71 research outputs found
Primordial power spectrum: a complete analysis with the WMAP nine-year data
We have improved further the error sensitive Richardson-Lucy deconvolution
algorithm making it applicable directly on the un-binned measured angular power
spectrum of Cosmic Microwave Background observations to reconstruct the form of
the primordial power spectrum. This improvement makes the application of the
method significantly more straight forward by removing some intermediate stages
of analysis allowing a reconstruction of the primordial spectrum with higher
efficiency and precision and with lower computational expenses. Applying the
modified algorithm we fit the WMAP 9 year data using the optimized
reconstructed form of the primordial spectrum with more than 300 improvement in
\chi^2 with respect to the best fit power-law. This is clearly beyond the reach
of other alternative approaches and reflects the efficiency of the proposed
method in the reconstruction process and allow us to look for any possible
feature in the primordial spectrum projected in the CMB data. Though the
proposed method allow us to look at various possibilities for the form of the
primordial spectrum, all having good fit to the data, proper error-analysis is
needed to test for consistency of theoretical models since, along with possible
physical artefacts, most of the features in the reconstructed spectrum might be
arising from fitting noises in the CMB data. Reconstructed error-band for the
form of the primordial spectrum using many realizations of the data, all
bootstrapped and based on WMAP 9 year data, shows proper consistency of
power-law form of the primordial spectrum with the WMAP 9 data at all wave
numbers. Including WMAP polarization data in to the analysis have not improved
much our results due to its low quality but we expect Planck data will allow us
to make a full analysis on CMB observations on both temperature and
polarization separately and in combination.Comment: 19 pages, 5 figures, discussions extended, results unchanged, matches
the final version published in JCAP. Note: JCAP published version contains
minor typesetting errors (introduced by JCAP at the proof stage) in the plot
label
Primordial power spectrum from Planck
Using modified Richardson-Lucy algorithm we reconstruct the primordial power
spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature
anisotropy data. In our analysis we use different combinations of angular power
spectra from Planck to reconstruct the shape of the primordial power spectrum
and locate possible features. Performing an extensive error analysis we found
the dip near represents the most prominent feature in the
data. Feature near is detectable with high confidence only
in 217 GHz spectrum and is apparently consequence of a small systematic as
described in the revised Planck 2013 papers. Fixing the background cosmological
parameters and the foreground nuisance parameters to their best fit baseline
values, we report that the best fit power law primordial power spectrum is
consistent with the reconstructed form of the PPS at 2 C.L. of the
estimated errors (apart from the local features mentioned above). As a
consistency test, we found the reconstructed primordial power spectrum from
Planck temperature data can also substantially improve the fit to WMAP-9
angular power spectrum data (with respect to power-law form of the PPS)
allowing an overall amplitude shift of . In this context low-
and 100 GHz spectrum from Planck which have proper overlap in the multipole
range with WMAP data found to be completely consistent with WMAP-9 (allowing
amplitude shift). As another important result of our analysis we do report the
evidence of gravitational lensing through the reconstruction analysis. Finally
we present two smooth form of the PPS containing only the important features.
These smooth forms of PPS can provide significant improvements in fitting the
data (with respect to the power law PPS) and can be helpful to give hints for
inflationary model building.Comment: 30 pages, 11 figures, 1 table, matches published version in JCA
Sharp inflaton potentials and bi-spectra: Effects of smoothening the discontinuity
Sharp shapes in the inflaton potentials often lead to short departures from
slow roll which, in turn, result in deviations from scale invariance in the
scalar power spectrum. Typically, in such situations, the scalar power spectrum
exhibits a burst of features associated with modes that leave the Hubble radius
either immediately before or during the epoch of fast roll. Moreover, one also
finds that the power spectrum turns scale invariant at smaller scales
corresponding to modes that leave the Hubble radius at later stages, when slow
roll has been restored. In other words, the imprints of brief departures from
slow roll, arising out of sharp shapes in the inflaton potential, are usually
of a finite width in the scalar power spectrum. Intuitively, one may imagine
that the scalar bi-spectrum too may exhibit a similar behavior, i.e. a
restoration of scale invariance at small scales, when slow roll has been
reestablished. However, in the case of the Starobinsky model (viz. the model
described by a linear inflaton potential with a sudden change in its slope)
involving the canonical scalar field, it has been found that, a rather sharp,
though short, departure from slow roll can leave a lasting and significant
imprint on the bi-spectrum. The bi-spectrum in this case is found to grow
linearly with the wavenumber at small scales, a behavior which is clearly
unphysical. In this work, we study the effects of smoothening the discontinuity
in the Starobinsky model on the scalar bi-spectrum. Focusing on the equilateral
limit, we analytically show that, for smoother potentials, the bi-spectrum
indeed turns scale invariant at suitably large wavenumbers. We also confirm the
analytical results numerically using our newly developed code BINGO. We
conclude with a few comments on certain related points.Comment: v1: 28 pages, 4 figures; v2: 29 pages, 4 figures, Version to appear
in JCA
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