The recent COVID-19 pandemic follows in its early stages an almost exponential expansion, with the number of cases as a function of time reasonably well fit by N(t) ∝ eαt, in many countries. We ...analyze the rate α in different countries, starting in each country from a threshold of 30 total cases and fitting for the following 12 days, capturing thus the early exponential growth in a rather homogeneous way. We look for a link between the rate α and the average temperature T of each country, in the month of the initial epidemic growth. We analyze a base set of 42 countries, which developed the epidemic at an earlier stage, an intermediate set of 88 countries and an extended set of 125 countries, which developed the epidemic more recently. Fitting with a linear behavior α(T), we find increasing evidence in the three datasets for a slower spread at high T, at 99.66% C.L., 99.86% C.L. and 99.99995% C.L. (p-value 5⋅10−7, or 5σ detection) in the base, intermediate and extended dataset, respectively. The doubling time at 25 °C is 40% ~ 50% longer than at 5 °C. Moreover we analyzed the possible existence of a bias: poor countries, typically located in warm regions, might have less intense testing. By excluding countries below a given GDP per capita from the dataset, we find that this affects our conclusions only slightly and only for the extended dataset. The significance always remains high, with a p-value of about 10−3 - 10−4 or less. Our findings give hope that, for northern hemisphere countries, the growth rate should significantly decrease as a result of both warmer weather and lockdown policies. In general, policy measures should be taken to prevent a second wave, such as safe ventilation in public buildings, social distancing, use of masks, testing and tracking policies, before the arrival of the next cold season.
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•We analyze the initial spread of COVID cases for each country with an exponential fit.•We use 12 days of data after 30 cases, for 3 datasets: with 42, 88 and 125 countries.•COVID-19 spread is slower at high Temperature in all datasets with high significance.•We use GDP per capita (GDPPC) as an indicator of testing capability.
A
bstract
We propose a new regime of minimal QCD axion dark matter that lies between the pre- and post-inflationary scenarios, such that the Peccei-Quinn (PQ) symmetry is restored only on ...sufficiently large spatial scales. This leads to a novel cosmological evolution, in which strings and domain walls re-enter the horizon and annihilate later than in the ordinary post-inflationary regime, possibly even after the QCD crossover. Such dynamics can occur if the PQ symmetry is restored by inflationary fluctuations, i.e. the Hubble parameter during inflation
H
I
is larger than the PQ breaking scale
f
a
, but it is not thermally restored afterwards. Solving the Fokker-Planck equation, we estimate the number of inflationary e-folds required for the PQ symmetry to be, on average, restored. Moreover, we show that, in the large parts of parameter space where the radial mode is displaced from the minimum by de Sitter fluctuations, a string network forms due to the radial mode oscillating over the top of its potential after inflation. In both cases we identify order one ranges in
H
I
/
f
a
and in the quartic coupling
λ
of the PQ potential that lead to the late-string dynamics. In this regime the cosmological dark matter abundance can be reproduced for axion decay constants as low as the astrophysical constraint 𝒪(10
8
) GeV, corresponding to axion masses up to 10
−2
eV, and with miniclusters with masses as large as 𝒪(10)
M
⊙
.
Upper bounds on the CP asymmetry relevant for leptogenesis are reexamined and found weaker than in previous literature, both for hierarchical and for quasi-degenerate right-handed neutrinos. ...Successful leptogenesis implies the usual lower bound on right-handed neutrino masses, and an upper bound on left-handed neutrino masses (which we obtain to be 0.15 eV at 3
σ) only if right-handed neutrinos are assumed to be much more hierarchical than left-handed neutrinos. Otherwise both bounds can be considerably relaxed. The constraint on light neutrino masses varies assuming different interpretations of why neutrinos should be quasi-degenerate. With conservative assumptions, we find that a mild quasi-degeneracy allows neutrinos heavier than an eV compatibly with leptogenesis.
We also extend computations of thermal leptogenesis to an alternative model of neutrino mass mediated by fermion triplets which was never considered so far for leptogenesis. Leptogenesis can be successful despite the effect of gauge interactions, resulting in only slightly stronger constraints on neutrino masses.
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