Dynamically avoiding fine-tuning the cosmological constant: the "Relaxed Universe"

We demonstrate that there exists a large class of action functionals of the scalar curvature and of the Gauss-Bonnet invariant which are able to relax dynamically a large cosmological constant (CC), whatever it be its starting value in the early universe. Hence, it is possible to understand, without fine-tuning, the very small current value of the CC as compared to its theoretically expected large value in quantum field theory and string theory. In our framework, this relaxation appears as a pure gravitational effect, where no ad hoc scalar fields are needed. The action involves a positive power of a characteristic mass parameter, M, whose value can be, interestingly enough, of the order of a typical particle physics mass of the Standard Model of the strong and electroweak interactions or extensions thereof, including the neutrino mass. The model universe emerging from this scenario (the "Relaxed Universe") falls within the class of the so-called LXCDM models of the cosmic evolution. Therefore, there is a "cosmon" entity X (represented by an effective object, not a field), which in this case is generated by the effective functional and is responsible for the dynamical adjustment of the cosmological constant. This model universe successfully mimics the essential past epochs of the standard (or "concordance") cosmological model (LCDM). Furthermore, it provides interesting clues to the coincidence problem and it may even connect naturally with primordial inflation.Comment: LaTeX, 63 pp, 8 figures. Extended discussion. Version accepted in JCA

Measuring the elements of the optical density matrix

Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.Comment: 6 pages and 1 figur

Scalar-Tensor Gravity and Quintessence

Scalar fields with inverse power-law effective potentials may provide a negative pressure component to the energy density of the universe today, as required by cosmological observations. In order to be cosmologically relevant today, the scalar field should have a mass $m_\phi = O(10^{-33} {\mathrm eV})$, thus potentially inducing sizable violations of the equivalence principle and space-time variations of the coupling constants. Scalar-tensor theories of gravity provide a framework for accommodating phenomenologically acceptable ultra-light scalar fields. We discuss non-minimally coupled scalar-tensor theories in which the scalar-matter coupling is a dynamical quantity. Two attractor mechanisms are operative at the same time: one towards the tracker solution, which accounts for the accelerated expansion of the Universe, and one towards general relativity, which makes the ultra-light scalar field phenomenologically safe today. As in usual tracker-field models, the late-time behavior is largely independent on the initial conditions. Strong distortions in the cosmic microwave background anisotropy spectra as well as in the matter power spectrum are expected.Comment: 5 pages, 4 figure

Renormalization group improved gravitational actions: a Brans-Dicke approach

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure

Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation

Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure

Hubble expansion and structure formation in the "running FLRW model" of the cosmic evolution

A new class of FLRW cosmological models with time-evolving fundamental parameters should emerge naturally from a description of the expansion of the universe based on the first principles of quantum field theory and string theory. Within this general paradigm, one expects that both the gravitational Newton's coupling, G, and the cosmological term, Lambda, should not be strictly constant but appear rather as smooth functions of the Hubble rate. This scenario ("running FLRW model") predicts, in a natural way, the existence of dynamical dark energy without invoking the participation of extraneous scalar fields. In this paper, we perform a detailed study of these models in the light of the latest cosmological data, which serves to illustrate the phenomenological viability of the new dark energy paradigm as a serious alternative to the traditional scalar field approaches. By performing a joint likelihood analysis of the recent SNIa data, the CMB shift parameter, and the BAOs traced by the Sloan Digital Sky Survey, we put tight constraints on the main cosmological parameters. Furthermore, we derive the theoretically predicted dark-matter halo mass function and the corresponding redshift distribution of cluster-size halos for the "running" models studied. Despite the fact that these models closely reproduce the standard LCDM Hubble expansion, their normalization of the perturbation's power-spectrum varies, imposing, in many cases, a significantly different cluster-size halo redshift distribution. This fact indicates that it should be relatively easy to distinguish between the "running" models and the LCDM cosmology using realistic future X-ray and Sunyaev-Zeldovich cluster surveys.Comment: Version published in JCAP 08 (2011) 007: 1+41 pages, 6 Figures, 1 Table. Typos corrected. Extended discussion on the computation of the linearly extrapolated density threshold above which structures collapse in time-varying vacuum models. One appendix, a few references and one figure adde

A model of the Universe including Dark Energy accounted for by both a Quintessence Field and a (negative) Cosmological Constant

In this work we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a future collapsing universe (for a given region of the parameter space), which is necessary for a consistent formulation of string theory and quantum field theory. We have also reproduced the measurements of modulus distance from supernovae with good accuracy.Comment: 11 pages, 4 figures, only the results for the single exponential potential are preserved. One author added. Some changes in the reference section. Submitted to Physical Review

Renormalization Group Approach to Generalized Cosmological models

We revisit here the problem of generalized cosmology using renormalization group approach. A complete analysis of these cosmologies, where specific models appear as asymptotic fixed-points, is given here along with their linearized stability analysis.Comment: 10 pages, to appear in the International Journal of Theoretical Physic

On exact solutions for quintessential (inflationary) cosmological models with exponential potentials

We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar fields can be connected to the inflationary phase, building up, for this class of potentials, a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have also been done by including radiation into the model.Comment: Revtex4, 10 figure