Spectrum Of Primordial Density Fluctuations Research Articles

Quasi‐nonlinear Evolution of Stochastic Bias

It is generally believed that the spatial distribution of galaxies does not trace that of the total mass. Understanding the bias effect is therefore necessary to determine the cosmological parameters and the primordial density fluctuation spectrum from the galaxy survey. The deterministic description of bias may not be appropriate because of the various stochasticity of galaxy formation process. In nature, the biasing is epoch dependent, and a recent deep survey of the galaxy shows large biasing at high redshift. Hence, we investigate quasi-nonlinear evolution of the stochastic bias by using the tree-level perturbation method. Especially the influence of the initial cross-correlation on the evolution of the skewness and the bi-spectrum is examined in detail. We find that the nonlinear bias can be generated dynamically. The small value of the initial cross-correlation can bend the δg-δm relation effectively and easily lead to the negative curvature (b2<0). We also propose a method to predict the bias, cross-correlation, and skewness at high redshift. As an illustration, the possibility of large biasing at high redshift is discussed. Provided the present bias parameter as b=1.5 and Ω=1.0, we predict the large-scale bias to be b=4.63 at z=3 by fitting the bi-spectrum to the Lick catalog data. Our results will be important for the future deep sky survey.

Galaxy Formation and Evolution: What to Expect from Hierarchical Clustering Models

In hierarchical clustering theories of galaxy formation, galaxies form by gas cooling and condensing into dark matter halos which, in turn, form by a hierarchy of mergers (White &amp; Rees 1978). The context in which this process takes place is specified by a cosmological model that determines the spectrum of primordial density fluctuations and the rate at which they grow by gravitational instability. The best known example of such a model is the cold dark matter (CDM) model (see Frenk 1991 for a review), but a number of alternatives (mostly variants of CDM), have recently become popular in response to new data on large-scale structure and the COBE detection of anisotropies in the microwave background radiation.

Scientific results from COBE

NASA's Cosmic Background Explorer (COBE1) carries three scientific instruments to make precise measurements of the spectrum and anisotropy of the cosmic microwave background (CMB) radiation on angular scales greater than 7° and to conduct a search for a diffuse cosmic infrared background (CIB) radiation with 0.7° angular resolution. Data from the Far-InfraRed Absolute Spectrophotometer (FIRAS) show that the spectrum of the CMB is that of a blackbody of temperature T=2.73±0.06 K, with no deviation from a blackbody spectrum greater than 0.25% of the peak brightness. The first year of data from the Differential Microwave Radiometers (DMR) show statistically significant CMB anisotropy. The anisotropy is consistent with a scale invariant primordial density fluctuation spectrum. Infrared sky brightness measurements from the Diffuse InfraRed Background Experiment (DIRBE) provide new conservative upper limits to the CIB. Extensive modeling of solar system and galactic infrared foregrounds is required for further improvement in the CIB limits.

COBE DMR data and the primordial index of density fluctuations

The angular correlation function of the cosmic microwave background temperature fluctuations observed by the COBE DMR experiment sets constraints on the shape and amplitude of the primordial density fluctuation spectrum. We discuss these constraints in the light of detailed Monte Carlo simulations. We find that a large range of primordial spectral indices n can still be allowed from present data, although n ≃ 1 is greatly favoured. For the scale-invariant case (n ≡ 1), we find an estimate for the ensemble-average quadrupole of Q rms PS = (14.5 ± 1.7)(1 ± 6 x 10 −2 )μK. This value has almost half of the uncertainty and is slightly smaller than the previously quoted one

Scientific results from the Cosmic Background Explorer (COBE).

The National Aeronautics and Space Administration (NASA) has flown the COBE satellite to observe the Big Bang and the subsequent formation of galaxies and large-scale structure. Data from the Far-Infrared Absolute Spectrophotometer (FIRAS) show that the spectrum of the cosmic microwave background is that of a black body of temperature T = 2.73 +/- 0.06 K, with no deviation from a black-body spectrum greater than 0.25% of the peak brightness. The data from the Differential Microwave Radiometers (DMR) show statistically significant cosmic microwave background anisotropy, consistent with a scale-invariant primordial density fluctuation spectrum. Measurements from the Diffuse Infrared Background Experiment (DIRBE) provide new conservative upper limits to the cosmic infrared background. Extensive modeling of solar system and galactic infrared foregrounds is required for further improvement in the cosmic infrared background limits.

