Observational tests for oscillating expansion rate of the Universe

We investigate the observational constraints on the oscillating scalar field model using data from type Ia supernovae, cosmic microwave background anisotropies, and baryon acoustic oscillations. According to a Fourier analysis, the galaxy number count $N$ from redshift $z$ data indicates that galaxies have preferred periodic redshift spacings. We fix the mass of the scalar field as $m_\phi=3.2\times 10^{-31}h$ ${\rm eV}$ such that the scalar field model can account for the redshift spacings, and we constrain the other basic parameters by comparing the model with accurate observational data. We obtain the following constraints: $\Omega_{m,0}=0.28\pm 0.03$ (95% C.L.), $\Omega_{\phi,0} -158$ (95% C.L.) (in the range $\xi \le 0$). The best fit values of the energy density parameter of the scalar field and the coupling constant are $\Omega_{\phi,0}= 0.01$ and $\xi= -25$, respectively. The value of $\Omega_{\phi,0}$ is close to but not equal to $0$. Hence, in the scalar field model, the amplitude of the galaxy number count cannot be large. However, because the best fit values of $\Omega_{\phi,0}$ and $\xi$ are not $0$, the scalar field model has the possibility of accounting for the periodic structure in the $N$--$z$ relation of galaxies. The variation of the effective gravitational constant in the scalar field model is not inconsistent with the bound from observation.Comment: 9 pages, 11 figures, 1 table, Accepted for publication in Physical Review

Finite-time singularities in f(R, T) gravity and the effect of conformal anomaly

We investigate $f(R,T)$ gravity models ($R$ is the curvature scalar and $T$ is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter in order to realise the cosmic acceleration and we introduce two parameters, $\alpha$ and $H_s$, which characterise each type of singularity. We address conformal anomaly and we observe that it cannot remove the sudden singularity or the type IV one, but, for some values of $\alpha$, the big rip and the type III singularity may be avoided. We also find that, even without taking into account conformal anomaly, the big rip and the type III singularity may be removed thanks to the presence of the $T$ contribution of the $f(R,T)$ theory.Comment: 18 pages; Accepted for publication in Canadian Journal of Physics (CJP

Primordial fractal density perturbations and structure formation in the Universe: 1-Dimensional collisionless sheet model

Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze the time evolution of fractal density perturbations in Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will come out. We assume a one-dimensional collisionless sheet model with initial Cantor-type fractal perturbations. The nonlinear structure seems to approach some attractor with a unique fractal dimension, which is independent of the fractal dimensions of initial perturbations. A discrete self-similarity in the phase space is also found when the universal nonlinear fractal structure is reached.Comment: 17 pages, 19 jpeg figures. Accepted for publication in ApJ. Figures are also available from http://www.phys.waseda.ac.jp/gravity/~tatekawa/0003124/figs.tar.g

Contiguous redshift parameterizations of the growth index

The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration. We suggest here parameterizations of the growth index as functions of the redshift. The first one is given by $\gamma(a)=\tilde\gamma(a) \frac{1}{1+(a_{_{ttc}}/a)}+\gamma_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tilde\gamma(a)=\gamma_{_{late}}(a)= \gamma_0 + (1-a) \gamma_a$ and a high redshift $\gamma_{_{early}}$ constant value. For example, our interpolated form $\gamma(a)$ can be used when including the CMB to the rest of the data while the form $\gamma_{_{late}}(a)$ can be used otherwise. It is found that the parameterizations proposed achieve a fit that is better than 0.004% for the growth rate in a $\Lambda$CDM model, better than 0.014% for Quintessence-Cold-Dark-Matter (QCDM) models, and better than 0.04% for the flat Dvali-Gabadadze-Porrati (DGP) model (with $\Omega_m^0=0.27$) for the entire redshift range up to $z_{_{CMB}}$. We find that the growth index parameters $(\gamma_0,\gamma_a)$ take distinctive values for dark energy models and modified gravity models, e.g. $(0.5655,-0.02718)$ for the $\Lambda$CDM model and $(0.6418,0.06261)$ for the flat DGP model. This provides a means for future observational data to distinguish between the models.Comment: 7 pages, 6 figures, matches PRD accepted versio

Limits on the integration constant of the dark radiation term in Brane Cosmology

We consider the constraints from primordial Helium abundances on the constant of integration of the dark radiation term of the brane-world generalized Friedmann equation derived from the Randall-Sundrum Single brane model. We found that -- using simple, approximate and semianalytical Method -- that the constant of integration is limited to be between -8.9 and 2.2 which limits the possible contribution from dark radiation term to be approximately between -27% to 7% of the background photon energy density.Comment: 8 page

