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Register a new userAffine equation of state from quintessence and k-essence fields
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Claudia Quercellini
Publication date
2007
fields
Physics
and research's language is
English
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We explore the possibility that a scalar field with appropriate Lagrangian can mimic a perfect fluid with an affine barotropic equation of state. The latter can be thought of as a generic cosmological dark component evolving as an effective cosmological constant plus a generalized dark matter. As such, it can be used as a simple, phenomenological model for either dark energy or unified dark matter. Furthermore, it can approximate (up to first order in the energy density) any barotropic dark fluid with arbitrary equation of state. We find that two kinds of Lagrangian for the scalar field can reproduce the desired behaviour: a quintessence-like with a hyperbolic potential, or a purely kinetic k-essence one. We discuss the behaviour of these two classes of models from the point of view of the cosmological background, and we give some hints on their possible clustering properties.
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The dynamical properties of a model of dark energy in which two scalar fields are coupled by a non-canonical kinetic term are studied. We show that overall the addition of the coupling has only minor effects on the dynamics of the two-field system for both potentials studied, even preserving many of the features of the assisted quintessence scenario. The coupling of the kinetic terms enlarges the regions of stability of the critical points. When the potential is of an additive form, we find the kinetic coupling has an interesting effect on the dynamics of the fields as they approach the inflationary attractor, with the result that the combined equation of state of the scalar fields can approach -1 during the transition from a matter dominated universe to the recent period of acceleration.
K-essence is a minimally-coupled scalar field whose Lagrangian density $mathcal{L}$ is a function of the field value $phi$ and the kinetic energy $X=frac{1}{2}partial_muphipartial^muphi$. In the thawing scenario, the scalar field is frozen by the large Hubble friction in the early universe, and therefore initial conditions are specified. We construct thawing k-essence models by generating Taylor expansion coefficients of $mathcal{L}(phi, X)$ from random matrices. From the ensemble of randomly generated thawing k-essence models, we select dark energy candidates by assuming negative pressure and non-growth of sub-horizon inhomogeneities. For each candidate model the dark energy equation of state function is fit to the Chevallier-Polarski-Linder parameterization $w(a) approx w_0+w_a(1-a)$, where $a$ is the scale factor. The thawing k-essence dark models distribute very non-uniformly in the $(w_0, w_a)$ space. About 90% models cluster in a narrow band in the proximity of a slow-roll line $w_aapprox -1.42 left(frac{Omega_m}{0.3}right)^{0.64}(1+w_0)$, where $Omega_m$ is the present matter density fraction. This work is a proof of concept that for a certain class of models very non-uniform theoretical prior on $(w_0, w_a)$ can be obtained to improve the statistics of model selection.
Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the universe. These theories generally include a potential V(phi) which is a function of the scalar field phi. Although V(phi) can be represented by a very diverse set of functions, recent work has shown the under some conditions, such as the slow roll conditions, the equation of state parameter w is either independent of the form of V(phi) or is part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of the model leading to possibly observable changes in the fundamental constants such as the fine structure constant alpha and the proton to electron mass ratio mu. This paper explores the limits this puts on the validity of various cosmologies that invoke rolling scalar fields. We find that the limit on the variation of mu puts significant constraints on the product of a cosmological parameter w+1 times a new physics parameter zeta_mu^2, the coupling constant between mu and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of zeta_mu must be at the lower end of or less than its expected values or the value of w+1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled with the electromagnetic field, small zeta_mu, very weakly coupled with gravity, w+1 ~ 0 or both. These results stress that adherence to the measured invariance in mu is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of mu also produces a significant tension with the reported changes in the value of alpha.
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $Pto X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/Hto X$ are treated as classical Higgs fields. Its most comprehensive example is metric-affine gauge theory on the category of natural bundles where gauge fields are general linear connections on a manifold $X$, classical Higgs fields are arbitrary pseudo-Riemannian metrics on $X$, and matter fields are spinor fields. In particular, this is the case of gauge gravitation theory.
The immediate observational consequence of a non-trivial spatial topology of the Universe is that an observer could potentially detect multiple images of radiating sources. In particular, a non-trivial topology will generate pairs of correlated circles of temperature fluctuations in the anisotropies maps of the cosmic microwave background (CMB), the so-called circles-in-the-sky. In this way, a detectable non-trivial spatial topology may be seen as an observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological dark energy (DE) equation of state (EOS) parameters. We show that the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of reducing the degeneracies in the DE EOS parameters. We concretely illustrate the topological role by assuming, as an exanple, a Poincar{e} dodecahedral space topology and reanalyzing the constraints on the parameters of a specific EOS which arise from the supernovae type Ia, baryon acoustic oscillations and the CMB plus the statistical topological contribution.
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