arXiv subjects

Robert J. Scherrer

Publications and source records attributed to Robert J. Scherrer.

123 records · Page 7Linked to original sources

arXiv1999

Inhomogeneous Neutrino Degeneracy and Big Bang Nucleosynthesis

We examine Big Bang nucleosynthesis (BBN) in the case of inhomogenous neutrino degeneracy, in the limit where the fluctuations are sufficiently small on large length scales that the present-day element abundances are homogeneous. We consider two representive cases: degeneracy of the electron neutrino alone, and equal chemical potentials for all three neutrinos. We use a linear programming method to constrain an arbitrary distribution of the chemical potentials. For the current set of (highly-restrictive) limits on the primordial element abundances, homogeneous neutrino degeneracy barely changes the allowed range of the baryon-to-photon ratio. Inhomogeneous degeneracy allows for little change in the lower bound on the baryon-to-photon ratio, but the upper bound in this case can be as large as 1.1 \times 10^{-8} (only electron neutrino degeneracy) or 1.0 \times 10^{-9} (equal degeneracies for all three neutrinos). For the case of inhomogeneous neutrino degeneracy, we show that there is no BBN upper bound on the neutrino energy density, which is bounded in this case only by limits from structure formation and the cosmic microwave background.

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arXiv1999

Improved Treatment of Cosmic Microwave Background Fluctuations Induced by a Late-decaying Massive Neutrino

A massive neutrino which decays after recombination (t > 10^{13} sec) into relativistic decay products produces an enhanced integrated Sachs-Wolfe effect, allowing constraints to be placed on such neutrinos from present cosmic microwave background anisotropy data. Previous treatments of this problem have approximated the decay products as an additional component of the neutrino background. This approach violates energy-momentum conservation, and we show that it leads to serious errors for some neutrino masses and lifetimes. We redo this calculation more accurately, by correctly incorporating the spatial distribution of the decay products. For low neutrino masses and long lifetimes, we obtain a much smaller distortion in the CMB fluctuation spectrum than have previous treatments. We combine these new results with a recent set of CMB data to exclude the mass and lifetime range m_h > 100 eV, τ> 10^{12} sec. Masses as low as 30 eV are excluded for a narrower range in lifetime.

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arXiv1998

Constraining Variations in the Fine-Structure Constant with the Cosmic Microwave Background

Any time variation in the fine-structure constant alters the ionization history of the universe and therefore changes the pattern of cosmic microwave background fluctuations. We calculate the changes in the spectrum of these fluctuations as a function of the change in the fine-structure constant, and we find that these changes are dominated by the change in the redshift of recombination due to the shift in the binding energy of hydrogen. We estimate the accuracy with which the next generation of cosmic microwave background experiments might constrain any variation in the fine-structure constant at z of roughly 1000. We find that such experiments could potentially be sensitive to $|Δα/α| \sim 10^{-2} - 10^{-3}$.

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arXiv1998

"Lattice-Free" Simulations of Topological Defect Formation

We examine simulations of the formation of domain walls, cosmic strings, and monopoles on a cubic lattice, in which the topological defects are assumed to lie at the zeros of a piecewise constant 1, 2, or 3 component Gaussian random field, respectively. We derive analytic expressions for the corresponding topological defect densities in the continuum limit and show that they fail to agree with simulation results, even when the fields are smoothed on small scales to eliminate lattice effects. We demonstrate that this discrepancy, which is related to a classic geometric fallacy, is due to the anisotropy of the cubic lattice, which cannot be eliminated by smoothing. This problem can be resolved by linearly interpolating the field values on the lattice, which gives results in good agreement with the continuum predictions. We use this procedure to obtain a lattice-free estimate (for Gaussian smoothing) of the fraction of the total length of string in the form of infinite strings: $f_\infty = 0.716 \pm 0.015$.

hep-ph↗

arXiv1998

Probing Unstable Massive Neutrinos with Current Cosmic Microwave Background Observations

The pattern of anisotropies in the Cosmic Microwave Background depends upon the masses and lifetimes of the three neutrino species. A neutrino species of mass greater than 10 eV with lifetime between 10^{13} sec and 10^{17} sec leaves a very distinct signature (due to the integrated Sachs-Wolfe effect): the anisotropies at large angles are predicted to be comparable to those on degree scales. Present data exclude such a possibility and hence this region of parameter space. For $m_ν\simeq 30$ eV, $τ\simeq 10^{13}$ sec, we find an interesting possibility: the Integrated Sachs Wolfe peak produced by the decaying neutrino in low-$Ω$ models mimics the acoustic peak expected in an $Ω= 1$ model.

