A.A. Starobinsky

Landau Institute for Theoretical Physics, Moscow, Russia

Abstract

If the Lorentz invariance is broken (or "deformed") at some large
energy close to the Planckian one, so that the dispersion law for
elementary particles E(p) differs from the standard one, expansion
of the Universe may result in gravitational creation of pairs of
particles and antiparticles with a very high energy. The expansion
of the Universe (both at present time and in the early Universe)
gradually redshifts momenta of all Fourier modes of a quantum field
and transports them from the trans-Planckian region of very high
momenta to the sub-Planckian region where the standard particle
interpretation is valid. Then, if the WKB condition is violated
somewhere in the trans-Planckian region, the field modes enter the
sub-Planckian region in a non-vacuum state containing equal number
of particles and antiparticles.

This effect, if exists at all, can be discovered or limited by
cosmological observations. The most restrictive upper limit follows
from the number of ultra-high energy cosmic rays created at the
present time. In turn, their total amount can be shown to be bounded
by the observed cosmic diffuse gamma-ray background. This limit rules
out the possibility to detect signatures of such short distance
effects by studying temperature anisotropies of the cosmic microwave
background. On the other hand, a remarkable possibility that some part
of observed ultra-high energy cosmic rays originates from new
trans-Planckian physics remains open.