Natural inflation: Particle physics models, power-law spectra for large-scale structure, and constraints from the Cosmic Background Explorer.

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if $f \sim M_{Pl}$ and $\Lambda \sim M_{GUT}$. We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models. We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires $f > 0.3 M_{Pl}$. The primordial density fluctuation spectrum generated is a non-scale-invariant power law, $P(k) \propto k^{n_s}$, with $n_s \simeq 1 - (M^2_{Pl}/8\pi f^2)$, leading to more power on large length scales than the $n_s = 1$ Harrison-Zeldovich spectrum. The standard CDM model with $0 \la n_s \la 0.6-0.7$ could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors, $b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to $n_s >0.6$, or $f > 0.3 M_{Pl}$ as well. For extended and power law inflation models, this constraint is even tighter, $n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.

Small-scale microwave background anisotropies implied by large-scale data

In the absence of reheating microwave background radiation (MBR) anisotropies on arcminute scales depend uniquely on the amplitude and the coherence length of the primordial density fluctuations (PDFs). These can be determined from the recent data on galaxy correlations, xi(r), on linear scales (APM survey). We develop here expressions for the MBR angular correlation function, C(theta), on arcminute scales in terms of the power spectrum of PDFs and demonstrate their accuracy by comparing with detailed calculations of MBR anisotropies. We then show how to evaluate C(theta) directly in terms of the observed xi(r) and show that the APM data give information on the amplitude, C(O), and the coherence angle of MBR anisotropies on small scales.

Consequences of the COBE satellite results for the inflationary scenario.

The discovery of the microwave background anisotropy by the Cosmic Background Explorer (COBE) satellite is in accord with the inflationary scenario. For five promising models involving a single scalar field, the coupling constants and the fluctuation spectra are calculated including a correction for gravitational radiation. The primordial density fluctuation spectrum computed from these models is not exactly scale-invariant; the spectral index is constrained to be n\ensuremath{\gtrsim}0.8 for inflation with an exponential potential (assuming that the biasing parameter for galaxies ${\mathit{b}}_{\mathrm{\ensuremath{\rho}}}$2). The implications for biased galaxy formation scenarios are discussed.

Latest COBE results, large-scale data, and predictions of inflation

One of the predictions of the inflationary scenario of cosmology is that the initial spectrum of primordial density fluctuations (PDFs) must have the Harrison-Zeldovich (HZ) form. Here, in order to test the inflationary scenario, predictions of the microwave background radiation (MBR) anisotropies measured by COBE are computed based on large-scale data for the universe and assuming Omega-1 and the HZ spectrum on large scales. It is found that the minimal scale where the spectrum can first enter the HZ regime is found, constraining the power spectrum of the mass distribution to within the bias factor b. This factor is determined and used to predict parameters of the MBR anisotropy field. For the spectrum of PDFs that reaches the HZ regime immediately after the scale accessible to the APM catalog, the numbers on MBR anisotropies are consistent with the COBE detections and thus the standard inflation can indeed be considered a viable theory for the origin of the large-scale structure in the universe.

The shape of the two-point correlation function - Evidence for a double power law

view Abstract Citations (15) References (66) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Shape of the Two-Point Correlation Function: Evidence for a Double Power Law Calzetti, Daniela ; Giavalisco, Mauro ; Meiksin, Avery Abstract We examine the two-point galaxy correlation functions of the Zwicky/CfA1, the Southern Sky Redshift Survey catalogs, and a sample of IRAS galaxies. To minimize the effects of peculiar velocities, we examine the angular and projected correlation functions and obtain the spatial correlation function for the CfA1 and SSRS samples by inverting the projected function. From the χ^2^ analysis, we find that a double power law model for 1 + ξ(r) is a fair generalization over the range of large separations (5 h^-1^ < r < 30 h^-1^ Mpc) of the single power law model for ξ(r) where ξ(r) is the two-point correlation function of galaxies. Indeed, the double power law fits the data over a factor of 2 larger in separation (~30 h^-1^ Mpc). The fit we obtain agrees well with those found by Dekel & Aarseth for the CfA1 survey and by Guzzo et al. for the Perseus-Pisces redshift catalog, based on redshift separations. Our analysis demonstrates that the double power law nature is geometrical and not a consequence of peculiar motions. We find the function 1 + ξ(r) for clusters of galaxies exhibits the same power law as that for the galaxies on large scales. We consider some consequences of such large-scale clustering, including a different normalization of the power spectrum of primordial density fluctuations. Publication: The Astrophysical Journal Pub Date: October 1992 DOI: 10.1086/171867 Bibcode: 1992ApJ...398..429C Keywords: Computational Astrophysics; Galactic Clusters; Statistical Correlation; Universe; Angular Correlation; Infrared Astronomy Satellite; Power Spectra; Red Shift; Sky Surveys (Astronomy); Astrophysics; GALAXIES: CLUSTERING; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE full text sources ADS |

