Statistical anisotropy of CMB as a probe of conformal rolling scenario

Search for the statistical anisotropy in the CMB data is a powerful tool for constraining models of the early Universe. In this paper we focus on the recently proposed cosmological scenario with conformal rolling. We consider two sub-scenarios, one of which involves a long intermediate stage between conformal rolling and conventional hot epoch. Primordial scalar perturbations generated within these sub-scenarios have different direction-dependent power spectra, both characterized by a single parameter h^2. We search for the signatures of this anisotropy in the seven-year WMAP data using quadratic maximum likelihood method, first applied for similar purposes by Hanson and Lewis. We confirm the large quadrupole anisotropy detected in V and W bands, which has been argued to originate from systematic effects rather than from cosmology. We construct an estimator for the parameter h^2. In the case of the sub-scenario with the intermediate stage we set an upper limit h^2 < 0.045 at the 95% confidence level. The constraint on h^2 is much weaker in the case of another sub-scenario, where the intermediate stage is absent.Comment: 27 pages, 4 figures. Stronger constraint in case of sub-scenario A obtained. Version accepted for publication in JCA

Revisiting constraints on (pseudo)conformal Universe with Planck data

We revisit constraints on the (pseudo)conformal Universe from the non-observation of statistical anisotropy in the Planck data. The quadratic maximal likelihood estimator is applied to the Planck temperature maps at frequencies 143 GHz and 217 GHz as well as their cross-correlation. The strongest constraint is obtained in the scenario of the (pseudo)conformal Universe with a long intermediate evolution after conformal symmetry breaking. In terms of the relevant parameter (coupling constant), the limit is h^2 <0.0013 at 95% C.L. (using the cross-estimator). The analogous limit is much weaker in the scenario without the intermediate stage (h^2 \ln \frac{H_0}{\Lambda}<0.52) allowing the coupling constant to be of order one. In the latter case, the non-Gaussianity in the 4-point function appears to be a more promising signature.Comment: 13 pages, 2 figures. Appendix with detailed computation of the Fisher matrix adde

Algebraic properties of Manin matrices 1

We study a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory. They are defined as "noncommutative endomorphisms" of a polynomial algebra. More explicitly their defining conditions read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}] = [M_{kj}, M_{il}]$ (e.g. $[M_{11},M_{22}] = [M_{21},M_{12}]$). The basic claim is that despite noncommutativity many theorems of linear algebra hold true for Manin matrices in a form identical to that of the commutative case. Moreover in some examples the converse is also true. The present paper gives a complete list and detailed proofs of algebraic properties of Manin matrices known up to the moment; many of them are new. In particular we present the formulation in terms of matrix (Leningrad) notations; provide complete proofs that an inverse to a M.m. is again a M.m. and for the Schur formula for the determinant of a block matrix; we generalize the noncommutative Cauchy-Binet formulas discovered recently [arXiv:0809.3516], which includes the classical Capelli and related identities. We also discuss many other properties, such as the Cramer formula for the inverse matrix, the Cayley-Hamilton theorem, Newton and MacMahon-Wronski identities, Plucker relations, Sylvester's theorem, the Lagrange-Desnanot-Lewis Caroll formula, the Weinstein-Aronszajn formula, some multiplicativity properties for the determinant, relations with quasideterminants, calculation of the determinant via Gauss decomposition, conjugation to the second normal (Frobenius) form, and so on and so forth. We refer to [arXiv:0711.2236] for some applications.Comment: 80 page

GRB observations by Fermi LAT revisited: new candidates found

We search the Fermi-LAT photon database for an extended gamma-ray emission which could be associated with any of the 581 previously detected gamma-ray bursts (GRBs) visible to the Fermi-LAT. For this purpose we compare the number of photons with energies E > 100 MeV and E > 1 GeV which arrived in the first 1500 seconds after the burst from the same region, to the expected background. We require that the expected number of false detections does not exceed 0.05 for the entire search and find the high-energy emission in 19 bursts, four of which (GRB 081009, GRB 090720B, GRB 100911 and GRB 100728A) were previously unreported. The first three are detected at energies above 100 MeV, while the last one shows a statistically significant signal only above 1 GeV.Comment: Updated after referee comments, published in MNRAS Letters; 5 pages, 2 table