Inflationary spacetimes are not past-complete

@article{Borde2001InflationarySA,
  title={Inflationary spacetimes are not past-complete},
  author={A. H. de Borde and Alan Harvey Guth and Alexander Vilenkin},
  journal={Physical Review Letters},
  year={2001}
}
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… 

Figures from this paper

Maximal extensions and singularities in inflationary spacetimes

Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature

Cyclic Inflation

We present an inflationary model that is geodesically complete and does not suffer from the transplanckian problem. In most inflationary models, massless (conformal) scalar field fluctuations in a

String Theory and Primordial Cosmology

String cosmology aims at providing a reliable description of the very early Universe in the regime where standard-model physics is no longer appropriate, and where we can safely apply the basic

Stable bounce and inflation in non-local higher derivative cosmology

One of the greatest problems of primordial inflation is that the inflationary space-time is past-incomplete. This is mainly because Einstein's GR suffers from a space-like Big Bang singularity. It

Nonsingular inflationary universe from polymer matter

We consider a polymer quantization of a free massless scalar field in a homogenous and isotropic classical cosmological spacetime. This quantization method assumes that field translations are

Probability of inflation in loop quantum cosmology

We discuss how initial conditions for cosmological evolution can be defined in Loop Quantum Cosmology with massive scalar field and how the presence of the bounce influences the probability of

Inflation without a beginning: A Null boundary proposal

We develop our recent suggestion that inflation may be made past eternal, so that there is no initial cosmological singularity or "beginning of time". Inflation with multiple vacua generically

Defocusing of null rays in infinite derivative gravity

Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this
...

References

SHOWING 1-10 OF 18 REFERENCES

The very early Universe

In these lectures we dwell upon the cosmological corner-stones of the Very Early Universe (VEU) theory: Parametric Amplification Effect (PAE) responsible for the generation of Primordial Cosmological

have proposed a model in which this new physics is in fact also inflation, but inflation in the time-reversed sense

    Phys

    • Rev. D65, 126003
    • 2002

    the of O, as seen in the rest frame of the comoving test particles. Furthermore, the frequently used definitionH = (1/3)u µ ;µ is obtained from ours by averaging over all directions

      Phys

      • Rev. D23, 347
      • 1981

      We do not require that this congruence be defined throughout spacetime, just along O. Away from O the members of this congruence may cross or focus, but such behavior does not affect our argument

        Phys

        • Lett. B175, 395
        • 1986

        Phys

        • Rev. Lett. 72, 3305 (1994); in Relativistic Cosmology: The Proceedings of the Eighth Yukawa Symposium, edited by M. Sasaki (Universal Academy Press, Tokyo, 1994), p 111; Int. J. Mod. Phys. D5, 813 (1996); A. Borde, Phys. Rev. D50, 3392
        • 1994

        Phys

        • Rev. D57, 2230
        • 1998

        Phys

        • Lett. B108, 389
        • 1982