Renormalization-group running of the cosmological constant and its implication for the Higgs boson mass in the standard model

Abstract

The renormalization-group equation for the zero-point energies associated with vacuum fluctuations of massive fields from the Standard Model is examined. Our main observation is that at any scale the running is necessarily dominated by the heaviest degrees of freedom, in clear contradistinction with the Appelquist & Carazzone decoupling theorem. Such an enhanced running would represent a disaster for cosmology, unless a fine-tuned relation among the masses of heavy particles is imposed. In this way, we obtain m H ≃ 550 GeV for the Higgs mass, a value safely within the unitarity bound, but far above the more stringent triviality bound for the case when the validity of the Standard Model is pushed up to the grand unification (or Planck) scale.There are now increasing indications, based on observations on rich clusters of galaxies [1], searches for Type Ia Supernovae [2] and measurements of the cosmic microwave background anisotropy [3], that the today's universe is undergoing a phase of accelerated expansion. This is usually attributed to the presence of a cosmological constant. Although the simplest explanation is a time-independent (i.e. "true") cosmological constant Λ, many scenarios have also been discussed involving a dynamical cosmological constant Λ(t). There have recently been a number of suggestions regarding the nature of the latter, the most popular candidate being known under *

Solving the main cosmological puzzles with a generalized time varying vacuum energy

“…Note that the above functional form includes the effect of the quantum field theory (for m = 0) (Shapiro & Solá 2000;Babić et al 2002;Grande et al 2006;Solá 2008) and it also extents recent studies (see for example Ray et al 2007;Carneiro et al 2008;Sil & Som 2008;Basilakos 2009). In this context we can easily prove that the cosmological constant is a particular solution of the general vacuum, that (γ, m) = (0, 0).…”

“…Attempts to provide a theoretical explanation for the Λ(t) have also been presented in the literature (see Shapiro & Solá 2000;Babić et al 2002;Grande et al 2006;Solá 2008, and references therein). There it was found that a time dependent vacuum could arise from the renormalization group (RG) in quantum field theory.…”

“…2, the above phenomenological functional form (see Eq. (38)) is motivated theoretically by the renormalization group (RG) in the quantum field theory (Shapiro & Solá 2000;Babić et al 2002;Solá 2008). Moreover, recent studies (see Grande et al 2006;and Grande et al 2009) find that this solution alleviates the cosmic coincidence problem (see Sect.…”

“Expansion” around the vacuum: how far can we go fromΛ?

“…In this case, Λ is treated as a dynamical quantity, whereas its constant EOS, w = −1, is preserved. This includes, among others, models based on renormalization group running Λ (Shapiro & Sola 2000Babic et al 2002;Shapiro et al 2005; and vacuum decay (Özer & Taha 1986;Bertolami 1986;Cunha et al 2002;Alcaniz & Lima 2005). Other DDE models, in which the potential energy density associated with a dynamical scalar field (φ) dominates the dynamics of the low-redshift Universe, have also been extensively discussed in the current literature (see, e.g., Ratra & Peebles 1988;Wetterich 1988;Caldwell et al 1998).…”

Modified dispersion relations from the renormalization group of gravity

“…The β-functions for gravity have also been discussed in different approaches (see e.g. [19,20,21,22,23,24]). The solutions to these ordinary differential equations are…”