CMB Constraint on Radion Evolution in the Brane World Scenario

In many versions of brane model, the modulus field of extra dimensions, the radion, could have cosmological evolution, which induces variation of the Higgs vacuum expectation value, , resulting in cosmological variation of the electron mass $m_e$. The formation of Cosmic Microwave Background (CMB) anisotropies is thus affected, causing changes both in the peaks positions and amplitudes in the CMB power spectra. Using the three-year Wilkinson Microwave Anisotropies Probe (WMAP) CMB data, with the Hubble parameter $H_0$ fixed to be the Hubble Space Telescope (HST) result 72 km s$^{-1}$ Mpc$^{-1}$, we obtain a constraint on $\rho$, the ratio of the value of at CMB recombination to its present value, to be [0.97, 1.02].Comment: 7 pages, 6 figures, minor changes of format to conform with PRD forma

Reconstructing the shape of the correlation function

We develop an estimator for the correlation function which, in the ensemble average, returns the shape of the correlation function, even for signals that have significant correlations on the scale of the survey region. Our estimator is general and works in any number of dimensions. We develop versions of the estimator for both diffuse and discrete signals. As an application, we examine Monte Carlo simulations of X-ray background measurements. These include a realistic, spatially-inhomogeneous population of spurious detector events. We discuss applying the estimator to the averaging of correlation functions evaluated on several small fields, and to other cosmological applications.Comment: 10 pages, 5 figures, submitted to ApJS. Methods and results unchanged but text is expanded and significantly reordered in response to refere

The ergodicity bias in the observed galaxy distribution

The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy distribution. The resultant difference between observed statistics (volume average) and the true cosmic value (ensemble average) is termed as the ergodicity bias. We perform explicit numerical investigation of the effect for a set of galaxy survey depths and near-end distance cuts. It is found that the ergodicity bias in observed two- and three-point correlation functions in most cases is insignificant for modern analysis of samples from galaxy surveys and thus close a loophole in precision cosmology. However, it may become non-negligible in certain circumstances, such as those applications involving three-point correlation function at large scales of local galaxy samples. Thus one is reminded to take extra care in galaxy sample construction and interpretation of the statistics of the sample, especially when the characteristic redshift is low.Comment: Revised version published as JCAP08(2010)01

Cosmological Three-Point Function: Testing The Halo Model Against Simulations

We perform detailed comparison of the semi-analytic halo model predictions with measurements in numerical simulations of the two and three point correlation functions (3PCF), as well as power spectrum and bispectrum. We discuss the accuracy and self-consistency of the halo model description of gravitational clustering in the non-linear regime and constrain halo model parameters. We exploit the recently proposed multipole expansion of three point statistics that expresses rotation invariance in the most natural way. This not only offers technical advantages by reducing the integrals required for the halo model predictions, but amounts to a convenient way of compressing the information contained in the 3PCF. We find that, with an appropriate choice of the halo boundary and mass function cut-off, halo model predictions are in good agreement with the bispectrum measured in numerical simulations. However, the halo model predicts less than the observed configuration dependence of the 3PCF on ~ Mpc scales. This effect is mainly due to quadrupole moment deficit, possibly related to the assumption of spherical halo geometry. Our analysis shows that using its harmonic decomposition, the full configuration dependence of the 3PCF in the non-linear regime can be compressed into just a few numbers, the lowest multipoles. Moreover, these multipoles are closely related to the highest signal to noise eigenmodes of the 3PCF. Therefore this estimator may simplify future analyses aimed at constraining cosmological and halo model parameters from observational data.Comment: Minor corrections. Accepted for publication by Ap

Nonlinear Velocity-Density Coupling: Analysis by Second-Order Perturbation Theory

Cosmological linear perturbation theory predicts that the peculiar velocity $V(x)$ and the matter overdensity $\delta(x)$ at a same point $x$ are statistically independent quantities, as log as the initial density fluctuations are random Gaussian distributed. However nonlinear gravitational effects might change the situation. Using framework of second-order perturbation theory and the Edgeworth expansion method, we study local density dependence of bulk velocity dispersion that is coarse-grained at a weakly nonlinear scale. For a typical CDM model, the first nonlinear correction of this constrained bulk velocity dispersion amounts to $\sim 0.3\delta$ (Gaussian smoothing) at a weakly nonlinear scale with a very weak dependence on cosmological parameters. We also compare our analytical prediction with published numerical results given at nonlinear regimes.Comment: 16 pages including 2 figures, ApJ 537 in press (July 1