Federico R. Urban

The cosmological constant from the QCD Veneziano ghost

Abstract We suggest that the solution to the cosmological vacuum energy puzzle is linked to the infrared sector of the effective theory of gravity interacting with standard model fields, with QCD fields specifically. We work in the framework of low energy quantum gravity as an effective field theory. In particular, we compute the vacuum energy in terms of QCD parameters and the Hubble constant H such that the vacuum energy is ϵ vac ∼ H ⋅ m q 〈 q ¯ q 〉 / m η ′ ∼ ( 3.6 ⋅ 10 − 3 eV ) 4 , which is amazingly close to the observed value today. The QCD ghost (responsible for the solution of the U ( 1 ) A problem) plays a crucial role in the computation of the vacuum energy, because the ghosts properties at very large but finite distances slightly deviate (as ∼ H / Λ QCD ) from their infinite volume Minkowski values. Another important prediction of this framework states that the vacuum energy owes its existence to the asymmetry of the cosmos. Indeed, this effect is a direct consequence of the embedding of our Universe on a non-trivial manifold such as a torus with (slightly) different linear sizes. Such a violation of cosmological isotropy is apparently indeed supported by WMAP, and will be confirmed (or ruled out) by future PLANCK data.

Cosmological constant from the ghost: A toy model

We suggest that the solution to the cosmological vacuum energy puzzle is linked to the infrared sector of the effective theory of gravity interacting with standard model fields. We propose a specific solvable two dimensional model where our proposal can be explicitly tested. We analyze the 2d Schwinger model on a 2-torus and in curved 2d space, mostly exploiting the properties of its topological susceptibility, its links with the nontrivial topology or deviations from spacetime flatness, and its relations to the real 4d world. The Kogut-Susskind ghost (which is a direct analogue of the Veneziano ghost in 4d) on a 2-torus and in curved 2d space plays a crucial role in the computation of the vacuum energy. The departure from Minkowski flatness, which is defined as the cosmological constant in our framework, is found to scale as 1/L, where L is the linear size of the torus. Therefore, in spite of the fact that the physical sector of 2d QED is represented by a single massive scalar particle, the deviation from Minkowski space is linear in L rather than exponentially suppressed as one could naievely expect.

Resonant magnetic fields from inflation

We propose a novel scenario to generate primordial magnetic fields during inflation induced by an oscillating coupling of the electromagnetic field to the inflaton. This resonant mechanism has two key advantages over previous proposals. First of all, it generates a narrow band of magnetic fields at any required wavelength, thereby allaying the usual problem of a strongly blue spectrum and its associated backreaction. Secondly, it avoids the need for a strong coupling as the coupling is oscillating rather than growing or decaying exponentially. Despite these major advantages, we find that the backreaction is still far too large during inflation if the generated magnetic fields are required to have a strength of (10−15 Gauss) today on observationally interesting scales. We provide a more general no-go argument, proving that this problem will apply to any model in which the magnetic fields are generated on subhorizon scales and freeze after horizon crossing.

On inflating magnetic fields, and the backreactions thereof

We investigate in more depth the issue of backreaction in models that attempt at generating cosmological magnetic fields at inflation. By choosing different, physically motivated, parametrisations, we are able to isolate the heart of the problem, namely the existence, alongside the wanted magnetic field, of its electric counterpart, which turns out quite generally to be stronger and redder. We were also able to identify a few more interwoven weak spots (the typically very high scale of inflation, the width of the spectrum of modes processed by inflation, the blindness of the amplification mechanism to the energy scale processed), in a way independent on the specifications of the coupling between inflation and electromagnetism. Despite having stripped down the problem to the core, the obstacles encountered appear insurmountable, thereby posing a challenge to inflation as the incubator of cosmological magnetism.

Gravitational production of Kaluza-Klein states

Gravitational particle production in the context of braneworlds is considered from a phenomenological point of view. The production of Kaluza-Klein modes for bulk fields is discussed and their abundances computed. The results have been applied to some specific fields such as gravitinos and axions, and their cosmologies have been outlined, exemplifying the constraints on the properties of the extra dimensional model in each case.

Dark energy from QCD

We review two mechanisms rooted in the infrared sector of QCD which, by exploiting the properties of the QCD ghost, as introduced by Veneziano, provide new insight on the cosmological dark energy problem, first, in the form of a Casimir‐like energy from quantising QCD in a box, and second, in the form of additional, time‐dependent, vacuum energy density in an expanding universe. Based on [1, 2].