PUMA is a proposal for an ultra-wideband, low-resolution and transit interferometric radio telescope operating at $200-1100,mathrm{MHz}$. Its design is driven by six science goals which span three science themes: the physics of dark energy (measuring the expansion history and growth of the universe up to $z=6$), the physics of inflation (constraining primordial non-Gaussianity and primordial features) and the transient radio sky (detecting one million fast radio bursts and following up SKA-discovered pulsars). We propose two array configurations composed of hexagonally close-packed 6m dish arrangements with 50% fill factor. The initial 5,000 element petite array is scientifically compelling, and can act as a demonstrator and a stepping stone to the full 32,000 element full array. Viewed as a 21cm intensity mapping telescope, the program has the noise equivalent of a traditional spectroscopic galaxy survey comprised of 0.6 and 2.5 billion galaxies at a comoving wavenumber of $k=0.5,hmathrm{Mpc}^{-1}$ spanning the redshift range $z = 0.3 - 6$ for the petite and full configurations, respectively. At redshifts beyond $z=2$, the 21cm technique is a uniquely powerful way of mapping the universe, while the low-redshift range will allow for numerous cross-correlations with existing and upcoming surveys. This program is enabled by the development of ultra-wideband radio feeds, cost-effective dish construction methods, commodity radio-frequency electronics driven by the telecommunication industry and the emergence of sufficient computing power to facilitate real-time signal processing that exploits the full potential of massive radio arrays. The project has an estimated construction cost of 55 and 330 million FY19 USD for the petite and full array configurations. Including R&D, design, operations and science analysis, the cost rises to 125 and 600 million FY19 USD, respectively.
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