The Black Hole Particle Accelerator as a Machine to make Baby Universes

General relativity predicts that the inner horizon of an astronomically realistic rotating black hole is subject to the mass inflation instability. The inflationary instability acts like a gravity-powered particle accelerator of extraordinary power, accelerating accreted streams of particles along the principal outgoing and ingoing null directions at the inner horizon to collision energies that would, if nothing intervened, typically exceed exponentially the Planck energy. The inflationary instability is fueled by ongoing accretion, and is occurring inevitably in essentially every black hole in our Universe. This extravagant machine, the Black Hole Particle Accelerator, has the hallmarks of a device to make baby universes. Since collisions are most numerous inside supermassive black holes, reproductive efficiency requires our Universe to make supermassive black holes efficiently, as is observed.Comment: 7 pages, 2 figures. NO honorable mention in the 2013 Essay Competition of the Gravity Research Foundatio

Ways to improve your correlation functions

This paper describes a number of ways to improve on the standard method for measuring the two-point correlation function of large scale structure in the Universe. Issues addressed are: (1) the problem of the mean density, and how to solve it; (2) how to estimate the uncertainty in a measured correlation function; (3) minimum variance pair weighting; (4) unbiased estimation of the selection function when magnitudes are discrete; and (5) analytic computation of angular integrals in background pair counts

Omega from the anisotropy of the redshift correlation function

Peculiar velocities distort the correlation function of galaxies observed in redshift space. In the large scale, linear regime, the distortion takes a characteristic quadrupole plus hexadecapole form, with the amplitude of the distortion depending on the cosmological density parameter omega. Preliminary measurements are reported here of the harmonics of the correlation function in the CfA, SSRS, and IRAS 2 Jansky redshift surveys. The observed behavior of the harmonics agrees qualitatively with the predictions of linear theory on large scales in every survey. However, real anisotropy in the galaxy distribution induces large fluctuations in samples which do not yet probe a sufficiently fair volume of the Universe. In the CfA 14.5 sample in particular, the Great Wall induces a large negative quadrupole, which taken at face value implies an unrealistically large omega 20. The IRAS 2 Jy survey, which covers a substantially larger volume than the optical surveys and is less affected by fingers-of-god, yields a more reliable and believable value, omega = 0.5 sup +.5 sub -.25

Nonlinear Cosmological Power Spectra in Real and Redshift--Space

We present an expression for the nonlinear evolution of the cosmological power spectrum based on following Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self- gravitating fields. We have extended this analysis into redshift-space and found a solution for the nonlinear, anisotropic redshift-space power spectrum in the limit of plane--parallel redshift distortions. The quadrupole-to- monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, $\beta$. The point of zero-crossing of the quadrupole, $k_0$, is found to obey a scaling relation. This model is found to be in agreement with $N$-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole--monopole ratio found in the merged QDOT+1.2 Jy IRAS redshift survey. We have estimated that the distortion parameter is constrained to be $\beta>0.5$ at the $95 \%$ level. The local primordial spectral slope is not well constrained, but analysis suggests $n \approx -2$ in the translinear regime. The zero-crossing scale of the quadrupole is $k_0=0.5 \pm 0.1 h/Mpc$ and from this we infer the amplitude of clustering is $\sigma_8=0.7 \pm 0.05$. We suggest that the success of this model is due to nonlinear redshift--space effects arising from infall onto caustics and is not dominated by virialised cluster cores.Comment: 13 pages, uufiles, Latex with 6 postscript figures, submitted to MNRA

Spherical Redshift Distortions

Peculiar velocities induce apparent line of sight displacements of galaxies in redshift space, distorting the pattern of clustering in the radial versus transverse directions. On large scales, the amplitude of the distortion yields a measure of the dimensionless linear growth rate $\beta \approx \Omega^{0.6}/b$, where $\Omega$ is the cosmological density and $b$ the linear bias factor. To make the maximum statistical use of the data in a wide angle redshift survey, and for the greatest accuracy, the spherical character of the distortion needs to be treated properly, rather than in the simpler plane parallel approximation. In the linear regime, the redshift space correlation function is described by a spherical distortion operator acting on the true correlation function. It is pointed out here that there exists an operator, which is essentially the logarithmic derivative with respect to pair separation, which both commutes with the spherical distortion operator, and at the same time defines a characteristic scale of separation. The correlation function can be expanded in eigenfunctions of this operator, and these eigenfunctions are eigenfunctions of the distortion operator. Ratios of the observed amplitudes of the eigenfunctions yield measures of the linear growth rate $\beta$ in a manner independent of the shape of the correlation function. More generally, the logarithmic derivative $\partial/\partial\ln r$ with respect to depth $r$, along with the square $L^2$ and component $L_z$ of the angular momentum operator, form a complete set of commuting operators for the spherical distortion operator acting on the density. The eigenfunctions of this complete set of operators are spherical waves about the observer, with radial part lying in logarithmic real or Fourier space.Comment: 15 pages, with 1 embedded EPS figur

Lagrangian Evolution of the Weyl Tensor

We derive the evolution equations for the electric and magnetic parts of the Weyl tensor for cold dust from both general relativity and Newtonian gravity. In a locally inertial frame at rest in the fluid frame, the Newtonian equations agree with those of general relativity. We give explicit expressions for the electric and magnetic parts of the Weyl tensor in the Newtonian limit. In general, the magnetic part does not vanish, implying that the Lagrangian evolution of the fluid is not purely local.Comment: 17 pages, AAS LateX v3.0, submitted to ApJ, MIT-CSR-94-0

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation of why the hierarchical ansatz does not provide a good model of the covariance matrix in the non-linear regime, and new constraints on the amplitudes Ra and Rb for general 4-pt function configurations in the non-linear regim