Solar System-scale interferometry on fast radio bursts could measure cosmic distances with sub-percent precision (2210.07159v3)

Abstract: The light from a source at a distance d will arrive at detectors separated by 100 AU at times that differ by as much as 120 (d/100 Mpc)^{-1} nanoseconds because of the curvature of the wavefront. At gigahertz frequencies, the arrival time difference can be determined to better than a nanosecond with interferometry. If the space-time positions of the detectors are known to a few centimeters, comparable to the accuracy to which very long baseline interferometry baselines and global navigation satellite systems (GNSS) geolocations are constrained, nanosecond timing would allow competitive cosmological constraints. We show that a four-detector constellation at Solar radii of >10 AU could measure distances to individual sources with sub-percent precision and, hence, cosmological parameters such as the Hubble constant to this precision. The precision increases quadratically with baseline length. FRBs are the only known bright extragalactic radio source that are sufficiently point-like. Galactic scattering limits the timing precision at <3 GHz, whereas at higher frequencies the precision is set by removing dispersion. Furthermore, for baselines greater than 100 AU, Shapiro time delays limit the precision, but their effect can be cleaned with two additional detectors. Accelerations that result in ~1 cm uncertainty in detector positions (from variations in the Sun's irradiance, dust collisions and gaseous drag) could be corrected for with weekly GNSS-like trilaterations. Gravitational accelerations from asteroids occur over longer timescales, and so a setup with a precise accelerometer and calibrating the detector positions off of distant FRBs may also be sufficient. The proposed interferometer would also resolve the radio emission region of Galactic pulsars, constrain the mass distribution in the outer Solar System, and reach interesting sensitivities to ~0.01-100 micro-Hz gravitational waves.

• The paper introduces a method using solar system-scale FRB interferometry to measure cosmic distances with sub-percent precision.
• It details leveraging arrival-time differences and nanosecond timing at gigahertz frequencies to extract geometric distances.
• The approach offers a compelling alternative to standard candles, enabling direct measurements of key cosmological parameters.

Measuring Cosmological Distances Using Solar System-Scale Interferometry on Fast Radio Bursts

The paper "Solar System-scale interferometry on fast radio bursts could measure cosmic distances with sub-percent precision" by Kyle Boone and Matthew McQuinn introduces an innovative approach to obtaining precise cosmological distance measurements. The authors propose using interferometry on fast radio bursts (FRBs) with a baseline separation of solar-system scale to extract geometrical distances to cosmological sources with exceptional precision. This method leverages the unique properties of FRBs to address existing challenges in cosmological measurements, offering potential insights into fundamental parameters of the universe.

Core Concept and Methodology

The central idea is to utilize the arrival-time differences of FRB wavefronts at detectors separated by vast distances within the solar system. The wavefront from an extragalactic source has a slight curvature when it arrives, and the time delay caused by this curvature can be measured using high-precision interferometry. The paper argues that a constellation of four detectors, each at a solar radius of approximately 10 AU or more, could measure these time delays to individual FRBs, enabling geometric distance determinations with sub-percent accuracy. The precision depends significantly on the baseline length and the accuracy in determining the detectors' positions, which needs to be within a few centimeters.

The method identifies gigahertz frequencies as optimal since they allow nanosecond timing precision. However, FRBs must be point-like sources at these frequencies to be suitable targets. The authors propose that repeating FRBs are ideal due to their known positions and repetitive nature, which allows for extended observation periods.

Technical Considerations and Limitations

Several factors affect the efficacy of this technique. Scattering: Signal scattering in the Galactic interstellar medium could degrade timing precision at frequencies below 3 GHz. Dispersion: Differential dispersion introduces temporal offsets that must be corrected. The paper shows that higher frequency observations and a wide bandwidth are essential for precision despite the inherent dispersive challenges. Gravitational Time Delays: Shapiro delays from stars and large-scale structures within the universe contribute additional timing errors but present a unique quadrupole signature that can be mitigated with additional detectors in the constellation.

Numerical Insights and Implications

The authors provide calculations illustrating how detector baselines of at least several AU are necessary for conducting cosmologically meaningful measurements. They conclude that such a system, operating optimally around 5 GHz with adequate baseline lengths, can effectively achieve sub-percent distance measurements to FRBs positioned within several hundred megaparsecs. These constraints translate to similar-level precision in determining cosmological parameters through the distance-redshift relation models.

The potential quality of such measurements offers a compelling alternative and complement to existing methods like Type Ia supernovae standard candles and gravitational wave sirens but does not rely on any of their underlying assumptions.

Speculative Future Developments

This research opens up pathways for several future developments in physics and astronomy. Not only does it promise advancements in cosmology, such as providing direct geometric measurements for the Hubble constant, but it also presents applications in:

1. Solar System Science: Measuring the spatial distribution of mass in the outer solar system.
2. Astrophysics of Pulsars: Offering geometric distance determination and constraints on pulsar models.
3. Interferometry Techniques: Enhancing precision in various astronomical measurements.

Moreover, the success of deploying such a Solar System-scale interferometric array would mark an ambitious leap in observational capabilities, contributing significantly to our understanding of dark energy and cosmic acceleration.

Conclusion

The proposal by Boone and McQuinn presents an innovative approach with the potential to redefine distance measurements in cosmology. While there are substantial technical challenges, the theoretical framework underscores its feasibility with clear strategies to mitigate anticipated systematic issues. The concept, bridging radio astronomy and cosmology, lays intriguing groundwork for further exploration and potential paradigm-shifting insights into the universe's dynamics. The compelling implications for cosmological research and auxiliary sciences signify a promising frontier in the quest for deeper cosmic understanding.