3D mapping of matter distribution in the universe through the 21 cm radio emission of atomic hydrogen HI is a complementary approach to optical surveys for the study of the Large Scale Structures, in particular for measuring the BAO (Baryon Acoustic
Oscillation) scale up to redshifts z < 3, and therefore constraining dark energy parameters. We propose a novel method to map the HI mass distribution in three dimensions in radio, without detecting or identifying individual compact sources. This method would require an instrument with a large instantaneous bandwidth (> 100 MHz) and high sensitivity, while a rather modest angular resolution (~ 10 arcmin) should be sufficient. These requirements can be met by a dense interferometric array or a phased array (FPA) in the focal plane of a large primary reflector, representing a total collecting area of a few thousand square meters with few hundred simultaneous beams covering a 20 to 100 square degrees field of view. We describe the development and qualification of an electronic and data processing system for digital radio interferometry and beam forming suitable for such instruments with several hundred receiver elements.
A simple method to compute numerically the lowest eigenmodes of the Laplacian in compact orientable hyperbolic spaces of dimension 3 is presented. It is applied to the Thurston manifold, the Weber-Seifert manifold, and to the spaces whose fundamental domain is a regular icosahedron.
Large Scale Structures (LSS) in the universe can be traced using the neutral atomic hydrogen HI through its 21cm emission. Such a 3D matter distribution map can be used to test the Cosmological model and to constrain the Dark Energy properties or its
equation of state. A novel approach, called intensity mapping can be used to map the HI distribution, using radio interferometers with large instantaneous field of view and waveband. In this paper, we study the sensitivity of different radio interferometer configurations, or multi-beam instruments for the observation of large scale structures and BAO oscillations in 21cm and we discuss the problem of foreground removal. For each configuration, we determine instrument response by computing the (u,v) or Fourier angular frequency plane coverage using visibilities. The (u,v) plane response is the noise power spectrum, hence the instrument sensitivity for LSS P(k) measurement. We describe also a simple foreground subtraction method to separate LSS 21 cm signal from the foreground due to the galactic synchrotron and radio sources emission. We have computed the noise power spectrum for different instrument configuration as well as the extracted LSS power spectrum, after separation of 21cm-LSS signal from the foregrounds. We have also obtained the uncertainties on the Dark Energy parameters for an optimized 21 cm BAO survey. We show that a radio instrument with few hundred simultaneous beams and a collecting area of ~10000 m^2 will be able to detect BAO signal at redshift z ~ 1 and will be competitive with optical surveys.
We compute the effects induced by the use of small CMB maps on the measurement of the $cl{l}$ coefficients of the angular power spectrum and show that small systematic effects have to be taken into account. We also compute numerically the cosmic vari
ance and covariance of the $cl{l}$ spectrum for various spherical cap like maps. Comparisons with simulations are presented. The calculations are done using the standard method based on the spherical harmonic transform or using the temperature angular correlation spectrum.
