dc.description.abstract |
ensor Minkowski Functionals (TMFs) are tensor generalizations of the usual
Minkowski Functionals which are scalar quantities. We introduce them here for use in cos-
mological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radi-
ation. They encapsulate information about the shapes of structures and the orientation of
distributions of structures. We focus on one of the TMFs, namely
W
1
,
1
2
, which is the (1
,
1)
rank tensor generalization of the genus. The ratio of the eigenvalues of the average of
W
1
,
1
2
over all structures,
α
, encodes the net orientation of the structures; and the average of the
ratios of the eigenvalues of
W
1
,
1
2
for each structure,
β
, encodes the net intrinsic anisotropy
of the structures. We have developed a code that computes
W
1
,
1
2
, and from it
α
and
β
, for
a set of structures on the 2-dimensional Euclidean plane. We use it to compute
α
and
β
as
functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature
and
E
mode fields. We obtain the value of
α
to be one for both temperature and
E
mode,
which means that we recover the statistical isotropy of density fluctuations that we input in
the simulations. We find that the standard ΛCDM model predicts a charateristic shape of
β
for temperature and
E
mode as a function of the threshold, and the average over thresholds
is
β
∼
0
.
62 for temperature and
β
∼
0
.
63 for
E
mode. Accurate measurements of
α
and
β
can be used to test the standard model of cosmology and to search for deviations from
it. For this purpose we compute
α
and
β
for temperature and
E
mode data of various data
sets from PLANCK mission.
1
We compare the values measured from observed data with
those obtained from simulations to which instrument beam and noise characteristics of the
44GHz frequency channel have been added (which are provided as part of the PLANCK data
release). We find very good agreement of
β
and
α
between all PLANCK temperature datasets with ΛCDM expectations.
E
mode data show good agreement for
β
but
α
for all data
sets deviate from ΛCDM predictions higher than 3
−
σ
. It is most likely that the deviations
are probing the anisotropy of the noise field and beam characteristics of the detector rather
than the true
E
mode signal since for 44GHz the signal-to-noise ratio is well below one. This
will be further investigated after the full PLANCK data becomes publicly available. |
en_US |