Weak lensing with 21 cm intensity mapping at z ∼ 2–3

ABSTRACT We study how 21 cm intensity mapping can be used to measure gravitational lensingover a wide range of redshift. This can extend weak lensing measurements to higherredshifts than are accessible with conventional galaxy surveys. We construct a con-vergence estimator taking into account the discreteness of galaxies and calculate theexpected noise level as a function of redshift and telescope parameters. At z ˘ 2 3 we nd that a telescope array with a collecting area ˘ 0:2km 2 spread over a region withdiameter ˘ 2km would be sucient to measure the convergence power spectrum tohigh accuracy for multipoles between 10 and 1,000. We show that these measurementscan be used to constrain interacting dark energy models.Key words: cosmology: theory | large-scale structure of the universe | gravita-tional lensing: weak | dark energy 1 INTRODUCTIONWe now live in an era of precision cosmology. Almost allof the information used to achieve this precision has comefrom redshifts below z˘1:5 or from the Cosmic MicrowaveBackground (CMB) at z˘1000. The vast regions betweenthese redshifts have been probed only sparsely. Given ourignorance of what is causing the apparent acceleration ofthe Universe, it is important that we explore the evolutionof expansion and structure formation over the widest pos-sible range of redshift. It is possible that dark energy, or amodi cation to general relativity, came into play at higherredshift than the standard cosmological constant model pre-dicts (Copeland, Sami & Tsujikawa 1006; Clifton et al.2012). Early dark energy models are an example of this. Inrecent years, several 21 cm surveys have been proposed tostudy the epoch of reionization (EoR) which could providesome cosmological information at z˘8 12. The gravita-tional lensing of the CMB also provides some information onthe intermediate redshifts, but the signal-to-noise is low. Theclustering of quasars and Ly- absorption lines in quasarspectra can be measured at high redshift, but here bias andmodeling uncertainties are serious problems. In this paperwe address the prospects for measuring gravitational lens-ing at redshifts after reionization, but before those probedby galaxy surveys in the visible bands.In Zahn & Zaldarriaga (2005) and Metcalf & White(2009) it was shown that if the EoR is at redshift z˘8 orlater, a large radio telescope such as SKA (Square KilometerArray) could measure the lensing convergence power spec-trum and constrain the standard cosmological parameters.The authors extended the Fourier-space quadratic estima-tor technique, which was rst developed by (Hu 2001) forCMB lensing observations to three dimensional observables,i.e. the 21 cm intensity eld I(;z). These studies did notconsider 21 cm observations from redshifts after reionizationwhen the average HI density in the universe is much smaller.It has also been proposed that lensing could be mea-sured at lower redshifts by counting the uctuations in thenumber density of detected 21 cm objects on the sky asa measure of the magni cation (Zhang & Pen 2005, 2006;Zhang & Yang 2011). The signal-to-noise is greatly reducedin this case because of the low number density of objectsand the intrinsic clustering of them.Lensing surveys in the visible are limited in redshift bythe number density of detected galaxies with measurableellipticities. This is strongly dependent on the depth of thesurvey, but any proposed survey that will cover a signi cantfraction of the sky will be quite sparse in sources above z˘1:5. Here we show that 21 cm observations can be used toextend weak lensing measurements to higher redshifts thanthis, but still well below the redshift of reionization or theCMB.21 cm intensity mapping is a technique that has beenproposed for measuring the distribution of HI gas beforeand during reionization (see Furlanetto et al. (2006) for areview) and measuring the BAO at redshifts of order unity(Chang et al. 2008, 2010; Seo et al. 2010; Masui et al. 2010;Ansari et al. 2012; Battye et al. 2012; Chen 2012; Pober etal. 2013). In this technique, no attempt is made to detectindividual objects. Instead the 21 cm emission is treated as acontinuous three dimensional eld. The angular resolution ofthe telescope need not be high enough to resolve individualgalaxies which makes observations at high redshift possiblewith a reasonably sized telescope. Foregrounds are expected