Ultraviolet completion of gravity and testable signatures

7 problems

• Does 4D quantum gravity with matter have an ultraviolet fixed point?

  Contested

  Asymptotic safety proposes that gravity stops getting stronger at short distances because the theory approaches a scale-invariant point, called a fixed point. The evidence comes from approximate calculations whose reliability is debated.

• Does causal dynamical triangulations have a continuum limit reproducing 4D gravity?

  Contested

  One approach builds spacetime from tiny four-dimensional building blocks glued with a fixed direction of time and sums over all gluings on a computer. A genuine theory needs a point where the blocks can be made infinitely small, a continuous phase transition, and whether one exists is unsettled.

• Does projectable Horava gravity reduce to general relativity at long distances?

  Open

  Horava gravity treats space and time differently at very short distances, which makes it calculable to arbitrarily high energies. Whether at everyday distances it turns back into Einstein's theory, despite an extra gravitational mode it carries, is open.

• Is four-dimensional $N=8$ supergravity ultraviolet finite to all loops?

  Open

  The most symmetric extension of Einstein gravity, $N=8$ supergravity, has unexpectedly mild short-distance behavior in explicit calculations. If it has no divergences at any order, it would be a finite perturbative quantum theory of gravity in four dimensions.

• Is the photon dispersion relation modified at linear order in $E/E_{\mathrm{P}}$?

  Open

  Some quantum gravity ideas make high-energy photons travel at slightly different speeds from low-energy ones. Gamma-ray bursts billions of light years away test this and already require any such linear effect to be weaker than Planck-scale estimates.

• Do spin foam models reproduce curved solutions of Einstein's equations?

  Contested

  Loop quantum gravity's sum over spacetime histories, called a spin foam, should reduce to Einstein's theory for large geometries. Calculations suggest that the standard model of this sum favors flat geometries, which would leave out the curvature that is gravity.

• Which theory completes general relativity at the Planck scale?

  Open

  String theory, asymptotic safety, loop quantum gravity and others each propose what happens at the shortest distances. None has been confirmed, and most make no prediction testable at reachable energies.