The local extragalactic velocity field, the local mean mass density, and biased galaxy formation

The biased galaxy formation picture accounts for the low apparent mass density derived from clustering dynamics by the assumption that the mass per galaxy is unusually low in the regions of high density where clustering has been studied. It would follow that the mass per galaxy is unusually high where the mass density is low, and, by continuity, that the mass per galaxy is close to the global mean in regions where the ambient mass density, p_t, is close to the global mean, P_b. That is, we would expect that the best chance for an unbiased estimate of the mean mass per galaxy, and hence of P_b, would be from the dynamics of regions with p_t ≈ P_b. The local density at redshifts 200 ≾ cz ≾ 400 km s^(-l) must be close to P_b because, as Sandage has emphasized, the local Hubble flow is so little perturbed. In this paper we derive a relationship between the local mass density and the perturbation of the local Hubble flow. The local mass density is estimated by the method used in the Virgocentric flow. We use the infrared Tully-Fisher distances of Aaronson et al. to find limits on the gravitational perturbation to the local Hubble flow, and we use bright galaxy counts, N, to estimate the local galaxy concentration. The statistics on the latter are weak because N is small. We can conclude, however, that if mass were proportional to N, with no fluctuations, and the local mass per galaxy were a fair sample, then the density parameter (Ω = P_b/Einstein-de Sitter density) would be Ω ≈ 0.1, consistent with the other dynamical estimates and inconsistent with the above naive interpretation of biasing

Information Equation of State

Landauer's principle is applied to information in the universe. Once stars began forming, the increasing proportion of matter at high stellar temperatures compensated for the expanding universe to provide a near constant information energy density. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10> z >0.8, over one half of cosmic time. A reasonable universe information bit content of only 10^87 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem.In answering the "Why now?" question we wonder "What next?" as we expect the information equation of state to tend towards w = 0 in the future.Comment: 10 pages, 2 figure

Holographic field theory models of dark energy in interaction with dark matter

We discuss two lagrangian interacting dark energy models in the context of the holographic principle. The potentials of the interacting fields are constructed. The models are compared with CMB distance information, baryonic acoustic oscilations, lookback time and the Constitution supernovae sample. For both models the results are consistent with a non vanishing interaction between dark sectors - with more than three standard deviations of confidence for one of them. Moreover, in both cases, the sign of coupling is consistent with dark energy decaying into dark matter, alleviating the coincidence problem.Comment: arXiv admin note: substantial text overlap with arXiv:0912.399

Newtonian and Relativistic Cosmologies

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.Comment: 35 pages; minor change

Dynamics of a Dark Matter Field with a Quartic Self-Interaction Potential

It may prove useful in cosmology to understand the behavior of the energy distribution in a scalar field that interacts only with gravity and with itself by a pure quartic potential, because if such a field existed it would be gravitationally produced, as a squeezed state, during inflation. It is known that the mean energy density in such a field after inflation varies with the expansion of the universe in the same way as radiation. I show that if the field initially is close to homogeneous, with small energy density contrast delta rho /rho and coherence length L, the energy density fluctuations behave like acoustic oscillations in an ideal relativistic fluid for a time on the order of L/|delta rho /rho|. This ends with the appearance of features that resemble shock waves, but interact in a close to elastic way that reversibly disturbs the energy distribution.Comment: 7 pages, 5 figures, submitted to Phys Rev

Spherical Collapse and the Halo Model in Braneworld Gravity

We present a detailed study of the collapse of a spherical perturbation in DGP braneworld gravity for the purpose of modeling simulation results for the halo mass function, bias and matter power spectrum. The presence of evolving modifications to the gravitational force in form of the scalar brane-bending mode lead to qualitative differences to the collapse in ordinary gravity. In particular, differences in the energetics of the collapse necessitate a new, generalized method for defining the virial radius which does not rely on strict energy conservation. These differences and techniques apply to smooth dark energy models with w unequal -1 as well. We also discuss the impact of the exterior of the perturbation on collapse quantities due to the lack of a Birkhoff theorem in DGP. The resulting predictions for the mass function, halo bias and power spectrum are in good overall agreement with DGP N-body simulations on both the self-accelerating and normal branch. In particular, the impact of the Vainshtein mechanism as measured in the full simulations is matched well. The model and techniques introduced here can serve as practical tools for placing consistent constraints on braneworld models using observations of large scale structure.Comment: 20 pages, 16 figures; v2: minor addition to appendix; matches published version; v3: typos in Eqs. (20), (23) correcte

Figures of merit and constraints from testing General Relativity using the latest cosmological data sets including refined COSMOS 3D weak lensing

We use cosmological constraints from current data sets and a figure of merit (FoM) approach to probe any deviations from general relativity (GR) at cosmological scales. The FoM approach is used to study the constraining power of various combinations of data sets on modified gravity (MG) parameters. We use recently refined HST-COSMOS weak-lensing tomography data, ISW-galaxy cross correlations from 2MASS and SDSS LRG surveys, matter power spectrum from SDSS-DR7 (MPK), WMAP7 temperature and polarization spectra, BAO from 2DF and SDSS-DR7, and Union2 compilation of supernovae, in addition to other bounds from H_0 measurements and BBN. We use 3 parametrizations of MG parameters that enter the perturbed field equations. In order to allow for variations with redshift and scale, the first 2 parametrizations use recently suggested functional forms while the third is based on binning methods. Using the first parametrization, we find that CMB + ISW + WL provides the strongest constraints on MG parameters followed by CMB+WL or CMB+MPK+ISW. Using the second parametrization or binning methods, CMB+MPK+ISW consistently provides some of the strongest constraints. This shows that the constraints are parametrization dependent. We find that adding up current data sets does not improve consistently uncertainties on MG parameters due to tensions between best-fit MG parameters preferred by different data sets. Furthermore, some functional forms imposed by the parametrizations can lead to an exacerbation of these tensions. Next, unlike some studies that used the CFHTLS lensing data, we do not find any deviation from GR using the refined HST-COSMOS data, confirming previous claims in those studies that their result may have been due to some systematic effect. Finally, we find in all cases that the values corresponding to GR are within the 95% confidence level contours for all data set combinations. (abridged)Comment: 18 pages, 6 figures, matches version published in PR