1,189 research outputs found
The gravitational wave contribution to CMB anisotropies and the amplitude of mass fluctuations from COBE results
A stochastic background of primordial gravitational waves may substantially
contribute, via the Sachs--Wolfe effect, to the large--scale Cosmic Microwave
Background (CMB) anisotropies recently detected by COBE. This implies a {\it
bias} in any resulting determination of the primordial amplitude of density
fluctuations. We consider the constraints imposed on (``tilted")
power--law fluctuation spectra, taking into account the contribution from both
scalar and tensor waves, as predicted by power--law inflation. The
gravitational--wave contribution to CMB anisotropies generally reduces the
required {\it rms} level of mass fluctuation, thereby increasing the linear
{\it bias parameter}, even in models where the spectral index is close to the
Harrison--Zel'dovich value . This ``gravitational--wave bias" helps to
reconcile the predictions of CDM models with observations on pairwise galaxy
velocity dispersion on small scales.Comment: 11 pages. Two figures available upon reques
Physical constraints on the halo mass function
We analyse the effect of two relevant physical constraints on the mass
multiplicity function of dark matter halos in a Press--Schechter type
algorithm. Considering the random--walk of linear Gaussian density fluctuations
as a function of the smoothing scale, we simultaneously i) account for mass
semi--positivity and ii) avoid the cloud--in--cloud problem. It is shown that
the former constraint implies a severe cutoff of low--mass objects, balanced by
an increase on larger mass scales. The analysis is performed both for
scale--free power--spectra and for the standard cold dark matter model. Our
approach shows that the well--known ``infrared" divergence of the standard
Press--Schechter mass function is caused by unphysical, negative mass events
which inevitably occur in a Gaussian distribution of density fluctuations.Comment: Revised version (accepted for publication in MNRAS) including a new
comparison with numerical results, a new appendix and new references.
uuencoded gzip'ed tar archive containing many LaTex files (the main file is
mass.tex). 16 pages with 6 figures (all included
The nonlinear redshift-space power spectrum of galaxies
We study the power spectrum of galaxies in redshift space, with third order
perturbation theory to include corrections that are absent in linear theory. We
assume a local bias for the galaxies: i.e. the galaxy density is sampled from
some local function of the underlying mass distribution. We find that the
effect of the nonlinear bias in real space is to introduce two new features:
first, there is a contribution to the power which is constant with wavenumber,
whose nature we reveal as essentially a shot-noise term. In principle this
contribution can mask the primordial power spectrum, and could limit the
accuracy with which the latter might be measured on very large scales.
Secondly, the effect of second- and third-order bias is to modify the effective
bias (defined as the square root of the ratio of galaxy power spectrum to
matter power spectrum). The effective bias is almost scale-independent over a
wide range of scales. These general conclusions also hold in redshift space. In
addition, we have investigated the distortion of the power spectrum by peculiar
velocities, which may be used to constrain the density of the Universe. We look
at the quadrupole-to-monopole ratio, and find that higher-order terms can mimic
linear theory bias, but the bias implied is neither the linear bias, nor the
effective bias referred to above. We test the theory with biased N-body
simulations, and find excellent agreement in both real and redshift space,
providing the local biasing is applied on a scale whose fractional r.m.s.
density fluctuations are .Comment: 13 pages, 7 figures. Accepted by MNRA
The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
We analyze the temperature three--point correlation function and the skewness
of the Cosmic Microwave Background (CMB), providing general relations in terms
of multipole coefficients. We then focus on applications to large angular scale
anisotropies, such as those measured by the {\em COBE} DMR, calculating the
contribution to these quantities from primordial, inflation generated, scalar
perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic
inflation we are able to provide a {\it universal} expression for the ensemble
averaged three--point function and for the corresponding skewness, which
accounts for all primordial second--order effects. These general expressions
would moreover apply to any situation where the bispectrum of the primordial
gravitational potential has a {\em hierarchical} form. Our results are then
specialized to a number of relevant models: power--law inflation driven by an
exponential potential, chaotic inflation with a quartic and quadratic potential
and a particular case of hybrid inflation. In all these cases non--Gaussian
effects are small: as an example, the {\em mean} skewness is much smaller than
the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation
field.Comment: 18 pages; LaTeX; 4 PostScript figures included at the end of the
file; SISSA REF.193/93/A and DFPD 93/A/8
The bias field of dark matter haloes
This paper presents a stochastic approach to the clustering evolution of dark
matter haloes in the Universe. Haloes, identified by a Press-Schechter-type
algorithm in Lagrangian space, are described in terms of `counting fields',
acting as non-linear operators on the underlying Gaussian density fluctuations.
