Eric Carlson

Quantum 2
Eric D. Carlson
Associate Professor of Physics


My research while at Wake Forest has covered a variety of topics. My earliest research, representing my background of particle physics, involved astroparticle physics. The idea behind this research is that the universe has natural laboratories, such as type II supernovas and the Sun, which allow one to study and place limits on particle physics under conditions not achievable in the laboratory.

I have also done some work in collaboration with G. Cook that involves Numerical General Relativity. Although Einstein's General Theory of Relativity is believed to be the correct theory of gravity, applying this theory in strong gravitational fields, such as the merger of neutron stars or black holes, is very difficult. This is partly due to general covariance, where arbitrary coordinates can be used to evolve the equations of motion. This can lead to instabilities, and handling these instabilities was an area I have done research on (Kidder, Scheel, Teukolsky, Carlson, and Cook).

Most of my current research, in conjunction with P. Anderson, involves Semi-Classical Gravity. The biggest fundamental problem facing physics is the incompatibility of Einstein's Theory of General Relativity with quantum mechanics. Normally, we use quantum mechanics to describe the behavior of matter on the smallest scale, and then treat that behavior as classical matter when we try to incorporate gravit. The goal of Semi-Classical Gravity is to go one step beyond this.

Although it is impossible (at present) to predict what the quantum effect of strong curvature on space-time might be, it is possible to determine the effect of strong curvature on various matter fields. Furthermore, if the number of matter fields is large compared to the number of new fields coming from quantum gravity, it is to be expected that the quantum effects will be dominated by the effects of the matter fields. If we treat space-time as fixed, then we can determine how quantum fluctuations in matter fields can cause changes in the local stress-energy-momentum tensor. Quantum mechanically, these will have unpredictable random fluctuations. As an approximation, we can take a quantum mechanical average of these fluctuations. This averaging is the essence of semi-classical gravity. Matter fields are treated as quantum mechanical in a curved space-time background. The equations of G.R. are solved classically, with the classical stress-energy-momentum tensor replaced with the quantum mechanical average value.

For simplicity, semi-classical gravity is normally calculated using non-interacting scalar fields. However, there is only one real fundamental scalar field, the Higgs boson. The vast majority of matter fields are spin-half fields, or fermions. Much of my research has been working on what happens when fermions, rather than scalar fields are involved.

My current research is studying whether any effects from the early universe can survive past inflation. Inflation is a hypothesized early stage in the expansion of the universe when the universe grew by an enormous amount before slowing down and ultimately leading to the universe we observe. Inflation can explain what would otherwise seem surprising features of the modern Universe, such as the fact that it is uniform on very large scales (homogeneity) and it has very little curvature (flatness) The standard wisdom is that any signature of what came before inflation would be "inflated away," and therefore undetectable. We hypothesize that there may have been a radiation-dominated era that preceded inflation. Our current (incomplete) research indicates that if the amount of inflation that occurred was just the right amount to account for homogeneity and flatness, then it is quite possible that a signature of the radiation-dominated universe could be detectable. It would result in a suppression of density fluctuations in the cosmic microwave background radiation. Indeed, such a suppression at the largest angular scales has already been noted.

Some of my most recent research involves alternate theories of gravity, specifically f(R,T) gravity. In f(R,T) gravity, the Lagrangian term responsible for gravity, which normally is just proportional to the scalar curvature R, is replaced by an arbitrary function of the curvature and the trace of the stress-energy tensor T. In research with T. Ordines, we demonstrated that by studying the effects of such a theory one could place strong limits on some of the terms in such a function. In research with S. Fisher, we demonstrated that in certain cases, the contribution of some terms in f(R,T) (especially those that don't depend on R) should be incorporated into the matter Lagrangian, and in fact do not belong in the gravity portion of the Lagrangian at all.


  • "Argument for the radiation-dominated behavior of matter fields in the preinflationary era", with Taylor M. Ordines, Phys. Rev. D106 (2022) 103537.
  • "Nuclear limits on nonminimally coupled gravity", with Sarah B. Fisher, Phys. Rev. D105 (2022) 024020.
  • "Semiclassical predictions regarding a pre-inflationary era and its effects on the power spectrum", with Paul R. Anderson, Taylor M. Ordines, and Bradley Hicks, Phs. Rev. D102 (2020) 063528.
  • "Response to 'Comment on "Reexamining f(R,T) Gravity"'", with Sarah B. Fisher, Phys. Rev D101 (2020) 108502.
  • "Reexamining f(R,T) Gravity", with Sarah B. Fisher, Phys. Rev. D100 (2019) 064059X.
  • "Limits on f(R,T) Gravity From Earth's Atmosphere", with Taylor M. Ordines, Phys. Rev. D99 (2019) 104052.
  • "Future singularities if the universe underwent Starobinsky inflation in the past", with Paul R. Anderson, John R. Einhorn, Bradley Hicks, and Andrew J. Lundeed, Phys. Rev. D95 (2017) 044012.
  • "Semiclassical gravity in the far field limit of stars, black holes, and wormholes", with Paul R. Anderson, Alessandro Fabbri, Serena Fagnocchi, William H. Hirsch, and Sarah A. Klyap, Phys Rev. D82 (2010) 12407.
  • "Stress-energy tensor for massless spin-1/2 in static black hole spacetimes", with William H. Hirsch, Benedikt Obermayer, Paul R. Anderson, and Peter B. Groves, Phys. Rev. Lett. 91 (2003) 051301.
  • "Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime", with Peter B. Groves, and Paul R. Anderson, Phys. Rev. D66 (2002) 124017.
  • "Black hole evolution by spectral methods", with Lawrence E. Kidder, Mark A.Scheel, Saul A. Teukolsky, and Greg B. Cook, Phys. Rev. D62 (2000) 084032.
  • "SN1987A Limits on Light Pseudoscalars", with J. Brockway and G.G. Raffelt, Phys. Lett. B383 (1996) 439.
  • "Pseudoscalar Conversion and X-Rays from the Sun", with Li-Sheng Tsen, Phys.Lett. B365 (1996) 193.

for questions or comments, contact
Back to Top