It is no argument against any project to say `The idea’s fantastic!’ Most of the things that have happened in the last fifty years have been fantastic, and it is only by assuming that they will continue to be so that we have any hope of anticipating the future.

Arthur C. Clarke

We lack methods to measure cosmic distances (and thereby constrain cosmological parameters) to better than a percent.   Type 1a supernova constraints are unlikely to significantly improve, and we will soon have measured the BAO scale from much of the available cosmic volume at low z.   Gravitational wave standard sirens with potential third generation instruments like the Einstein telescope are very interesting, although estimates for the rates of events with electromagnetic counterparts vary widely and many estimates for sensitivity still find percent-level constraints similar to the 1a.  Furthermore, current methods disagree with less direct methods like the CMB, at the 10% level a 4-5 sigma discrepancy!  It can be hard to resolve such tensions without significantly improved constraints.

 I am aware of only one idea that can significantly improve constraints, one I was involved with in collaboration with Kyle Boone who was a postdoc at UW  -- to time the arrival time of FRBs and detect the curvature of the wavefront!  One can time 1-10 GHz signals to much better than a nanosecond  -- this is regularly done with VLBI--, and it turns out that the curvature effect is 10 nanoseconds for detectors separated by 10 AU.     In addition, Galactic scattering, dispersion, and gravitational time delays all seem to be at a level that is managable.

This signal can be isolated with four detectors, for a similar reason  that four satellites are needed for GPS geolocations (there are four parameters that need to be constrained that specify the geometry and timing, just like your four space-time positions).  So, four radio dishes in the outer Solar System would be able to do potentially much higher precision cosmology than has been done.  We forecast that once the baselines become longer than 10AU, cosmological interesting constraints are possible to sources in the Hubble flow at 100s of megaparsecs. 

The other side of the coin is you need to measure the distances between the detectors. Here it turns out that you can just borrow how we constrain distances with GPS -- the satellites send signals between each other.  Amazingly several dishes separated by 100 AU only need to broadcast 10 Watt signals to measure the distance in a minute to 0.1 ns!  They would need to do this every week because of various stochastic sources of acceleration.  Several meter dishes when combined with a large ground-based radio dishes also have the the sensitivity to detect many of repeating FRBs that have been detected.

Okay, when it's all said and done, you can measure the distance to fractional accuracy given by the panels on the left.  See the paper for more details.  Even just 25 AU baselines can constrain the distance to a burst at 200Mpc to a percent at 8 GHz. (The errors are larger at 4 GHz because of Galactic scattering, but we are likely being pessimistic here.)   For context, the median distance/redshift of the SHOES supernova sample is 200Mpc/0.04.  Longer baselines than 25AU can do even more ridiculous things!   

An electromagnetic wave (typically with frequencies in the radio) is delayed as it travels through the intervening plasma.  The measurement of this delay (often called the dispersion measure) towards pulsars has been used to map the Galactic electron distribution.  However, until 2013 (or maybe 2008), there were no indications that there was a class of extragalactic sources to which dispersion could be ascertained.  In 2013 fast radio bursts were (re)discovered, and  I wrote a paper on how cosmological dispersion could be used to learn about the distribution of cosmic gas at low redshifts.  This paper is discussed in more detail on this page.

Soon after I published this paper, in a study led by Chris Hirata, we showed that dispersion measure -- and hence electron column -- cannot be measured to time-steady sources of incoherent radiation.  This paper was in response to a total of three papers in 2013 proposing schemes that were claimed to be able to do this.  Too bad!!!

I've continued working on this, including being part of the ASKAP team that made the now famous 'Maquart relation' plot on the left in 2020.

With Eric Switzer, we studied a new extragalactic observable that has the potential to teach us about Big Bang Nucleosynthesis and helium reionization, the 8.7 GHz hyperfine absorption line of 3He+ (which is much more observable than one would naively guess, but still quite hard...possibly detectable with an Arecibo or FAST dishes...and it should be with the SKA).  Aside from HI 21cm, this is the only other radio line from a primordial element that can in the foreseeable future be detected from the IGM.

While not radio, Eric and I also wrote a paper about the 584 A UV line of neutral helium, which we thought would be detectable with HST and would constrain helium reionization and UV backgrounds.  Unfortunately, it turned out to be challenging owing to a malfunctioning near UV spectrograph.  Alas...  The constellation is that I'm likely the record holder for the most astro papers  on helium :)