Cosmology
Within cosmology I have worked on several different topics. An early project explored how well supernova observations can constrain the dark energy equation of state [1]. Several later papers concern gravitational radiation from the early universe; in 2008 we showed that symmetry-breaking phase transitions can give rise to a scale-invariant spectrum of gravitational radiation by virtue of cosmic expansion [2]. A scalar field can be correlated on horizon-sized scales, but as the horizon grows uncorrelated regions come into contact. The ordering dynamics can generate gravitational radiation, and in the case of the nonlinear sigma model we studied, we find the spectrum is scale-invariant. This is an important result because observation of a scale-invariant spectrum of gravitational radiation was widely considered to constitute `smoking gun' evidence that a primordial inflationary epoch had occurred, and our findings showed that non-inflationary mechanisms can produce the same spectrum. This work led to [3],[4], and my involvement in the CMBPol Mission Concept Study [5].
In 2010 we showed that oscillating cosmic strings can emit particles and gravitational radiation via the Aharonov-Bohm mechanism, a purely quantum mechanical effect. This work was published in Physical Review D [6] and was featured as a research highlight in Nature Physics in 2010. The detection of gravitational radiation by the LIGO collaboration in 2016 ushers in a new era of gravitational wave astronomy, in which such signatures of cosmic strings might be observable. Recently I have been interested in the 'chameleon' model of dark energy and other scalar-tensor theories of gravity. In one analysis [7] we show that the baryonic Jeans mass is different in chameleon models compared to general relativity, and this could have observable astrophysical consequences. In 2012 we showed that the chameleon scalar field is mathematically analogous to the electrostatic potential familiar from introductory physics [8]. Under certain circumstances, including those relevant to terrestrial experiments, the chameleon obeys Laplace's equation therefore constitutes an 'electrostatic analogy'. Among other things, the analogy shows that for the same reason lightning rods are more effective with pointed ends rather than rounded ones, experimenters could use highly elongated objects to improve their prospects for detecting these models of dark energy in table-top atom interferometry and torsion pendulum experiments.
In the last few years I have worked with Hamilton students on several cosmology projects. We recently showed [9] that the symmetron scalar field also obeys an electrostatic analogy and offers several interesting contrasts from Newtonian gravity. In another project [10], we derive several important results from popular theories with extra spatial dimensions using mathematics that is accessible at the undergraduate level. We show that a simple scalar field closely mirrors the behavior of the more complicated gravitational field in some models with extra spatial dimensions. In another paper we present an account of the binary black hole merger observed by LIGO last year using simple concepts from Newtonian physics. We show that back-of-the-envelope calculations give a remarkably good estimate of some parameters of the merger, for example the masses of the black holes involved.
[1] Krauss, Lawrence M., Katherine Jones-Smith, and Dragan Huterer. "Dark energy, a cosmological constant, and type Ia supernovae." New Journal of Physics 9.5 (2007): 141. PDF available here.
[2] Jones-Smith, Katherine, Lawrence M. Krauss, and Harsh Mathur. "Nearly scale invariant spectrum of gravitational radiation from global phase transitions." Physical review letters 100.13 (2008): 131302. PDF available here.
[3] Krauss, Lawrence M., Jones-Smith, K., Mathur, H., & Dent, J. "Probing the gravitational wave signature from cosmic phase transitions at different scales." Physical Review D 82.4 (2010): 044001. PDF available here.
[4] Jones-Smith, Katherine, Lawrence M. Krauss, and Mathur, H. "Implications of Broken Symmetry for Superhorizon Conservation
Theorems in Cosmology". PDF available here.
[5] Baumann, Daniel, et al. "Probing inflation with CMB polarization." AIP Conference Proceedings. Vol. 1141. No. 1. AIP, 2009. PDF available here.
[6] Jones-Smith, Katherine, Harsh Mathur, and Tanmay Vachaspati. "Aharonov-Bohm Radiation." Physical Review D 81.4 (2010): 043503. PDF available here.
[7] Jones-Smith, Katherine. "Chameleon effects on small scale structure and the baryonic Jeans mass." Physical Review D 85.4 (2012): 043502. PDF available here.
[8] Jones-Smith, Katherine, and Francesc Ferrer. "Detecting Chameleon Dark Energy via an Electrostatic Analogy." Physical review letters 108.22 (2012): 221101. PDF available here.
[9] Ogden, Lillie, Katherine Brown, Harsh Mathur and Kevin Rovelli. "An Electrostatic Analogy for Symmetron Gravity." Physical Review D 96, (2017): 124029. PDF available here.
[10] Brown, Katherine, Harsh Mathur, and Michael Verostek. "Exploring extra dimensions with scalar waves." Accepted at American Journal of Physics. PDF available here.
[11] Mathur, Harsh, Katherine Brown, and Ashton Lowenstein. "An analysis of the LIGO discovery based on introductory physics." American Journal of Physics 85.9 (2017): 676-682. PDF available here.