Renormalization-group running of the cosmological constant and the fate of the universe

For a generic quantum field theory we study the role played by the renormalization-group (RG) running of the cosmological constant (CC) in determining the ultimate fate of the universe. We consider the running of the CC of generic origin (the vacuum energy of quantum fields and the potential energy of classical fields), with the RG scale proportional to the (total energy density$\rm{)^{1/4}}$ as the most obvious identification. Starting from the present-era values for cosmological parameters we demonstrate how the running can easily provide a negative cosmological constant, thereby changing the fate of the universe, at the same time rendering compatibility with critical string theory. We also briefly discuss the recent past in our scenario.Comment: 9 pages, 7 figures, revtex4; version to appear in PR

A new scheme for the running coupling constant in gauge theories using Wilson loops

We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. We perform a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step-scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations.Comment: 30pages, figs and comments added,reference added(v3

New Physics and the Landau Pole

In scalar field theories the Landau pole is an ultraviolet singularity in the running coupling constant that indicates a mass scale at which the theory breaks down and new physics must intervene. However, new physics at the pole will in general affect the running of the low energy coupling constant, which will in turn affect the location of the pole and the related upper limit (``triviality'' bound) on the low energy coupling constant. If the new physics is strongly coupled to the scalar fields these effects can be significant even though they are power suppressed. We explore the possible range of such effects by deriving the one loop renormalization group equations for an effective scalar field theory with a dimension 6 operator representing the low energy effects of the new physics. As an independent check we also consider a renormalizable model of the high-scale physics constructed so that its low energy limit coincides with the effective theory.Comment: 26 pages, 5 figure

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field $\phi$ played in Brans-Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with $\phi$; and almost all of the fundamental components of our universe can be unified into the dynamical equation for $\phi$. As a generalization of Brans-Dicke theory, we propose a new gravity theory with a complex scalar field $\phi$ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.Comment: 6 page

High Energy Quark-Antiquark Elastic scattering with Mesonic Exchange

We studies the high energy elastic scattering of quark anti-quark with an exchange of a mesonic state in the $t$ channel with $-t/\Lambda^{2} \gg 1$. Both the normalization factor and the Regge trajectory can be calculated in PQCD in cases of fixed (non-running) and running coupling constant. The dependence of the Regge trajectory on the coupling constant is highly non-linear and the trajectory is of order of $0.2$ in the interesting physical range.Comment: 29 page

Asymptotic Freedom and Bound States in Hamiltonian Dynamics

We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by introducing similarity factors and the running coupling constant. This approximation loses accuracy for the small widths on the order of the bound state energy and it is improved by using the expansion in powers of the running coupling constant. The coupling constant for small widths is order 1. The small width effective hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized and the exact bound state energy is obtained with accuracy of the order of 10% using the first three terms in the expansion. We briefly describe options for improving the accuracy.Comment: plain latex file, 15 pages, 6 latex figures 1 page each, 1 tabl

Running of the Spectral index in Deformed Matter Bounce Scenarios with Hubble-rate-dependent Dark Energy

As a deformed matter bounce scenario with a dark energy component we propose a deformed one with running vacuum model (RVM) in which the dark energy density is written as a power series of $H^2$ and $\dot H$ with a constant equation of state parameter same as the cosmological constant. Our results in analytical and numerical point of views show that in some cases same as LCDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index is obtained which is not compatible with inflationary paradigm where it predicts a small negative value for $\alpha_s$. However, by extending the power series up to $H^4$, $\rho_{\Lambda}=n_0+n_2 H^2+n_4 H^4$, and estimating a set of consistent parameters, we obtain the spectral index $n_s$, a small negative value of running $\alpha_s$ and tensor to scalar ratio $r$, which these reval a degeneracy between deformed matter bounce scenario with RVM-DE and inflationary cosmology.Comment: 27 pages, 6 figure