What does inflation really predict?

By Max Tegmark. 2004

209 citations recorded by the source corpus.

If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory ‘landscape’, inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Ωtot), dark energy (ρΛ, w etc), the primordial density fluctuations (Q, ns, d ns/d ln k etc) and primordial gravitational waves (r, nt etc). We compute this multivariate probability distribution for various classes of single-field slow-roll models, exploring its dependence on the characteristic inflationary energy scales, the shape of the potential V and the choice of measure underlying the calculation. We find that unless the characteristic scale Δϕ on which V varies happens to be near the Planck scale, the only aspect of V that matters observationally is the statistical distribution of its peaks and troughs. For all energy scales and plausible measures considered, we obtain the predictions , w = −1 and ρΛ in the observed ballpark but uncomfortably high. The high energy limit predicts , , and , consistent with observational data and indistinguishable from eternal inflation. The low energy limit predicts five parameters but favours larger Q and redder ns than observed. We discuss the coolness problem, the smoothness problem and the pothole paradox, which severely limit the viable class of models and measures. Predictions insensitive to pre-inflationary conditions can arise either from eternal inflation attractor behaviour or from anthropic selection effects probing merely a tiny non-special part of the initial distribution. We argue that these two mechanisms are severely challenged by the coolness problem and the smoothness problem, respectively. Our findings bode well for detecting an inflationary gravitational wave signature with future CMB polarization experiments, with the arguably best-motivated single-field models favouring the detectable level .

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a1c6d0aa138ba6b1ad05e75c57ec0aeeb4eec555

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Citations in the corpus

Predictive Landscapes and New Physics at a TeV (2005, background): “Inflation in particular seems ideally suited to use the landscape–as a number of authors have argued, inflation may not be natural but nonetheless occur “accidentally” somewhere on the landscape [54, 55, 56].”
Inflationary Constraints on Type IIA String Theory (2007, background): “Specifically, by assuming that there exist one or more scalar fields that undergo slow rolling in the early Universe in a potential energy function of just the right shape, one can explain these large-scale properties and predict the numerical values of as many as eight cosmological parameters, many”
Eternal inflation and its implications (2007, background): “For many years Vilenkin and his collaborators [26, 38] were almost the only cosmologists working on this issue, but now the field is growing rapidly [39].”
Inflationary paradigm after Planck 2013 (2013, background): “Given the well-known attractor behavior of slow-roll inflation [8,37], quantitative predictions for observable quantities such as Ωk , ns , r, and α = dns/d ln k are essentially independent of anything that preceded the final phase of inflation.”
Sinks in the landscape, Boltzmann brains and the cosmological constant problem (2006, background): “(3) If one uses the standard probability distribution P for predicting the part of the universe where we should live, one may conclude that the universe surrounding us must be very young (the youngness paradox [75]) and unacceptably hot [16].”
Inflation and string cosmology (2001, methodology): “I should mention, in particular, the discovery of the topological eternal inflation [46], calculation of the fractal dimension of the universe [43, 47], and development of various methods describing statistical/probabilistic aspects of the self-reproducing universe, see [43, 48, 49, 50] and referenc”
Axion cosmology and the energy scale of inflation (2008, background): “This problem is not alleviated by anthropic considerations [12].”
Boltzmann brains and the scale-factor cutoff measure of the multiverse (2008, background): “In particular, if one uses the proper-time cutoff measure [11–15], one encounters the “youngness paradox,” predicting that humans should have evolved at a very early cosmic time, when the conditions for life were rather hostile [28].”
Observational consequences of a landscape (2005, background): “Tegmark [16] modelled the landscape and its predictions.”
Inflationary Cosmology after Planck 2013 (2014, background): “Later it was found that one of these two probability measures introduced in [58] leads to paradoxical conclusions, which are associated with the so-called “youngness problem” [165, 166].”