Abstract
Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation—a priori, one of the more immediate corollaries of detecting primordial tensor modes—one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza–Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.
Highlights
1 E.g. via Cavendish type experiments where we have precise knowledge of two masses, or equivalently in principle through gravitational scattering experiments
We discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales
As detailed in Appendix B, every massive species contributes to lowering the scale at which strong gravity effects become important, one has to distinguish between species that universally couple directly to the matter energymomentum tensor at tree level [such as massive Kaluza– Klein (KK) gravitons, non-minimally coupled scalars, and U (1) gauge fields] from ordinary four-dimensional fields that couple at one loop, in terms of their effects on the strength of gravity as one crosses the threshold set by the mass M of the species, but are still far below the scale M∗∗
Summary
Massive particles are interesting for the threshold effects they impart once we start to probe energies above their mass M, i.e. at distances below M−1. This can be understood via a simple thought experiment [5]: consider scattering a test particle off a very heavy point mass. The strength of gravity is increased by this effective ‘vacuum polarization’ far enough away from the threshold induced by a particle of mass M j that couples to gravity, i.e. as we probe increasingly shorter distances x M−j 1. One can quantitatively understand this effective strengthening through the computation of the graviton propagator with loops of the massive fields contributing to the graviton self-energy insertions. Consider the correction to the graviton propagator induced by loops of various particles—suppressing all index structure, we find that the leading correction will have the form
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