114 research outputs found
Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
We include the effect of neutrino free streaming into the spectrum of relic
gravitational waves (RGWs) in the currently accelerating universe. For the
realistic case of a varying fractional neutrino energy density and a
non-vanishing derivative of mode function at the neutrino decoupling, the
integro-differential equation of RGWs is solved by a perturbation method for
the period from the neutrino decoupling to the matter-dominant stage.
Incorporating it to the analytic solution of the whole history of expansion of
the universe, the analytic solution of GRWs is obtained, evolving from the
inflation up to the current acceleration. The resulting spectrum of GRWs covers
the whole range of frequency Hz, and improves the
previous results. It is found that the neutrino free-streaming causes a
reduction of the spectral amplitude by in the range Hz, and leaves the other portion of the spectrum almost unchanged.
This agrees with the earlier numerical calculations. Examination is made on the
difference between the accelerating and non-accelerating models, and our
analysis shows that the ratio of the spectral amplitude in accelerating
CDM model over that in CDM model is , and within the various
accelerating models of the spectral amplitude is
proportional to for the whole range of frequency.
Comparison with LIGO S5 Runs Sensitivity shows that RGWs are not yet detectable
by the present LIGO, and in the future LISA may be able to detect RGWs in some
inflationary models.Comment: 22 pages,12 figures, accepeted by PR
Modifications by QCD transition and annihilation on analytic spectrum of relic gravitational waves in accelerating universe
As predicted by quantum chromodynamics(QCD), around MeV in the
early universe, the QCD transition occurs during which the quarks are combined
into the massive hadrons. This process reduces the effective relativistic
degree of freedom, and causes a change in the expansion behavior of the
universe. Similarly, the annihilation occurred around Mev
has the same kind of effect. Besides, the dark energy also drives the present
stage accelerating expansion. We study these combined effects on the relic
gravitational waves (RGWs). In our treatment, the QCD transition and the
annihilation, each is respectively represented by a short period of
expansion inserted into the radiation era. Incorporating these effects, the
equation of RGWs is analytically solved for a spatially flat universe, evolving
from the inflation up to the current acceleration, and the spectrum of RGWs is
obtained, covering the whole range of frequency Hz. It is found
that the QCD transition causes a reduction of the amplitude of RGWs by in the range Hz, and the annihilation causes a
reduction in the range Hz. In the presence of the dark
energy, the combination of the QCD transition and the annihilation,
causes a larger reduction of the amplitude by for the range
Hz, which covers the bands of operation of LIGO and LISA. By
analysis, it is shown that RGWs will be difficult to detect by the present
LIGO, but can be tested by LISA for certain inflationary models.Comment: 21 pages, 14 figures, to appear in PR
Signature of Gravity Waves in Polarization of the Microwave Background
Using spin-weighted decomposition of polarization in the Cosmic Microwave
Background (CMB) we show that a particular combination of Stokes and
parameters vanishes for primordial fluctuations generated by scalar modes, but
does not for those generated by primordial gravity waves. Because of this
gravity wave detection is not limited by cosmic variance as in the case of
temperature fluctuations. We present the exact expressions for various
polarization power spectra, which are valid on any scale. Numerical evaluation
in inflation-based models shows that the expected signal is of the order of 0.5
, which could be directly tested in future CMB experiments.Comment: 4 pages, 1 figure, RevTeX, matches the accepted version (to appear in
Phys. Rev. Lett.); code available at
http://arcturus.mit.edu:80/~matiasz/CMBFAST/cmbfast.htm
CMB Temperature Polarization Correlation and Primordial Gravitational Waves
We examine the use of the CMB's TE cross correlation power spectrum as a
complementary test to detect primordial gravitational waves (PGWs). The first
method used is based on the determination of the lowest multipole, ,
where the TE power spectrum, , first changes sign. The second
method uses Wiener filtering on the CMB TE data to remove the density
perturbations contribution to the TE power spectrum. In principle this leaves
only the contribution of PGWs. We examine two toy experiments (one ideal and
another more realistic) to see their ability to constrain PGWs using the TE
