Spherical collapse with dark energy

I discuss the work of Maor and Lahav [1], in which the inclusion of dark energy into the spherical collapse formalism is reviewed. Adopting a phenomenological approach, I consider the consequences of - a) allowing the dark energy to cluster, and, b) including the dark energy in the virialization process. Both of these issues affect the final state of the system in a fundamental way. The results suggest a potentially differentiating signature between a true cosmological constant and a dynamic form of dark energy. This signature is unique in the sense that it does not depend on a measurement of the value of the equation of state of dark energy.Comment: To appear in the proceedings of the ``Peyresq Physics 10" Workshop, 19 - 24 June 2005, Peyresq, Franc

On virialization with dark energy

We review the inclusion of dark energy into the formalism of spherical collapse, and the virialization of a two-component system, made of matter and dark energy. We compare two approaches in previous studies. The first assumes that only the matter component virializes, e.g. as in the case of a classic cosmological constant. The second approach allows the full system to virialize as a whole. We show that the two approaches give fundamentally different results for the final state of the system. This might be a signature discriminating between the classic cosmological constant which cannot virialize and a dynamical dark energy mimicking a cosmological constant. This signature is independent of the measured value of the equation of state. An additional issue which we address is energy non-conservation of the system, which originates from the homogeneity assumption for the dark energy. We propose a way to take this energy loss into account.Comment: 15 pages, 5 figures. Accepted for publication in JCA

Dynamics and constraints of the Unified Dark Matter flat cosmologies

We study the dynamics of the scalar field FLRW flat cosmological models within the framework of the Unified Dark Matter (UDM) scenario. In this model we find that the main cosmological functions such as the scale factor of the Universe, the scalar field, the Hubble flow and the equation of state parameter are defined in terms of hyperbolic functions. These analytical solutions can accommodate an accelerated expansion, equivalent to either the dark energy or the standard $\Lambda$ models. Performing a joint likelihood analysis of the recent supernovae type Ia data and the Baryonic Acoustic Oscillations traced by the SDSS galaxies, we place tight constraints on the main cosmological parameters of the UDM cosmological scenario. Finally, we compare the UDM scenario with various dark energy models namely $\Lambda$ cosmology, parametric dark energy model and variable Chaplygin gas. We find that the UDM scalar field model provides a large and small scale dynamics which are in fair agreement with the predictions by the above dark energy models although there are some differences especially at high redshifts.Comment: 11 pages, 7 figures, published in Physical Review D, 78, 083509, (2008

Electrospun Ca3Co4−xO9+δ nanofibers and nanoribbons: Microstructure and thermoelectric properties

Oxide-based ceramics offer promising thermoelectric (TE) materials for recycling high-temperature waste heat, generated extensively from industrial sources. To further improve the functional performance of TE materials, their power factor should be increased. This can be achieved by nanostructuring and texturing the oxide-based ceramics creating multiple interphases and nanopores, which simultaneously increase the electrical conductivity and the Seebeck coefficient. The aim of this work is to achieve this goal by compacting electrospun nanofibers of calcium cobaltite Ca3Co4−xO9+δ, known to be a promising p-type TE material with good functional properties and thermal stability up to 1200 K in air. For this purpose, polycrystalline Ca3Co4−xO9+δ nanofibers and nanoribbons were fabricated by sol–gel electrospinning and calcination at intermediate temperatures to obtain small primary particle sizes. Bulk ceramics were formed by sintering pressed compacts of calcined nanofibers during TE measurements. The bulk nanofiber sample pre-calcined at 973 K exhibited an improved Seebeck coefficient of 176.5 S cm−1 and a power factor of 2.47 μW cm−1 K−2 similar to an electrospun nanofiber-derived ceramic compacted by spark plasma sintering

Superior Thermoelectric Performance of Textured Ca3Co4−xO9+δ Ceramic Nanoribbons

Calcium cobaltite Ca3Co4−xO9+δ (CCO) is a promising p-type thermoelectric (TE) material for high-temperature applications in air. The grains of the material exhibit strong anisotropic properties, making texturing and nanostructuring mostly favored to improve thermoelectric performance. On the one hand multitude of interfaces are needed within the bulk material to create reflecting surfaces that can lower the thermal conductivity. On the other hand, low residual porosity is needed to improve the contact between grains and raise the electrical conductivity. In this study, CCO fibers with 100% flat cross sections in a stacked, compact form are electrospun. Then the grains within the nanoribbons in the plane of the fibers are grown. Finally, the nanoribbons are electrospun into a textured ceramic that features simultaneously a high electrical conductivity of 177 S cm−1 and an immensely enhanced Seebeck coefficient of 200 µV K−1 at 1073 K are assembled. The power factor of 4.68 µW cm−1 K−2 at 1073 K in air surpasses all previous CCO TE performances of nanofiber ceramics by a factor of two. Given the relatively high power factor combined with low thermal conductivity, a relatively large figure-of-merit of 0.3 at 873 K in the air for the textured nanoribbon ceramic is obtained

