Is space really expanding? A counterexample

In all Friedman models, the cosmological redshift is widely interpreted as a consequence of the general-relativistic phenomenon of EXPANSION OF SPACE. Other commonly believed consequences of this phenomenon are superluminal recession velocities of distant galaxies and the distance to the particle horizon greater than c*t (where t is the age of the Universe), in apparent conflict with special relativity. Here, we study a particular Friedman model: empty universe. This model exhibits both cosmological redshift, superluminal velocities and infinite distance to the horizon. However, we show that the cosmological redshift is there simply a relativistic Doppler shift. Moreover, apparently superluminal velocities and `acausal' distance to the horizon are in fact a direct consequence of special-relativistic phenomenon of time dilation, as well as of the adopted definition of distance in cosmology. There is no conflict with special relativity, whatsoever. In particular, INERTIAL recession velocities are subluminal. Since in the real Universe, sufficiently distant galaxies recede with relativistic velocities, these special-relativistic effects must be at least partly responsible for the cosmological redshift and the aforementioned `superluminalities', commonly attributed to the expansion of space. Let us finish with a question resembling a Buddhism-Zen `koan': in an empty universe, what is expanding?Comment: 12 pages, no figures; added Appendix with a calculation of the cosmological redshift in `private space

Measuring the galaxy power spectrum with multiresolution decomposition -- II. diagonal and off-diagonal power spectra of the LCRS galaxies

The power spectrum estimator based on the discrete wavelet transform (DWT) for 3-dimensional samples has been studied. The DWT estimator for multi-dimensional samples provides two types of spectra with respect to diagonal and off-diagonal modes, which are very flexible to deal with configuration-related problems in the power spectrum detection. With simulation samples and mock catalogues of the Las Campanas redshift survey (LCRS), we show (1) the slice-like geometry of the LCRS doesn't affect the off-diagonal power spectrum with ``slice-like'' mode; (2) the Poisson sampling with the LCRS selection function doesn't cause more than 1-$\sigma$ error in the DWT power spectrum; and (3) the powers of peculiar velocity fluctuations, which cause the redshift distortion, are approximately scale-independent. These results insure that the uncertainties of the power spectrum measurement are under control. The scatter of the DWT power spectra of the six strips of the LCRS survey is found to be rather small. It is less than 1-$\sigma$ of the cosmic variance of mock samples in the wavenumber range $0.1 < k < 2$ h Mpc$^{-1}$. To fit the detected LCRS diagonal DWT power spectrum with CDM models, we find that the best-fitting redshift distortion parameter $\beta$ is about the same as that obtained from the Fourier power spectrum. The velocity dispersions $\sigma_v$ for SCDM and $\Lambda$CDM models are also consistent with other $\sigma_v$ detections with the LCRS. A systematic difference between the best-fitting parameters of diagonal and off-diagonal power spectra has been significantly measured. This indicates that the off-diagonal power spectra are capable of providing information about the power spectrum of galaxy velocity field.Comment: AAS LaTeX file, 41 pages, 10 figures included, accepted for publication in Ap

Imprints of deviations from the gravitational inverse-square law on the power spectrum of mass fluctuations

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 cutoff 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.Comment: 8 pages, 7 figures; submitted to MNRA

Baryonic Signatures in Large-Scale Structure

We investigate the consequences of a non-negligible baryon fraction for models of structure formation in Cold Dark Matter dominated cosmologies, emphasizing in particular the existence of oscillations in the present-day matter power spectrum. These oscillations are the remnants of acoustic oscillations in the photon-baryon fluid before last scattering. For acceptable values of the cosmological and baryon densities, the oscillations modulate the power by up to 10%, with a `period' in spatial wavenumber which is close to Delta k approximately 0.05/ Mpc. We study the effects of nonlinear evolution on these features, and show that they are erased for k > 0.2 h/ Mpc. At larger scales, the features evolve as expected from second-order perturbation theory: the visibility of the oscillations is affected only weakly by nonlinear evolution. No realistic CDM parameter combination is able to account for the claimed feature near k = 0.1 h/ Mpc in the APM power spectrum, or the excess power at 100 Mpc/h wavelengths quoted by several recent surveys. Thus baryonic oscillations are not predicted to dominate existing measurements of clustering. We examine several effects which may mask the features which are predicted, and conclude that future galaxy surveys may be able to detect the oscillatory features in the power spectrum provided baryons comprise more than 15% of the total density, but that it will be a technically challenging achievement.Comment: 16 pages, 13 Figures, to be published in MNRA