By ensemble averaging these counting fields, the standard Press-Schechter mass
function as well as analytic expressions for the halo correlation function and
corresponding bias factors of linear theory are obtained, thereby extending the
recent results by Mo and White. The non-linear evolution of our halo population
is then followed by solving the continuity equation, under the sole hypothesis
that haloes move by the action of gravity. This leads to an exact and general
formula for the bias field of dark matter haloes, defined as the local ratio
between their number density contrast and the mass density fluctuation. Besides
being a function of position and `observation' redshift, this random field
depends upon the mass and formation epoch of the objects and is both non-linear
and non-local. The latter features are expected to leave a detectable imprint
on the spatial clustering of galaxies, as described, for instance, by
statistics like bispectrum and skewness. Our algorithm may have several
interesting applications, among which the possibility of generating mock halo
catalogues from low-resolution N-body simulations.Comment: 23 pages, LaTeX (included psfig.tex), 4 figures. Few comments and
references have been added, and minor typos and errors corrected. This
version matches the refereed one, in press in MNRA
Projection and Galaxy Clustering Fourier Spectra
Second order perturbation theory predicts a specific dependence of the
bispectrum, or three-point correlation function in the Fourier transform
domain, on the shape of the configuration of its three wave vector arguments,
which can be taken as a signature of structure formed by gravitational
instability. Comparing this known dependence on configuration shape with the
weak shape dependence of the galaxy bispectrum has been suggested as an
indication of bias in the galaxy distribution. However, to interpret results
obtained from projected catalogs, we must first understand the effects of
projection on this shape dependence. We present expressions for the projected
power spectrum and bispectrum in both Cartesian and spherical geometries, and
we examine the effects of projection on the predicted bispectrum with
particular attention to the dependence on configuration shape. Except for an
overall numerical factor, for Cartesian projection with characteristic depth
\Dstar there is little effect on the shape dependence of the bispectrum for
wavelengths small compared to \Dstar or projected wavenumbers q \Dstar
\gg 1 . For angular projection, a scaling law is found for spherical harmonic
index , but there is always a mixing of scales over the range of
the selection function. For large it is sufficient to examine a small
portion of the sky.Comment: aastex, 7 figure
The Variance of QSO Counts in Cells
{}From three quasar samples with a total of 1038 objects in the redshift
range we measure the variance of counts in cells of
volume . By a maximum likelihood analysis applied separately on these
samples we obtain estimates of , with .
The analysis from a single catalog for Mpc and from a
suitable average over the three catalogs for and
Mpc, gives , ,
and , respectively, where the
confidence ranges account for both sampling errors and statistical
fluctuations in the counts. This allows a comparison of QSO clustering on large
scales with analogous data recently obtained both for optical and IRAS
galaxies: QSOs seem to be more clustered than these galaxies by a biasing
factor .Comment: 13 pages in plain Tex, 5 figures available in postscript in a
separate file, submitted to ApJ, DAPD-33
Living with ghosts in Horava-Lifshitz gravity
We consider the branch of the projectable Horava-Lifshitz model which
exhibits ghost instabilities in the low energy limit. It turns out that, due to
the Lorentz violating structure of the model and to the presence of a finite
strong coupling scale, the vacuum decay rate into photons is tiny in a wide
range of phenomenologically acceptable parameters. The strong coupling scale,
understood as a cutoff on ghosts' spatial momenta, can be raised up to TeV. At lower momenta, the projectable Horava-Lifshitz gravity is
equivalent to General Relativity supplemented by a fluid with a small positive
sound speed squared () , that could
be a promising candidate for the Dark Matter. Despite these advantages, the
unavoidable presence of the strong coupling obscures the implementation of the
original Horava's proposal on quantum gravity. Apart from the Horava-Lifshitz
model, conclusions of the present work hold also for the mimetic matter
scenario, where the analogue of the projectability condition is achieved by a
non-invertible conformal transformation of the metric.Comment: 33 pages, 1 figure. The proof of an equivalence between the IR limit
of the projectable Horava-Lifshitz gravity and the mimetic matter scenario is
given in Appendix A. Version accepted for publication in JHE
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