power spectrum alone. We found that an ideal experiment, one limited only by
cosmic variance, can detect PGWs with a ratio of tensor to scalar metric
perturbation power spectra at 99.9% confidence level using only the TE
correlation. This value is comparable with current constraints obtained by WMAP
based on the upper limits to the B-mode amplitude. We demonstrate
that to measure PGWs by their contribution to the TE cross correlation power
spectrum in a realistic ground based experiment when real instrumental noise is
taken into account, the tensor-to-scalar ratio, , should be approximately
three times larger.Comment: 13 pages, 13 figures, version matches published version. Combined
with 0710.365
Separating E and B types of polarization on an incomplete sky
Detection of magnetic-type (-type) polarization in the Cosmic Microwave
Background (CMB) radiation plays a crucial role in probing the relic
gravitational wave (RGW) background. In this paper, we propose a new method to
deconstruct a polarization map on an incomplete sky in real space into purely
electric and magnetic polarization type maps, and
, respectively. The main properties of our
approach are as follows: Firstly, the fields and
are constructed in real space with a minimal loss
of information. This loss of information arises due to the removal of a narrow
edge of the constructed map in order to remove various numerical errors,
including those arising from finite pixel size. Secondly, this method is fast
and can be efficiently applied to high resolution maps due to the use of the
fast spherical harmonics transformation. Thirdly, the constructed fields,
and , are scalar
fields. For this reason various techniques developed to deal with temperature
anisotropy maps can be directly applied to analyze these fields. As a concrete
example, we construct and analyze an unbiased estimator for the power spectrum
of the -mode of polarization . Basing our results on the
performance of this estimator, we discuss the RGW detection ability of two
future ground-based CMB experiments, QUIET and POLARBEAR.Comment: 43 pages, 15 figures, 1 table. The finial version, will appear in PR
Relic gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission
The new release of data from Wilkinson Microwave Anisotropy Probe improves
the observational status of relic gravitational waves. The 7-year results
enhance the indications of relic gravitational waves in the existing data and
change to the better the prospects of confident detection of relic
gravitational waves by the currently operating Planck satellite. We apply to
WMAP7 data the same methods of analysis that we used earlier [W. Zhao, D.
Baskaran, and L.P. Grishchuk, Phys. Rev. D 80, 083005 (2009)] with WMAP5 data.
We also revised by the same methods our previous analysis of WMAP3 data. It
follows from the examination of consecutive WMAP data releases that the maximum
likelihood value of the quadrupole ratio , which characterizes the amount of
relic gravitational waves, increases up to , and the interval
separating this value from the point (the hypothesis of no gravitational
waves) increases up to a level. The primordial spectra of density
perturbations and gravitational waves remain blue in the relevant interval of
wavelengths, but the spectral indices increase up to and
. Assuming that the maximum likelihood estimates of the perturbation
parameters that we found from WMAP7 data are the true values of the parameters,
we find that the signal-to-noise ratio for the detection of relic
gravitational waves by the Planck experiment increases up to , even
under pessimistic assumptions with regard to residual foreground contamination
and instrumental noises. We comment on theoretical frameworks that, in the case
of success, will be accepted or decisively rejected by the Planck observations.Comment: 27 pages, 12 (colour) figures. Published in Phys. Rev. D. V.3:
modifications made to reflect the published versio
Polarization of the Microwave Background in Reionized Models
I discuss the physics of polarization in models with early reionization. For
sufficiently high optical depth to recombination the polarization is boosted on
large scales while it is suppressed on smaller scales. New peaks appear in the
polarization power spectrum, their position is proportional to the square root
of the redshift at which the reionization occurs while their amplitude is
proportional to the optical depth. For standard scenarios the rms degree of
linear polarization as measured with a 7 degree FWHM antenna (like the one of
the Brown University experiment) is , , for an optical depth of 1, 0.5 or 0 respectively. For a 1 degree FWHM
antenna this same models give , and .
