Helical Magnetic Fields from Inflation

We analyze the generation of seed magnetic fields during de Sitter inflation considering a non-invariant conformal term in the electromagnetic Lagrangian of the form $-\frac14 I(\phi) F_{\mu \nu} \widetilde{F}^{\mu \nu}$, where $I(\phi)$ is a pseudoscalar function of a non-trivial background field $\phi$. In particular, we consider a toy model, that could be realized owing to the coupling between the photon and either a (tachyonic) massive pseudoscalar field and a massless pseudoscalar field non-minimally coupled to gravity, where $I$ follows a simple power-law behavior $I(k,\eta) = g/(-k\eta)^{\beta}$ during inflation, while it is negligibly small subsequently. Here, $g$ is a positive dimensionless constant, $k$ the wavenumber, $\eta$ the conformal time, and $\beta$ a real positive number. We find that only when $\beta = 1$ and $0.1 \lesssim g \lesssim 2$ astrophysically interesting fields can be produced as excitation of the vacuum, and that they are maximally helical.Comment: 17 pages, 1 figure, subsection IIc and references added; accepted for publication in IJMP

Cosmological quests in the CMB sky

Observational Cosmology has indeed made very rapid progress in recent years. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and, more recently, polarization have played a very important role. Besides precise determination of various parameters of the `standard' cosmological model, observations have also established some important basic tenets that underlie models of cosmology and structure formation in the universe -- `acausally' correlated initial perturbations in a flat, statistically isotropic universe, adiabatic nature of primordial density perturbations. These are consistent with the expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early universe. Further, gravitational instability is the established mechanism for structure formation from these initial perturbations. In the next decade, future experiments promise to strengthen these deductions and uncover the remaining crucial signature of inflation -- the primordial gravitational wave background.Comment: Plenary talk at the International Conference on Einstein's Legacy in the New Millennium, December 15 - 22, 2005, Puri, India; to appear in the Proceedings to be published in IJMPD; 18 pages, 7 figure

Reconstructing the Primordial Spectrum with CMB Temperature and Polarization

We develop a new method to reconstruct the power spectrum of primordial curvature perturbations, $P(k)$, by using both the temperature and polarization spectra of the cosmic microwave background (CMB). We test this method using several mock primordial spectra having non-trivial features including the one with an oscillatory component, and find that the spectrum can be reconstructed with a few percent accuracy by an iterative procedure in an ideal situation in which there is no observational error in the CMB data. In particular, although the previous ``cosmic inversion'' method, which used only the temperature fluctuations, suffered from large numerical errors around some specific values of $k$ that correspond to nodes in a transfer function, these errors are found to disappear almost completely in the new method.Comment: 18 pages, 17 figures, submitted to PR

Circular Polarization from Gamma-ray Burst Afterglows

We investigate the circular polarization (CP) from Gamma-Ray Burst (GRB) afterglows. We show that a tangled magnetic field cannot generate CP without an ordered magnetic field because there is always an oppositely directed field, so that no handedness exists. This implies the observation of CP could be a useful probe of an ordered field, which carries valuable information on the GRB central engine. By solving the transfer equation of polarized radiation, we find that the CP reaches 1% at radio frequencies and 0.01% at optical for the forward shock, and 10-1% at radio and 0.1-0.01% at optical for the reverse shock.Comment: 12 pages, 3 figure

Reconstructing the primordial power spectrum - a new algorithm

We propose an efficient and model independent method for reconstructing the primordial power spectrum from Cosmic Microwave Background (CMB) and large scale structure observations. The algorithm is based on a Monte Carlo principle and therefore very simple to incorporate into existing codes such as Markov Chain Monte Carlo. The algorithm has been used on present cosmological data to test for features in the primordial power spectrum. No significant evidence for features is found, although there is a slight preference for an overall bending of the spectrum, as well as a decrease in power at very large scales. We have also tested the algorithm on mock high precision CMB data, calculated from models with non-scale invariant primordial spectra. The algorithm efficiently extracts the underlying spectrum, as well as the other cosmological parameters in each case. Finally we have used the algorithm on a model where an artificial glitch in the CMB spectrum has been imposed, like the ones seen in the WMAP data. In this case it is found that, although the underlying cosmological parameters can be extracted, the recovered power spectrum can show significant spurious features, such as bending, even if the true spectrum is scale invariant.Comment: 22 pages, 12 figures, matches JCAP published versio

Primordial Power Spectrum Reconstruction

In order to reconstruct the initial conditions of the universe it is important to devise a method that can efficiently constrain the shape of the power spectrum of primordial matter density fluctuations in a model-independent way from data. In an earlier paper we proposed a method based on the wavelet expansion of the primordial power spectrum. The advantage of this method is that the orthogonality and multiresolution properties of wavelet basis functions enable information regarding the shape of $P_{\rm in}(k)$ to be encoded in a small number of non-zero coefficients. Any deviation from scale-invariance can then be easily picked out. Here we apply this method to simulated data to demonstrate that it can accurately reconstruct an input $P_{\rm in}(k)$, and present a prescription for how this method should be used on future data.Comment: 4 pages, 2 figures. JCAP accepted versio

A diffuse scattering model of ultracold neutrons on wavy surfaces

Metal tubes plated with nickel-phosphorus are used in many fundamental physics experiments using ultracold neutrons (UCN) because of their ease of fabrication. These tubes are usually polished to a average roughness of 25-150 nm. However, there is no scattering model that accurately describes UCN scattering on such a rough guide surface with a mean-square roughness larger than 5 nm. We therefore developed a scattering model for UCN in which scattering from random surface waviness with a size larger than the UCN wavelength is described by a microfacet Bidirectional Reflectance Distribution Function model (mf-BRDF model), and scattering from smaller structures by the Lambert's cosine law (Lambert model). For the surface waviness, we used the statistical distribution of surface slope measured by an atomic force microscope on a sample piece of guide tube as input of the model. This model was used to describe UCN transmission experiments conducted at the pulsed UCN source at J-PARC. In these experiments, a UCN beam collimated to a divergence angle smaller than $\pm 6^{\circ}$ was directed into a guide tube with a mean-square roughness of 6.4 nm to 17 nm at an oblique angle, and the UCN transport performance and its time-of-flight distribution were measured while changing the angle of incidence. The mf-BRDF model combined with the Lambert model with scattering probability $p_{L} = 0.039\pm0.003$ reproduced the experimental results well. We have thus established a procedure to evaluate the characteristics of UCN guide tubes with a surface roughness of approximately 10 nm.Comment: 15 pages, 11 figure

Natural Inflation, Planck Scale Physics and Oscillating Primordial Spectrum

In the ``natural inflation'' model, the inflaton potential is periodic. We show that Planck scale physics may induce corrections to the inflaton potential, which is also periodic with a greater frequency. Such high frequency corrections produce oscillating features in the primordial fluctuation power spectrum, which are not entirely excluded by the current observations and may be detectable in high precision data of cosmic microwave background (CMB) anisotropy and large scale structure (LSS) observations.Comment: 20 pages, 11 figures. To appear in Int J Mod. Phys.