Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-09-06
Gen.Rel.Grav. 34 (2002) 1461-1481
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages RevTex4, 4 figures. Changes to the abstract and the section on Realistic Estimates
Scientific paper
We show that in the case of positively-curved Friedmann-Lema\^{\i}tre universes $(k=+1)$, an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of $\Omega_{\Lambda}$, $\Omega_{\Lambda} \gg 1$, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a $k=+1$ frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.
Dunsby Peter
Ellis George F. R.
McEwan P.
Stoeger William
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