Abstract
Over 30 years ago, Barrow & Tipler proposed the principle according to which the action integrated over the entire 4-manifold describing the universe should be finite. Here we explore the cosmological consequences of a related criterion, namely that semi-classical transition amplitudes from the early universe up to current field values should be well defined. On a classical level, our criterion is weaker than the Barrow-Tipler principle, but it has the advantage of being sensitive to quantum effects. We find significant consequences for early universe models, in particular: eternal inflation and strictly cyclic universes are ruled out. Within general relativity, the first phase of evolution cannot be inflationary, and it can be ekpyrotic only if the scalar field potential is trustworthy over an infinite field range. Quadratic gravity eliminates all non-accelerating backgrounds near a putative big bang (thus imposing favourable initial conditions for inflation), while the expected infinite series of higher-curvature quantum corrections eliminates Lorentzian big bang spacetimes altogether. The scenarios that work best with the principle of finite amplitudes are the no-boundary proposal, which gives finite amplitudes in all dynamical theories that we have studied, and string-inspired loitering phases. We also comment on the relationship of our proposal to the swampland conjectures.
Highlights
Cosmology has made enormous progress in the last century, with our understanding of the universe evolving from a static, infinite universe to a dynamical one in which space and time themselves have a history
Progress in physics has repeatedly been associated with getting rid of infinities: in this case, the infinite arena of never changing space and time, which had led to puzzles regarding the gravitational stability of the universe and to Olbers’ paradox
Physics abounds with examples where infinities were removed, including the appreciation of causality when the speed of light was found to be finite, the quantum resolution of the classically diverging attraction between an electron and the atomic nucleus at short distances, or the quantum taming of the ultraviolet catastrophe
Summary
Cosmology has made enormous progress in the last century, with our understanding of the universe evolving from a static, infinite universe to a dynamical one in which space and time themselves have a history. When talking about the early history of the universe, we must specify field values that correspond to a possible “initial” configuration, such as a zero spatial volume of the universe, or perhaps a zero expansion rate when thinking about the so-called emergent or loitering scenarios In some cases, such configurations will effectively be in the infinite past, while in other cases the beginning will have occurred a finite time ago. With that caveat in mind, let us point out that a principle of finite amplitudes can be very powerful: a specific example in the context of quadratic gravity was recently discussed in [3], where it was concluded that only accelerating spacetimes are allowed near the big bang (we will improve the analysis of this case in this work). N ≥ 3 on Lorentzian FLRW bckg all n included See [10]: nonsingular anisotropic universe k-essence theory NEC, e.g., ghost condensate (beyond-)Horndeski Loitering phase in EH action
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