Ilya L. Shapiro

On the possible running of the cosmological ``constant{''}

Abstract Despite the many outstanding cosmological observations leading to a strong evidence for a non-vanishing cosmological constant (CC) term Λ in the gravitational field equations, the theoretical status of this quantity seems to be lagging well behind the observational successes. It thus seems timely to revisit some fundamental aspects of the CC term in Quantum Field Theory (QFT). We emphasize that, in curved space–time, nothing a priori prevents this term from potentially having a mild running behavior associated to quantum effects. Remarkably, this could be the very origin of the dynamical nature of the Dark Energy, in contrast to many other popular options considered in the literature. In discussing this possibility, we also address some recent criticisms concerning the possibility of such running. Our conclusion is that, while there is no comprehensive proof of the CC running, there is no proof of the non-running either. The problem can be solved only through a deeper understanding of the vacuum contributions of massive quantum fields on a curved space–time background. We suggest that such investigations are at the heart of one of the most important endeavors of fundamental theoretical cosmology in the years to come.

Scaling behavior of the cosmological constant and the possible existence of new forces and new light degrees of freedom

Abstract A large value of the cosmological constant (CC) is induced in the Standard Model (SM) of Elementary Particle Physics because of Spontaneous Symmetry Breaking. To provide a small value of the observable CC one has to introduce the vacuum term which cancels the induced one at some point in the very far infrared cosmic scale. Starting from this point we investigate whether the cancellation is preserved at different energy scales. We find that the running of the Higgs mass, couplings and the vacuum term inevitably result in a scaling dependence of the observable value. As a consequence one meets a nonzero CC at an energy scale comparable to the typical electron neutrino mass suggested by some experiments, and the order of magnitude of this constant is roughly the one derived from recent supernovae observations. However the sign of it is negative – opposite to what is suggested by these observations. This discrepancy may be a hint of the existence of an extra very light scalar, perhaps a Cosmon-like dilaton, which should essentially decouple from the SM Lagrangian, but that it nevertheless could mediate new macroscopic forces in the submillimeter range.

Running G and Lambda at low energies from physics at M(X): Possible cosmological and astrophysical implications

The renormalization group (RG) approach to cosmology is an efficient method for studying the possible evolution of the cosmological parameters from the point of view of quantum field theory (QFT) in curved space–time. In this work we continue our previous investigations of the RG method based on potential low-energy effects induced from physics at very high energy scales . In the present instance we assume that both the Newton constant, G, and the cosmological term, Λ, can be functions of a scale parameter μ. It turns out that G(μ) evolves according to a logarithmic law which may lead to asymptotic freedom of gravity, similar to the gauge coupling in QCD. At the same time Λ(μ) evolves quadratically with μ. We study the consistency and cosmological consequences of these laws when . Furthermore, we propose to extend this method to the astrophysical domain after identifying the local RG scale at the galactic level. It turns out that Keplers third law of celestial mechanics receives quantum corrections that may help to explain the flat rotation curves of the galaxies without introducing the dark matter hypothesis. The origin of these effects (cosmological and astrophysical) could be linked, in our framework, to physics at GeV.

Variable cosmological constant as a Planck scale effect

Abstract We construct a semiclassical Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological model assuming a running cosmological constant (CC). It turns out that the CC becomes variable at arbitrarily low energies due to the remnant quantum effects of the heaviest particles, e.g., the Planck scale physics. These effects are universal in the sense that they lead to a low-energy structure common to a large class of high-energy theories. Remarkably, the uncertainty concerning the unknown high-energy dynamics is accumulated into a single parameter ν , such that the model has an essential predictive power. Future Type Ia supernovae experiments (like SNAP) can verify whether this framework is correct. For the flat FLRW case and a moderate value ν ∼10 −2 , we predict an increase of 10–20% in the value of Ω Λ at redshifts z =1–1.5 perfectly reachable by SNAP.

Renormalization group and decoupling in curved space

It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for important cosmological applications like the graceful exit from the inflation and low-energy quantum dynamics of the cosmological constant. We investigate, using both covariant and non-covariant methods of calculations and mass-dependent renormalization scheme, the vacuum quantum effects of a massive scalar field in curved space-time. In the higher derivative sector we arrive at the explicit form of decoupling and obtain the β-functions in both UV and IR regimes as the limits of general expressions. For the cosmological and Newton constants the corresponding β-functions are not accessible in the perturbative regime and in particular the form of decoupling remains unclear.

Higher derivative quantum gravity with Gauss-Bonnet term

Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the

Conformal quantum gravity with the Gauss-Bonnet term

4\ensuremath{-}ϵ

Superrenormalizable quantum gravity with complex ghosts

renormalization group for this theory, an approach which proved fruitful in

On the stability of the anomaly-induced inflation

2\ensuremath{-}ϵ

Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions

models. A consistent formulation in dimension