Evolution of Spherical Overdensity in Thawing Dark energy Models

We study the general evolution of spherical over-densities for thawing class of dark energy models. We model dark energy with scalar fields having canonical as well as non-canonical kinetic energy. For non-canonical case, we consider models where the kinetic energy is of the Born-Infeld Form. We study various potentials like linear, inverse-square, exponential as well as PNGB-type. We also consider the case when dark energy is homogeneous as well as the case when it is inhomogeneous and virializes together with matter. Our study shows that models with linear potential in particular with Born-Infeld type kinetic term can have significant deviation from the $\Lambda$CDM model in terms of density contrast at the time of virialization. Although our approach is a simplified one to study the nonlinear evolution of matter overdensities inside the cluster and is not applicable to actual physical situation, it gives some interesting insights into the nonlinear clustering of matter in the presence of thawing class of dark energy models.Comment: 11 pages, mnras style, 8 EPS figures, 1 table, improved version, Accepted for publication in MNRA

Spherical collapse of dark energy with an arbitrary sound speed

We consider a generic type of dark energy fluid, characterised by a constant equation of state parameter w and sound speed c_s, and investigate the impact of dark energy clustering on cosmic structure formation using the spherical collapse model. Along the way, we also discuss in detail the evolution of dark energy perturbations in the linear regime. We find that the introduction of a finite sound speed into the picture necessarily induces a scale-dependence in the dark energy clustering, which in turn affects the dynamics of the spherical collapse in a scale-dependent way. As with other, more conventional fluids, we can define a Jeans scale for the dark energy clustering, and hence a Jeans mass M_J for the dark matter which feels the effect of dark energy clustering via gravitational interactions. For bound objects (halos) with masses M >> M_J, the effect of dark energy clustering is maximal. For those with M << M_J, the dark energy component is effectively homogeneous, and its role in the formation of these structures is reduced to its effects on the Hubble expansion rate. To compute quantitatively the virial density and the linearly extrapolated threshold density, we use a quasi-linear approach which is expected to be valid up to around the Jeans mass. We find an interesting dependence of these quantities on the halo mass M, given some w and c_s. The dependence is the strongest for masses lying in the vicinity of M ~ M_J. Observing this M-dependence will be a tell-tale sign that dark energy is dynamic, and a great leap towards pinning down its clustering properties.Comment: 25 pages, 6 figures, matches version published in JCA

Structure formation in the presence of dark energy perturbations

We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations as well. In order to compute the rate of formation of massive objects we employ the Spherical Collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the Pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations as well. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press-Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift.Comment: 21 pages, 8 figures. Matches published version, with caption of Fig. 6 correcte

The formation and gas content of high redshift galaxies and minihalos

We investigate the suppression of the baryon density fluctuations compared to the dark matter in the linear regime. Previous calculations predict that the suppression occurs up to a characteristic mass scale of ~ 1,000,000 solar masses, which suggests that pressure has a central role in determining the properties of the first luminous objects at early times. We show that the expected characteristic mass scale is in fact substantially lower (by a factor of ~ 3-10, depending on redshift), and thus the effect of baryonic pressure on the formation of galaxies up to reionization is only moderate. This result is due to the influence on perturbation growth of the high pressure that prevailed in the period from cosmic recombination to z ~ 200, when the gas began to cool adiabatically and the pressure then dropped. At z ~ 10 the suppression of the baryon fluctuations is still sensitive to the history of pressure in this high-redshift era. We calculate the fraction of the cosmic gas that is in minihalos and find that it is substantially higher than would be expected with the previously-estimated characteristic mass. Expanding our investigation to the non-linear regime, we calculate in detail the spherical collapse of high-redshift objects in a Lambda-CDM universe. We include the gravitational contributions of the baryons and radiation and the memory of their kinematic coupling before recombination. We use our results to predict a more accurate halo mass function as a function of redshift.Comment: 11 pages, 9 figures, submitted to MNRA

Large Scale Structures in Kinetic Gravity Braiding Model That Can Be Unbraided

We study cosmological consequences of a kinetic gravity braiding model, which is proposed as an alternative to the dark energy model. The kinetic braiding model we study is characterized by a parameter n, which corresponds to the original galileon cosmological model for n=1. We find that the background expansion of the universe of the kinetic braiding model is the same as the Dvali-Turner's model, which reduces to that of the standard cold dark matter model with a cosmological constant (LCDM model) for n equal to infinity. We also find that the evolution of the linear cosmological perturbation in the kinetic braiding model reduces to that of the LCDM model for n=\infty. Then, we focus our study on the growth history of the linear density perturbation as well as the spherical collapse in the nonlinear regime of the density perturbations, which might be important in order to distinguish between the kinetic braiding model and the LCDM model when n is finite. The theoretical prediction for the large scale structure is confronted with the multipole power spectrum of the luminous red galaxy sample of the Sloan Digital Sky survey. We also discuss future prospects of constraining the kinetic braiding model using a future redshift survey like the WFMOS/SuMIRe PFS survey as well as the cluster redshift distribution in the South Pole Telescope survey.Comment: 41 pages, 20 figures; This version was accepted for publication in JCA