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tokens: corresponding to the 1σ uncertainties of log A and γ at z ∼ 6 from the [C ii ] power spectrum in the fiducial survey. The L18, deL14d, deL14 z , O17, and V15 relations are assumed for generating the input power spectrum. In each panel, the regions with dark (light) colour refer to using the full power spectrum (shot noise only). We use δν 0 = 1.0 GHz to translate the [C ii ] luminosity into the flux per beam; see the top x -axis. We also mark with vertical lines the detection limits by HST ( M UV ∼ −16.5, dashed–dotted), ALMA (∼10 8 L ⊙ , dashed), and the 5σ level of the underlying IM survey (solid), respectively. Figure 10. The 1σ constraint contours of the log A– γ parameters from the full power spectrum for the five relations. The ‘ + ’ symbols mark the input values. Ideally, this is the key result that we can expect from our fiducial-like IM experiment combined with the existing upper limits on the LF coming from pointed observations. We warn that these results depend on the underlying assumption of a single power-law form for –SFR relation, , and shown in Fig. 2 . At present, this remains only an educated guess for high-redshift galaxies, as also hinted by the more complex shape found by state-of-the-art simulations in P15 , and more recently by Pallottini et al. ( 2019 ). ALMA surveys covering a larger area and/or reaching to fainter fluxes, plus a more accurate determination of the galaxy SFR, would be of fundamental importance for this issue. 4.2 Survey strategies We finally investigate how to optimize a survey for a [C ii ] IM experiment. Generally, given the observation time and bandwidth, when , , a narrow and deep field has larger S/N. However, when , , wider field has larger S/N. For some applications, though, a highest S/N is not necessarily the first priority indicator for optimizing surveys; instead, a wide survey is preferred in order to sample long-wavelength k -modes carrying cosmological information and break parameter degeneracy, even at the price of lowering the S/N. We discuss this issue in the context of recovering a fundamental physical quantity as the [C ii ] luminosity density, 10 the first moment of the LF We compute the expected relative variance of the recovered [C ii ] luminosity density, , as a function of t obs for four different surveys with different telescope diameter D , survey area Ω survey , or bandwidth. These cases allow us to compare the survey performances in terms of small and large diameters (S1 versus S3), narrow and wide field (S1 versus S2), low and high angular resolution (S1 versus S3), and number of bolometers and higher noise level (S4). We use the L18 relation to make the input signal. The details of each survey are listed in Table 3 . The results (in units of percentage) are plotted in Fig. 11 , where the relative variances obtained from the shot noise only (power spectrum at k max ) and from the full power spectrum are shown separately by thin and thick lines, respectively. Figure 11.