Luke Butcher

Theoretical Physicist

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Research

Quantum Bias Cosmology

The universe is expanding at an accelerating rate, ostensibly due to dark energy at every point in space. However, the origin and nature of this energy is unknown, and the standard dark energy model - the cosmological constant \(\Lambda\) - provides no fundamental explanation for the incredibly tiny value \(\Lambda \sim 10^{-120}\) needed to fit observations.

I have recently developed a new cosmological framework, Quantum Bias Cosmology, in which the cosmic accleration occurs spontaneously, driven by an overlooked quantum phenomenon, without the need for dark energy or modified gravity. Here's a very quick overview:

Gravitational Lensing

To tackle the controversy that had arisen over the effect of a cosmological constant \(\Lambda\) on the power of a gravitational lens, I conducted a comprehensive analysis of the deflection of light by \(\Lambda\ne 0\) black hole. Proving that the lensing effect was in precise agreement with the standard \(\Lambda=0\) result, I re-established the recieved wisdom that "Lambda does not lens".

lensed distance diagram
Constructing lensed angular diameter distances in the Schwarzschild-de Sitter spacetime.

Gravitational Waves

There is no question that gravitational waves carry energy, but it has been notoriously difficult to describe where in spacetime this energy resides. This problem was so widely believed to be unsolvable that the prevailing wisdom (expressed most famously in the textbook Gravitation) held that trying to localise gravitational energy was "looking for the right answer to the wrong question". During my PhD I sought a right question to ask, and was lead to a remarkable new description of the energy, momentum and angular-momentum carried by weak gravitational fields: \begin{align}\kappa \bar{\tau}_{\mu\nu}&= \tfrac{1}{4} \partial_{\mu}h_{\alpha\beta} \partial_{\mu}\bar{h}^{\alpha\beta},\\ \kappa s^\alpha_{\phantom{\alpha}\mu\nu} &= 2 \bar{h}_{\beta[\nu}\partial^{[\alpha} \bar{h}_{\mu]}{}^{\beta]}.\end{align} In the above formulae, \(h_{\mu\nu}\equiv g_{\mu\nu}- \eta_{\mu\nu}\) is the gravitational field, and \(\tau_{\mu\nu}\) and \(s^\alpha{}_{\mu\nu}\) are tensors that quantify the energy, momentum, and spin of \(h_{\mu\nu}\) at every point in space.

These tensors (i) account for the energy, momentum and angular-momentum exchanged between gravity and matter, (ii) can be derived by symmetry arguments, and (iii) describe gravitational self-interaction, so that gravitational energy curves space just like the energy of matter.

gravitational energy density
Moreover, \(\tau_{\mu\nu}\) and \(s^\alpha{}_{\mu\nu}\) display a variety of desirable properties that have not been seen in previous attempts to localise gravitational energy. In particular, with \(h_{\mu\nu}\) in transverse-traceless gauge, \(\tau_{\mu\nu}\) always describes positive gravitational energy-density that never flows faster than light. This means we always arrive at a physically meaningful and intuitive local desription of gravitational energy; e.g. the figure on the left, displaying gravitational energy flowing away from two orbiting bodies of equal mass.

Interested readers should take a look at the introductory paper; this was followed by a treatment of spin, and further theoretical developments. This work has also been used to produce some hypnotic animations of gravitational energy flowing away from compact sources. v

Wormholes

Our present understanding of gravity allows spacetime to be curved into strange shapes, at least in principle. One particularly interesting prospect is for space to be warped into a tube-like shortcut called a wormhole, which could permit faster-than-light communications and time-travel. Unfortunately, wormholes require exotic matter with negative energy to survive — without it, the throat will collapse before anything can cross from one side to the other.

I have been examining whether the negative energy needed by the wormhole can in fact be generated by the wormhole itself. Can the curvature of a wormhole cause a quantum field to occupy a state with negative energy, and will this energy be enough to keep the wormhole open? wormhole My first paper on this subject focussed on the Casimir energy \(\rho^\mathrm{Casimir}\) produced by wormholes which are very long and thin (\(L\gg a\)). Although this negative energy was not enough to completely stabilise the wormhole, preliminary calculations suggested that it may keep the wormhole open just long enough for a small amount of light to squeeze through. This work received some coverage in the popular press. For a slightly more detailed explanation of this research, see my summary for a general audience. A more technical overview is available in the form of a poster.

It's not all good news for science-fiction fans, however. My more recent paper proves that one particular idea for a stable wormhole (supported by a non-minimally coupled classical scalar field) cannot work.