Constraints on the power spectrum of the primordial density field from large-scale data - Microwave background and predictions of inflation

view Abstract Citations (7) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Constraints on the Power Spectrum of the Primordial Density Field from Large-Scale Data: Microwave Background and Predictions of Inflation Kashlinsky, A. Abstract One of the most robust predictions of the inflationary scenario for the early universe is the Harrison-Zeldovich (n = 1) spectrum of primordial density fluctuations (PDF). The later evolution of such spectrum is also uniquely specified in terms of its transfer function T^2^(k). We show that these assumptions about the early universe can be tested by measurements of the microwave background radiation (MBR) anisotropies with present techniques from COBE and other ground and balloon-based experiments; coupled with the data from galaxy catalogs (APM) they predict MBR anisotropies whose amplitudes restrict the primordial n. We compute MBR anisotropies corresponding to the minimum of C(0), the large-scale variance of the MBR anisotropy, and show that models with the Harrison-Zeldovich spectrum predicted by inflation should have quadrupole anisotropy Q > 1.2 x 10^-5^(a_2_ >= 2 x 10^-5^) and can soon be probed by COBE. If P(k) had n = 4 on large scales, the quadrupole anisotropy would he Q >= (a few) x 10^-8^ well below the quadrupole induced by the local motion. We show that experiments with FWHM ~1^deg^ would be ideal for probing the primordial n and present numbers for an experiment with FWHM = 1.5^deg^ conducted by Lubin and colleagues-in this case one should see δT|T|_~2^deg^_>=(a few) x 10^-5^ if n= 1 or if the universe is flat. If the universe is open and n = 4, the numbers should still be detectable with the ultimate resolution of this experiment. COBE should detect anisotropies if the universe is flat or if n = 1 on large scales. The minimal anisotropies implied by the APM data are inconsistent with the upper limits from the MIT experiment if n = 1. Publication: The Astrophysical Journal Pub Date: March 1992 DOI: 10.1086/186292 Bibcode: 1992ApJ...387L...1K Keywords: Density Distribution; Power Spectra; Relic Radiation; Universe; Computational Astrophysics; Cosmic Background Explorer Satellite; Probability Density Functions; Space Density; Astrophysics; COSMOLOGY: COSMIC MICROWAVE BACKGROUND; GALAXIES: CLUSTERING; GALAXIES: FORMATION; GRAVITATION full text sources ADS |

Large-scale structure in the Universe

A variety of observations constrain models of the origin of large-scale cosmic structures. Enough observational data have accumulated to constrain (and perhaps determine) the power spectrum of primordial density fluctuations over a very large range of scales, independently of the particular cosmogonical theory assumed. Observations in the near future should be able to weed out many such theories.