Old Galaxies at High Redshift and the Cosmological Constant

In a recent striking discovery, Dunlop {\bf \it et al} observed a galaxy at redshift z=1.55 with an estimated age of 3.5 Gyr. This is incompatible with age estimates for a flat matter dominated universe unless the Hubble constant is less than $45 kms^{-1}Mpc^{-1}$. While both an open universe, and a universe with a cosmological constant alleviate this problem, I argue here that this result favors a non-zero cosmological constant, especially when considered in light of other cosmological constraints. In the first place, for the favored range of matter densities, this constraint is more stringent than the globular cluster age constraint, which already favors a non-zero cosmological constant. Moreover, the age-redshift relation for redshifts of order unity implies that the ratio between the age associated with redshift 1.55 and the present age is also generally larger for a cosmological constant dominated universe than for an open universe. In addition, structure formation is generally suppressed in low density cosmologies, arguing against early galaxy formation. The additional constraints imposed by the new observation on the parameter space of $h$ vs $\Omega_{matter}$ (where $H= 100 h kms^{-1}Mpc^{-1}$) are derived for both cosmologies. For a cosmological constant dominated universe this constraint is consistent with the range allowed by other cosmological constraints, which also favor a non-zero value.Comment: latex, 10 pages, including two embedded postscript figure

Radio Galaxy Clustering at z~0.3

Radio galaxies are uniquely useful as probes of large-scale structure as their uniform identification with giant elliptical galaxies out to high redshift means that the evolution of their bias factor can be predicted. As the initial stage in a project to study large-scale structure with radio galaxies we have performed a small redshift survey, selecting 29 radio galaxies in the range 0.19<z<0.45 from a contiguous 40 square degree area of sky. We detect significant clustering within this sample. The amplitude of the two-point correlation function we measure is consistent with no evolution from the local (z<0.1) value. This is as expected in a model in which radio galaxy hosts form at high redshift and thereafter obey a continuity equation, although the signal:noise of the detection is too low to rule out other models. Larger surveys out to z~1 should reveal the structures of superclusters at intermediate redshifts and strongly constrain models for the evolution of large-scale structure.Comment: 7 pages, 3 figures, accepted by ApJ Letter

Measuring the galaxy power spectrum with future redshift surveys

Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method, the linear (Karhunen-Loeve; KL), and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and mis-estimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.Comment: Major revisions for clarity. Matches accepted ApJ version. 23 pages, with 2 figs included. Color figure and links at http://www.sns.ias.edu/~max/galpower.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/galpower.html (faster from Europe) or from [email protected]

Correlations in the Spatial Power Spectrum Inferred from Angular Clustering: Methods and Application to APM

We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices loosens the constraints on large-scale structure inferred from the APM survey by over a factor of two. We present a new inversion technique based on singular value decomposition that allows one to propagate the covariance matrix on the angular correlation function through to that of the spatial power spectrum and to reconstruct smooth power spectra without underestimating the errors. Within a parameter space of the CDM shape Gamma and the amplitude sigma_8, we find that the angular correlations in the APM survey constrain Gamma to be 0.19-0.37 at 68% confidence when fit to scales larger than k=0.2h Mpc^-1. A downturn in power at k<0.04h Mpc^-1 is significant at only 1-sigma. These results are optimistic as we include only Gaussian statistical errors and neglect any boundary effects.Comment: 37 pages, LaTex, 9 figures. Submitted to Ap

Simulated Extragalactic Observations with a Cryogenic Imaging Spectrophotometer

In this paper we explore the application of cryogenic imaging spectrophotometers. Prototypes of this new class of detector, such as superconducting tunnel junctions (STJs) and transition edge sensors (TESs), currently deliver low resolution imaging spectrophotometry with high quantum efficiency (70-100%) and no read noise over a wide bandpass in the visible to near-infrared. In order to demonstrate their utility and the differences in observing strategy needed to maximize their scientific return, we present simulated observations of a deep extragalactic field. Using a simple analytic technique, we can estimate both the galaxy redshift and spectral type more accurately than is possible with current broadband techniques. From our simulated observations and a subsequent discussion of the expected migration path for this new technology, we illustrate the power and promise of these devices.Comment: 30 pages, 10 figures, accepted for publication in the Astronomical Journa