Kosowsky, and Stebbins, 1997

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Testing Parity Violation through CMB anisotropies
Primordial helicity generation Cornawll 1997,
Giovannini and Shaposhnikov 1998, Caroll and
Field 2000, Giovannini 2000, Vachaspati 2001,
Sigl 2002

• CMB anisotropy parity odd power spectra (tensor
  mode)
• might reflect the presence of primordial helicity
  ClTB/ClTE (black) ClEB/ClEE (red)

Caprini, Durrer, and Kahniashvili 2004
GWs generated by an helical source have a
parity odd spectrum. In particular, magnetic or
kinetic helicity induces circularly polarized GWs
Kahniashvili, Gogoberidze, and Ratra, 2005
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Phase transitions turbulence and bubble
collisions

• Hubble frequency f010-4Hz (T/1Tev)
• Large Hadron Collider (LHC) Ã! relic GWs
• LISAs peak sensitivity corresponds to ¼ 1/10
• of Hubble horizon at 1 Tev energy scale

• Previous works
• Pioneering Witten 1984, Hogan 1984
• Earlier 90s
• Turner and Wilczek, 1990
• Kosowsky, Turner, and Watkins, 1992
• Kosowsky and Turner, 1993
• Kamionkowsky, Kosowsky, and Turner, 1994
• Ten years after
• Kosowsky, Mack, and Kahniashvili, 2002
• Dolgov, Grasso, and Nicolis, 2002
• Aprenda, Maggiore, Nicolis and Riotto, 2002
• Nicolis, 2004
• Recent
• Kahniashvili, Gogoberidze, and Ratra, 2005
• Crojean and Servant, 2006
• Caprini and Durrer, 2006
• Caprini, Durrer, and Sturani, 2006
• Randall and Servant, 2006

New Physics from LISA?

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Different ? and ? key-parameters of phase
transitions
Grojean and Servant, 2006

• the ratio between the false vacuum energy and
  plasma thermal energy.
• ? time variation rate of bubbles nucleation

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GWs by Turbulence Turbulence model

• We assume that in the early Universe at time tin
  vacuum energy ?vac is converted into turbulent
  energy with an efficiency ? over a time scale
  ?stir on a characteristic length scale LS.
• After generation, the turbulence energy
  cascades from larger to smaller scales. The
  cascade stops at a damping scale, LD, where the
  turbulence energy is removed by dissipation.
• As usual, we assume that the turbulence is
  produced in a time much less than the Hubble
  time, ?stir 1/Hin and generates GWs.
• We assume stationary turbulence that lasts at
  least few turn-over time of the largest size
  eddy.

• Turbulent fluid kinetic energy is present on all
  scales in the inertial range kSltkltkD. Where
  kS2?/LS and kD2?/LD, and the inertial range
  includes length scales L 2 (LD, LS), i.e., length
  scales shorter than those on which energy flows
  into the turbulence and larger than those on
  which the turbulence energy is dissipated.
• We assume that the energy is injected into the
  turbulence continuously over a time ?, rather
  than as an instantaneous impulse

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General formalism equations and solutions

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• The energy density of GWs
• Two-point correlation function of GWs
• (in far field approximation)
• Time-delayed forth-point correlation function
  (Fourier transform)

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Kolmogoroff like turbulence spectrum

• Turbulent motion two point correlation
• Power spectrum (space and time auto-correlations)

Kolmogoroff 1941
Kraichnan 1964
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Analogy acoustic waves generation by turbulence
Goldstein 1976

• Eddies length l0 and velocity v0
• Eddies characteristic frequency v0/ l0
• Eddies characteristic wave-number 1/ l0
• Because v0 lt1, the dark area is stretched along k
  axis.
• GWs generating turbulent elements lie along k?
  line, so ?GW is given by eddy inverse turn-over
  time v0/ l0 .

Hijij(k, ?) !! Hijij(0, ?)
GWs propagate with c (speed of light), and there
is no super-luminal GWs GWs spectral energy
density is completely determined by the source
time-characteristics and not by the spatial
structure of the source.
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GWs generation efficiency

• Machs number Mv0/c, M3?/k0
• ?1 8?G/(3H2) critical density
• LH Hubble horizon size at GWs generation

• Efficiency of generation process is defined as a
  ratio between GWs energy density and dissipated
  energy of turbulence
• Energy dissipation for turbulence

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Relic GWs Spectrum

• Peak amplitude
• Converting the radiation frequency ? at time
  of phase transitions to the today frequency f
• ? is the stirring scale's fraction of the Hubble
  length and ? is the turbulence duration's
  fraction of the Hubble length.

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Asymptotical solutions Low frequency regime
hc(f) f1/2 Intermediate regime hc(f)
f-13/4 High frequency regime exponential
suppression of the power
Parameters ?T turbulence lasting time k0
stirring scale M3?/k0 - Mach
number R3/4kd/k0 - Reynolds number
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Discussions

• We have calculated the spectrum of relic
  gravitational radiation resulting from a period
  of turbulence in the early universe, in terms of
  the turbulence duration, stirring scale, Reynolds
  and Mach numbers, and the temperature of the
  universe when the turbulence occurs. The
  turbulence model parameters (M, R, ?T) are
  related to the key-parameters of phase
  transitions ( ? and ?)

• Cosmological turbulence will never be precisely
  stationary since the Universe is expanding The
  duration time of turbulence source is comparable
  with the turn-over time of the stirring scale
  size eddy.
• Even so, as long as the eddies on a given length
  scale can be treated as uncorrelated sources of
  turbulence, the resulting radiation spectrum will
  be close to that from a stationary source, simply
  due to the inevitable cascade of energy.
• Justification (Proudman 1975) If the
  turbulence is decaying additional terms
  proportional to time derivatives appear. But
  since the decay time ?d is at least several times
  larger than the turnover time, then the
  additional terms proportional to 1/?d can be
  safely neglected

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Results

• LISA has a 5? sensitivity to stochastic
  backgrounds of below hc10--23 between
  frequencies 10-3 and 10-2 Hz, and decreasing to
  around hc10--20 at 10--4 Hz, for one year of
  integration.
• Turbulence with a Mach number M1 would be a
  factor of 1000 larger than the LISA detection
  threshold at the peak frequency around 10--3 Hz.
  For a Mach number M0.1, the peak amplitude
  decreases by a factor of 100 due to the M-3/2
  scaling and the different signal spectrum.
  However, the peak frequency also shifts to 10--4
  Hz, at which point LISA's sensitivity has
  declined greatly.
• Future space-based interferometers could be
  configured to give strain sensitivities
  comparable to
• LISA, but with a frequency window between 10--4
  and 10--6 Hz. Such an experiment would easily
  detect turbulence at the electroweak scale with a
  Mach number M0.1, and would even lirt with a
  detection at M0.01.

• We have no guarantees of violent events in the
  early universe. However, turbulence is completely
  generic result of energy injection on a
  characteristic length scale, and we have shown
  that the resulting relic gravitational waves are
  within the realm of detectability, even for
  turbulence with Mach numbers as low as 0.01,
  corresponding to an energy input into the early
  universe of 10-4 of the total energy density

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Conclusions

• Since gravitational waves propagate freely after
  being generate, they keep the information on
  their source characteristics
• Direct detection of gravitational waves could
  open a window into new physics (parity symmetry
  violation, quantum gravity models, physics of
  phase transitions).

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THANKS
Dark Energy Conference and Workshop Organizing
Committee Collaborators Grigol Gogoberidze and
Arthur Kosowsky