Detailed measurement of polarization on large angular scales could provide an
accurate determination of the epoch of reionization, which cannot be obtained
from temperature measurements alone.Comment: 19 pages, 12 figures, Revised to match PRD accepeted version.
Improved COBE normaliztion so some numerical results change slightl
Temperature and Polarization Patterns in Anisotropic Cosmologies
We study the coherent temperature and polarization patterns produced in
homogeneous but anisotropic cosmological models. We show results for all
Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V,
VII, VII and IX) to illustrate the range of possible behaviour. We
discuss the role of spatial curvature, shear and rotation in the geodesic
equations for each model and establish some basic results concerning the
symmetries of the patterns produced. We also give examples of the
time-evolution of these patterns in terms of the Stokes parameters , and
.Comment: 24 pages, 7 Figures, submitted to JCAP. Revised version: numerous
references added, text rewritten, and errors corrected
Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
A strong variable gravitational field of the very early Universe inevitably
generates relic gravitational waves by amplifying their zero-point quantum
oscillations. We begin our discussion by contrasting the concepts of relic
gravitational waves and inflationary `tensor modes'. We explain and summarize
the properties of relic gravitational waves that are needed to derive their
effects on CMB temperature and polarization anisotropies. The radiation field
is characterized by four invariants I, V, E, B. We reduce the radiative
transfer equations to a single integral equation of Voltairre type and solve it
analytically and numerically. We formulate the correlation functions
C^{XX'}_{\ell} for X, X'= T, E, B and derive their amplitudes, shapes and
oscillatory features. Although all of our main conclusions are supported by
exact numerical calculations, we obtain them, in effect, analytically by
developing and using accurate approximations. We show that the TE correlation
at lower \ell's must be negative (i.e. an anticorrelation), if it is caused by
gravitational waves, and positive if it is caused by density perturbations.
This difference in TE correlation may be a signature more valuable
observationally than the lack or presence of the BB correlation, since the TE
signal is about 100 times stronger than the expected BB signal. We discuss the
detection by WMAP of the TE anticorrelation at \ell \approx 30 and show that
such an anticorrelation is possible only in the presence of a significant
amount of relic gravitational waves (within the framework of all other common
assumptions). We propose models containing considerable amounts of relic
gravitational waves that are consistent with the measured TT, TE and EE
correlations.Comment: 61 pages including 15 figures, v.2: additional references and
clarifications, to be published in Phys. Rev.
Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments
Inflation produces nearly Harrison-Zel'dovich scalar and tensor perturbation
spectra which lead to anisotropy in the cosmic microwave background (CMB). The
amplitudes and shapes of these spectra can be parametrized by , , and where and are the scalar and
tensor contributions to the square of the CMB quadrupole and and
are the power-lawspectral indices. Even if we restrict ourselves to information
from angles greater than one third of a degree, three of these observables can
be measured with some precision. The combination can be
known to better than . The scalar index can be determined to
better than . The ratio can be known to about for and slightly better for smaller . The precision with which
can be measured depends weakly on and strongly on . For
can be determined with a precision of about . A
full-sky experiment with a beam using technology available today, similar
to those being planned by several groups, can achieve the above precision. Good
angular resolution is more important than high signal-to-noise ratio; for a
given detector sensitivity and observing time a smaller beam provides
significantly more information than a larger beam. The uncertainties in
and are roughly proportional to the beam size. We briefly discuss the
effects of uncertainty in the Hubble constant, baryon density, cosmological
constant and ionization history.Comment: 28 pages of uuencoded postscript with 8 included figures. A
postscript version is also available by anonymous ftp at
ftp://astro.uchicago.edu/pub/astro/knox/fullsim.p
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