Inflationary Spacetimes Are Incomplete in Past Directions

Abstract

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating--or just expanding sufficiently fast--must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.

Probabilities in the inflationary multiverse

“…It is well known that, although inflating spacetimes are generically eternal to the future, all past-directed geodesics in such spacetimes are incomplete, except perhaps a set of measure zero (see [24] and references therein). This indicates that the inflating region of spacetime has a boundary in the past, and some new physics (other than inflation) is necessary to determine the initial conditions at that boundary.…”

Inflationary universe in loop quantum cosmology

“…This accelerated period of expansion also generates superhorizon fluctuations and thus predicts an almost scale-invariant density perturbation power spectrum, which has received strong observational support from the measurement of the temperature fluctuation in the cosmic microwave background (CMB) radiation [3,4,5]. Conceptually, however, the inflationary scenario is incomplete due to the existence of the big bang singularity [6]. Einstein's classical theory of general relativity (GR) breaks down near such a singularity since quantum effects are expected to be important at very high energies in the early universe.…”

Emergent cosmology revisited

“…These pertain both to the nature of the inflaton field and to the state of the universe prior to the commencement of inflation. Indeed, as originally pointed out in [2], inflation (within a general relativistic setting) could not have been past eternal. This might be seen to imply one of several alternative possibilities including the following: E m e r g e n t U n i v e r s e C o n t r a c t i n g U n i v e r s e Einstein Static Universe Figure 1.…”