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tokens: H 0 has been proposed previously (Zibin et al. 2007 ). We take the additional step of propagating the uncertainties on T CMB to H 0 and present example noise curves to produce such a measurement, including a detailed treatment of foregrounds. Studies of the time evolution of the CMB angular power spectrum and forecasts for observations have also been conducted (Lange et al. 2007 ; Zibin et al. 2007 ; Moss et al. 2008 ). In particular, Lange Page ( 2007 ) found that the change in the power spectrum could in principle be detected over the course of a century. 2. Method 2.1. Hubble Cooling of <italic>T</italic><sub>CMB</sub> The monopole temperature of the CMB, hereafter denoted , decreases in time with the scale factor asThe time derivative of T is then . This can be evaluated to first order, taking as an example and T 0 = 2.725 K, 6 6 The forecast for depends on the true value of the current CMB temperature T 0 but the change in is small given the current sub-mK constraints on T 0 from COBE/FIRAS (Fixsen et al. 1996 , 2011 ). Therefore the temperature of the CMB decreases by 2 nK over a 10 yr period. One could thus in principle measure the real-time cooling of the CMB due to the expansion of space and from this infer the value of the Hubble constant. 2.2. Requirements to Measure <italic>H</italic><sub>0</sub> The simplest method to measure the Hubble constant from the monopole temperature would amount to fitting for the slope of T as it decreases in time. The model is linear in time with a slope of ,We have in mind a future version of the COBE/FIRAS experiment, where the data can be reduced in discrete time intervals to evaluate the monopole temperature of the CMB repeatedly over the mission duration. For example, the mission could take data continuously for 10 yr, potentially mapping out large portions of the sky, and the monopole CMB temperature would be inferred from these data every year. Given the expected level of cooling, we can then propagate uncertainties from T ( t ) to H 0 and determine what sensitivity to T ( t ) is required to measure H 0 with a given precision. We make some simplifying assumptions that will allow us to analytically calculate the uncertainty on H 0 using an ordinary least-squares estimator. First, we assume that T ( t ) is measured with (foreground-marginalized) uncertainty σ T in discrete uniform time intervals with spacing Δ t , such that t = k Δ t , where k = 1,2..., N . The mission duration is thus t total = N Δ t with N data points. Second, the uncertainties on T ( t ) are time-independent, parameter-independent, and Gaussian uncorrelated. 7 7 This is not entirely true as the CMB photon noise is one of the dominant noise sources and therefore the noise depends on T CMB . However, the change in the CMB photon noise over these timescales is negligible. The foreground-marginalized uncertainty σ T can then be written in terms of an effective sensitivity s T of the experiment such that,where s T is understood as