Evidence for the multiverse in the standard model and beyond

Abstract

In any theory it is unnatural if the observed values of parameters lie very close to special values that determine the existence of complex structures necessary for observers. A naturalness probability, P , is introduced to numerically evaluate the degree of unnaturalness. If P is very small in all known theories, corresponding to a high degree of fine-tuning, then there is an observer naturalness problem. In addition to the well-known case of the cosmological constant, we argue that nuclear stability and electroweak symmetry breaking represent significant observer naturalness problems. The naturalness probability associated with nuclear stability depends on the theory of flavor, but for all known theories is conservatively estimated as P nuc < ∼ (10 −3 -10 −2 ), and for simple theories of electroweak symmetry breaking P EWSB < ∼ (10 −2 -10 −1 ). This pattern of unnaturalness in three different arenas, cosmology, nuclear physics, and electroweak symmetry breaking, provides evidence for the multiverse, since each problem may be easily solved by environmental selection. In the nuclear case the problem is largely solved even if the multiverse distribution for the relevant parameters is relatively flat. With somewhat strongly varying distributions, it is possible to understand both the close proximity to neutron stability and the values of m e and m d − m u in terms of the electromagnetic mass difference between the proton and neutron, δ EM ≃ 1 ± 0.5 MeV. It is reasonable that multiverse distributions are strong functions of Lagrangian parameters, since they depend not only on the landscape of vacua, but also on the population mechanism, "integrating out" other parameters, and on a density of observers factor. In any theory with mass scale M that is the origin of electroweak symmetry breaking, strongly varying multiverse distributions typically lead either to a little hierarchy, v/M ≈ (10 −2 -10 −1 ), or to a large hierarchy, v ≪ M . In certain multiverses, where electroweak symmetry breaking occurs only if M is below some critical value, we find that a little hierarchy develops with the value of v 2 /M 2 suppressed by an extra loop factor, as well as by the strength of the distribution. Since the correct theory of electroweak symmetry breaking is unknown, our estimate for P EWSB is theoretical. The LHC will lead to a much more robust determination of P EWSB , and, depending on which theory is indicated by the data, the observer naturalness problem of electroweak symmetry breaking may be removed or strengthened. For each of the three arenas, the discovery of a natural theory would eliminate the evidence for the multiverse; but in the absence of such a theory, the multiverse provides a provisional understanding of the data.

A finely-predicted Higgs boson mass from a finely-tuned weak scale

“…The two fine-tuning problems of SM + GR would have a common solution, with other solutions either unknown or disproved. Through nuclear stability, the multiverse accounts for the values of the up quark, down quark and electron masses remarkably well [51,52]. Furthermore, the multiverse may also explain the cosmological mystery of why the time scales of structure formation, galaxy cooling and vacuum domination do not differ by many orders of magnitude, but are all comparable to the present age of the universe [53].…”

Non-perturbative reheating and Nnaturalness

“…Unlike the oscillating scenario, the inflaton only passes through the important region in field space once, so there is no Bose enhancement and a relatively small fraction of its energy is transferred. Despite this if the inflaton potential is sufficiently flat the remainder of its energy is kinetic and redshifts away as 1/a (t) 6 , where a (t) is the scale factor of the universe. Meanwhile the inflaton decay products are assumed to be part of an interacting sector and form a relativistic plasma.…”

“…Away from the adiabatic limit the number density of particles produced is comparable to that from a quartic interaction with the same value of g, given by eq.(2.14). 6 The production rate is not always exponentially suppressed in the limitṁ/m 2 1. For example, an inflaton coupling 17) corresponding to reflection off a negative quadratic potential in the region t < 0, can be calculated analytically, again assuming a constant inflaton speed (expressions for the coefficients are given in e.g.…”

“…This happens provided sufficient time passes between particle production and the visible sector temperature dropping to ∼ MeV for the inflaton kinetic energy to redshift enough. Taking the energy density in the visible sector immediately after reheating to be E 0 , the energy densities in the inflaton and visible sectors at later times are 1 2φ 2 0 (a 0 /a (t)) 6 and E 0 (a 0 /a (t)) 4 respectively, where a 0 is the scale factor of the universe at reheating andφ 0 is the inflaton speed at this time (previously just calledφ). Therefore these two sectors have the same energy density when…”

“…First, it is unclear how essential a low EW scale is for life if the Standard Model (SM) Lagrangian parameters are allowed to vary. Even if the light fermion masses are fixed by requiring nuclei and atoms, the distribution of Yukawa couplings must still be assumed [6][7][8]. Second, a small EW scale could have been realised through technicolour [9], but instead the landscape must prefer a fine tuned Higgs.…”