How long before the end of inflation were observable perturbations produced

By Andrew R. Liddle, Samuel Leach. 2003

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We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ model which reduces the uncertainties in that case and favors a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $\mathrm{aH}.$ Finally, we discuss the impact of nonstandard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/dbf34123417af83a8161489a5217d455c90e9d1a

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Citations in the corpus

The landscape of QCD axion models (2020, methodology): “Adiabatic curvature perturbations generated during inflation show a nearly scale-invariant dimensionless power spectrum of primordial curvature perturbations with amplitude ∆R(k0), with a mild dependence on the co-moving wavenumber k which is parametrised by a scalar spectral index nS around an arbi”
The clustering of galaxies in the SDSS‐III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large‐scale two‐point correlation function (2012, methodology): “60 (Dodelson & Hui 2003; Liddle & Leach 2003b), corresponding to ǫ2 & 0.017 (indicated by the dotted line in Fig.”
The first WIMPy halos (2005, unknown): “7.2.1. m 2 φ 2 chaotic inflation In this model ǫ1 = ǫ2/2 = ǫ3/2 = 1/(2N + 1) (see e.g. Ref. [44]) and we take N = 55 [ 45 ].”
Primordial black holes from α-attractors (2018, background): “05 is related to the post-inflationary cosmic expansion rate [85] via the expression”
Inflation and the scale dependent spectral index: prospects and strategies (2010, background): “Assuming a matter dominated phase followed by thermalization (w̃ = 0) one can derive the result quoted by [20, 43]”
Primordial black hole dark matter from single field inflation (2017, background): “001 becomes equal to aH during inflation and the end of the process [61, 62].”
Dynamically induced Planck scale and inflation (2015, background): “In figure 2 we plot the inflaton mass as a function of ξS for both negative-field and positive-field inflation (the two regions are partially overlapping) for 50 < N < 60 [83–85].”
Scalaron from R2-gravity as a heavy field (2017, methodology): “This method was developed in [91], and has some recent developments [100–104].”
Reheating predictions in single field inflation (2015, background): “J C A P 0 4 ( 2 0 1 5 ) 0 4 7 a relation between inflationary and reheating parameters [75]”
Planck2018 results (2018, background): “…to second order, which can be expressed in terms of the parameters of the inflationary model and the number of e-folds to the end of inflation, N∗ (Liddle & Leach 2003; Martin & Ringeval 2010), given by (PCI13) N∗ ' 67 − ln ( k∗ a0H0 ) + 1 4 ln V2∗M4pl ρend + 1 − 3wint 12(1 + wint) ln ( ρth…”
FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2008, unknown): “We take N = 50 and 60 as a reasonable range (Liddle & Leach 2003).”
Mechanisms for primordial black hole production in string theory (2018, methodology): “Parametrizing our ignorance about the postinflationary Universe by an average equation of state wp and the energy density at the time of reheating ρrh, we can quantify this uncertainty by using the matching equation [49, 77, 78],”