Local gravity and large-scale structure

view Abstract Citations (69) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Local Gravity and Large-Scale Structure Juszkiewicz, Roman ; Vittorio, Nicola ; Wyse, Rosemary F. G. Abstract The magnitude and direction of the observed dipole anisotropy of the galaxy distribution can in principle constrain the amount of large-scale power present in the spectrum of primordial density fluctuations. We here confront the data, provided by a recent redshift survey of galaxies detected by the IRAS satellite, with the predictions of two cosmological models with very different levels of large-scale power: the biased Cold Dark Matter dominated model (CDM) and a baryon-dominated model (BDM) with isocurvature initial conditions. We investigate model predictions for the Local Group peculiar velocity, v_R_, induced by mass inhomogeneities distributed out to a given radius, R, for R <~ 10,000 km s^-1^. We develop several convergence measures for v_R_, which can become powerful cosmological tests when deep enough samples become available. For the present data sets, the CDM and BDM predictions are indistinguishable at the 2 σ level and both are consistent with observations. A promising discriminant between cosmological models is the misalignment angle between v_R_ and the apex of the dipole anisotropy of the microwave background. Publication: The Astrophysical Journal Pub Date: February 1990 DOI: 10.1086/168324 Bibcode: 1990ApJ...349..408J Keywords: Galactic Structure; Gravitation Theory; Relic Radiation; Space Density; Astronomical Models; Dark Matter; Infrared Sources (Astronomy); Astrophysics; COSMIC BACKGROUND RADIATION; COSMOLOGY; DARK MATTER; INFRARED: SOURCES full text sources ADS |

Large-scale structure formation and cosmic microwave anisotropy in a cold plus hot dark matter universe

Several particle physics models suggest the simultaneous existence of both cold and hot forms of dark matter particles. Assuming a Harrison-Zel'dovich spectrum of primordial density fluctuations and Omega = 1, the formation of structure in a universe dominated by a combination of cold dark matter and massive neutrinos is explored. It is found that the presence of the hot dark matter component can cause enough power on large scales to explain some recent observations, while there is still sufficient power on small scales to allow galactic structure formation. Spatial anisotropies in the microwave background radiation are computed and found to be compatible with observational limits.

Gravitational clustering and the origin of the correlation function of clusters of galaxies

The evolution of the two-point correlation function xi on different scales due to gravitational clustering is studied. It is shown that for a given spectrum of primordial density fluctuations xi would be increased for those fluctuations that turned around on scales that are bigger than the typical turnaround scale of clustering hierarchy at the present epoch (scale of groups of galaxies); the increase depends on the mass (scale) of cluster and the power-slope of the spectrum of density fluctuations. It is suggested that clusters of galaxies have large (r) correlation strength because they are the objects that turned around on a large mass scale. The correlation of xi of clusters with their richness (mass) and mean separation are then explained naturally. 16 references.

Galaxy Formation

Theories of galaxy formation via hierarchical clustering of cold dark matter and by fragmentation of gaseous pancakes or shells are reviewed and compared. Dissipative processes are crucial to all theories of galaxy formation, and are discussed in terms of a simple model involving multiple cloud interactions. Stellar energy input is found to play an important role in protogalaxies, both supporting the gas against collapse, thereby prolonging the duration of the active star formation phase, and driving winds from the less massive galaxies. The significance of such processes is explored both for chemical and dynamical evolution and for biasing galaxy formation towards density peaks in the primordial density fluctuation spectrum.

Protogalactic evolution

view Abstract Citations (38) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Protogalactic evolution Silk, J. Abstract The high star formation rate in a gas-rich protogalaxy provides a substantial energy and momentum input into the interstellar gas and is capable of regulating the rate of gas collapse and star formation. Wind support of protogalactic gas is found to be inevitable over the density range where a steady wind is quenched by effective cooling and ensuing thermal instability, but where the energy input suffices to support the gas against collapse. Wind stripping constrains the star formation efficiency and masks the role of the primordial density fluctuation spectrum in determining the characteristic properties of the old stellar components. The observed mean density and metallicity dependences on stellar velocity dispersion of the spheroidal and old disk components of galaxies are in reasonable accord with predictions of this model. Publication: The Astrophysical Journal Pub Date: October 1985 DOI: 10.1086/163497 Bibcode: 1985ApJ...297....9S Keywords: Cosmology; Energy Transfer; Galactic Evolution; Stellar Evolution; Universe; Hubble Diagram; Interstellar Gas; Momentum Transfer; Morphology; Star Formation Rate; Astrophysics full text sources ADS |

Dynamical aspects of galaxy clustering

Some recent work on the origin and evolution of galaxy clustering is reviewed, particularly within the context of the gravitational instability theory and the hot big-bang cosmological model. Statistical measures of clustering, including correlation functions and multiplicity functions, are explained and discussed. The close connection between galaxy formation and clustering is emphasized. Additional topics include the dependence of galaxy clustering on the spectrum of primordial density fluctuations and the mean mass density of the Universe.