Adiabatic initial conditions for a particle gas in cosmology

Calculations of microwave backgrond anisotropies at various angular scales and of expected large-scale bulk velocities and mass correlation functions are presented for a variety of models which include baryons, radiation, cold dark matter (CDM), and massive and massless neutrinos. Nearly 100 different models are considered. Open and flat models with both adiabatic and isocurvature initial conditions are calculated for models without massive neurinos. A set of flat models with both massive neutrinos and CDM with adiabatic initial conditions is also considered. Fitting functions for the mass transfer function and small-angle radiation correlation function are provided for all of the models. A discussion of the evolution of the perturbations is presented. Results are compared with some recent observations of large-scale velocities and limits on microwave background anisotropies. CDM and baryon models have difficulty satisfying observational limits, although they are not completely ruled out. Hybrid models with massive neutrinos and CDM satisfy current observational data. 42 refs.

We consider a nonminimally coupled scalar field as a potential cold dark matter candidate. These models are natural extensions of the ultralight axion models which are based on minimally coupled scalar fields. Such ultralight scalar fields are motivated by string theory and, in particular, have been studied in the context of the axiverse scenario. For a nonminimally coupled field, the scalar-field energy density behaves as radiation at early times, which yields a bound on the coupling constant, $\ensuremath{\xi}\ensuremath{\lesssim}10$, from the primordial nucleosynthesis theory. The first-order perturbations of the nonminimally coupled field with adiabatic initial conditions cause the gravitational potential to decay on large scales. A comparison of the cosmological data with the theoretical matter power spectrum yields the following constraint on the coupling constant: $\ensuremath{\xi}\ensuremath{\lesssim}0.01$. We also consider isocurvature modes in our analysis. We argue that a mix of adiabatic and isocurvature initial conditions for a nonminimally coupled scalar field might allow one to obtain the usual adiabatic CDM power spectrum.

We present a new systematic analysis of the early radiation era solution in an interacting dark energy model to find the adiabatic initial conditions for the Boltzmann integration. In a model where the interaction is proportional to the dark matter density, adiabatic initial conditions and viable cosmologies are possible if the early-time dark energy equation of state parameter is $w_e > -4/5$. We find that when adiabaticity between cold dark matter, baryons, neutrinos and photons is demanded, the dark energy component satisfies automatically the adiabaticity condition. As supernovae Ia or baryon acoustic oscillation data require the recent-time equation of state parameter to be more negative, we consider a time-varying equation of state in our model. In a companion paper [arXiv:0907.4987] we apply the initial conditions derived here, and perform a full Monte Carlo Markov Chain likelihood analysis of this model.

Theoretical studies of real-fluid oxidation of hydrogen under supercritical conditions by using the virial equation of state

An experimental investigation of convection heat transfer during filling of a composite-fibre pressure vessel at low Reynolds number

In this chapter, we show how the inhomogeneity in the matter distribution created until the time of thelast scattering surface in the light of some spatially homogeneous but anisotropic models, created anisotropies that on large angular scales (larger than \(\vartheta \gtrsim 2^ \circ\)) not differ from those considered in Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. The mark left in the cosmic microwave background radiation by variations density primordial, in the form of a fractional variance in the temperature of this radiation, is controlled by the same expression used by FLRW models for these anisotropic models. The classical Sachs-Wolfe effect is recovered under adiabatic initial conditions, since the anisotropy of the global expansion is minimal at the time of the last scattering surface. This conclusion is consistent with previous work on the same anisotropic models, in which the Hubble parameters along orthogonal directions are considered to be roughly equal to the current present epoch, and the observations are unable to differentiate them from the FLRW models. The current values of the anisotropic parameters imposed by COBE observations were used to determine upper limits.

Large-scale galaxy bias

In this article we investigate the time evolution of the adiabatic (curvature) and isocurvature (entropy) spectral indices after inflation era for all cosmological scales with two different initial conditions. For this purpose, we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It would be cleared that the evolution of adiabatic spectral index severely depends on the initial conditions moreover, as expected it is constant only for the super-Hubble scales and adiabatic initial conditions. Additionally, the adiabatic spectral index after recombination approaches a constant value for the isocurvature perturbations. Finally, we re-investigate the Sachs-Wolfe effect and show that the fudge factor 1/3 in the adiabatic ordinary Sachs-Wolfe formula must be replaced by 0.4.

WMAP polarization results

Deviations from the gravitational inverse-square law would imprint scale-dependent features on the power spectrum of mass density fluctuations. We model such deviations as a Yukawa-like contribution to the gravitational potential and discuss the growth function in a mixed dark matter model with adiabatic initial conditions. Evolution of perturbations is considered in general non-flat cosmological models with a cosmological constant, and an analytical approximation for the growth function is provided. The coupling between baryons and cold dark matter across recombination is negligibly affected by modified gravity physics if the proper cut-off length of the long-range Yukawa-like force is ≳10 h−1 Mpc. Enhancement of gravity affects the subsequent evolution, boosting large-scale power in a way that resembles the effect of a lower matter density. This phenomenon is almost perfectly degenerate in power-spectrum shape with the effect of a background of massive neutrinos. Back-reaction on density growth from a modified cosmic expansion rate should, however, also affect the normalization of the power spectrum, with a shape distortion similar to the case of a non-modified background.

In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.

In this paper we show how the inhomogeneity in the matter distribution produced until the time of the last scattering surface in the light of some spatially homogeneous but anisotropic models, produced anisotropies that on large angular scales (larger than ϑ<img src=image/18402315_001.png>2^。) not differ from those considered in Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. For these anisotropic models the mark left in the cosmic microwave background radiation by fluctuations density primordial, in the form of a fractional variation of temperature of this radiation, is governed by the same expression which is used for FLRW models. More specifically, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, since the anisotropy of the global expansion is small at the time of the last scattering surface. This conclusion is in agreement with previous work on the same anisotropic models, where they undergo a process of ‘isotropization’ to the extent that the observations are unable to distinguish them from the FLRW models, if the Hubble parameters along the orthogonal directions are assumed approximately equal to the current present epoch. We considered upper bounds for the current values of the anisotropic parameters imposed by COBE observations.

We study the possibility of generating magnetic fields during the evolution of electron, proton, and photon plasma in the pre-recombination era. We show that a small magnetic field can be generated in the second order of perturbation theory for scalar modes with adiabatic initial conditions. The amplitude of the field is $\la 10^{-30} \rm G$ at the present epoch for scales from sub-kpc to $\ga 100 \rm Mpc$.

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to $n_s = 0.9603 \pm 0.0073$, ruling out exact scale invariance at over 5 $\sigma$. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V" < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n > 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining $d n_s/d ln k = -0.0134 \pm 0.0090$. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit $\chi^2$ by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with bounds on $f_\mathrm{NL}$ measured by Planck. The fractional primordial contribution of CDM isocurvature modes in the curvaton and axion scenarios has upper bounds of 0.25% or 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelation can improve $\chi^2$ by approximatively 4 as a result of slightly lowering the theoretical prediction for the $\ell<40$ multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

It is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the last scattering surface produce anisotropies on large angular scales (larger than θ > 2°) which do not differ from the ones produced in Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an ‘isotropization’ process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropy parameters imposed by COBE observations.