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arXiv1997

Constraints on the Effects of Locally-biased Galaxy Formation

While it is well-known that "biased galaxy formation" can increase the strength of galaxy clustering, it is less clear whether straightforward biasing schemes can change the shape of the galaxy correlation function on large scales. Here we consider "local" biasing models, in which the galaxy density field $δ_g$ at a point is a function of the matter density field $δ$ at that point: $δ_g = f(δ)$. We consider both deterministic biasing, where $f$ is simply a function, and stochastic biasing, in which the galaxy density is a random variable whose distribution depends on the matter density: $δ_g=X(δ)$. We show that even when this mapping is performed on a highly nonlinear density field with a hierarchical correlation structure, the correlation function $ξ$ is simply scaled up by a constant, as long as $ξ<< 1$. In stochastic biasing models, the galaxy autocorrelation function behaves exactly as in deterministic models, with the mean value of $X$ for a given value of $δ$ taking the role of the deterministic bias function. We extend our results to the power spectrum P(k), showing that for sufficiently small k, the effect of local biasing is equivalent to the multiplication of P(k) by a constant, with the addition of a constant term. If a cosmological model predicts a large-scale mass correlation function in conflict with the shape of the observed galaxy correlation function, then the model cannot be rescued by appealing to a complicated but local relation between galaxies and mass.

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arXiv1997

Cosmic String Formation from Correlated Fields

We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum $P(k) \propto k^n$, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over previous simulations: we include a non-zero random background field in our box to simulate the effect of long-wavelength modes, and we examine the effects of smoothing the field on small scales. The inclusion of the background field significantly reduces the fraction of length in infinite strings for $n < -2$. Our results are consistent with the possibility that infinite strings disappear at some $n = n_c$ in the range $-3 \le n_c < -2.2$, although we cannot rule out $n_c = -3$, in which case infinite strings would disappear only at the point where the mean string density goes to zero. We present an analytic argument which suggests the latter case. Smoothing on small scales eliminates closed loops on the order of the lattice cell size and leads to a ``lattice-free" estimate of the infinite string fraction. As expected, this fraction depends on the type of window function used for smoothing.

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arXiv1996

Testing Tree-Level Perturbation Theory for Large-Scale Structure with the Local Lagrangian Approximation

We test tree-level perturbation theory for Gaussian initial conditions with power spectra $P(k)\propto k^n$ by comparing the probability distribution function (PDF) for the density predicted by the Local Lagrangian Approximation (LLA) with the results of numerical gravitational clustering simulations. Our results indicate that our approximation correctly reproduces the evolved density PDF for $-3 \leq n \leq-1$ power spectra up to the weakly nonlinear regime, while it shows marginal agreement for power indices n=0 and +1 in the linear regime and poor agreement beyond this point. This suggests that tree-level perturbation theory (as realized in the Local Lagrangian Approximation) can accurately predict the density distribution function for $-3 \leq n \leq -1$ but fails for $n \ge 0$.

astro-ph↗

arXiv1996

Skewness of the Large-Scale Velocity Divergence from Non-Gaussian Initial Conditions

We compute the skewness $t_3$ and the corresponding hierarchical amplitude $T_3$ of the divergence of the velocity field for arbitrary non-Gaussian initial conditions. We find that $T_3$ qualitatively resembles the corresponding hierarchical amplitude for the density field, $S_3$, in that it contains a term proportional to the initial skewness, which decays inversely as the linear growth factor, plus a constant term which differs from the corresponding Gaussian term by a complex function of the initial three- and four- point functions. We extend the results for $S_3$ and $T_3$ with non-Gaussian initial conditions to evolved fields smoothed with a spherical tophat window function. We show that certain linear combinations, namely $S_3 + {1 \over 2} T_3$, $S_3 + T_3$, and $s_3 + t_3$, lead to expressions which are much simpler, for non-Gaussian initial conditions, than $S_3$ and $T_3$ (or $s_3$ and $t_3$) considered separately.

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arXiv1996

Local Lagrangian Approximations for the Evolution of the Density Distribution Function in Large-Scale Structure

We examine local Lagrangian approximations for the gravitational evolution of the density distribution function. In these approximations, the final density at a Lagrangian point q at a time t is taken to be a function only of t and of the initial density at the same Lagrangian point. A general expression is given for the evolved density distribution function for such approximations, and we show that the vertex generating function for a local Lagrangian mapping applied to an initially Gaussian density field bears a simple relation to the mapping itself. Using this result, we design a local Lagrangian mapping which reproduces nearly exactly the hierarchical amplitudes given by perturbation theory for gravitational evolution. When extended to smoothed density fields and applied to Gaussian initial conditions, this mapping produces a final density distribution function in excellent agreement with full numerical simulations of gravitational clustering. We also examine the application of these local Lagrangian approximations to non-Gaussian initial conditions.

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arXiv1995

A linear programming approach to inhomogeneous primordial nucleosynthesis

We examine inhomogeneous primordial nucleosynthesis for {\it arbitrary} distributions $f$ of the baryon-to-photon ratio $η$, in the limit where neither particle diffusion nor gravitational collapse is important. By discretizing $f(η)$ and using linear programming, we show that for a set of $m$ constraints on the primordial element abundances, the maximum and minimum possible values of $\bar η$ (the final mean value of $η$) are given when $f(η)$ is a sum of at most $m+1$ delta functions. Our linear programming results indicate that when $f$ is taken to be an arbitrary function, there is no lower bound on $\bar η$, while the upper bound is essentially the homogeneous upper bound.

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arXiv1995

Differential neutrino heating and reduced $^4$He production from decaying particles in the early universe

A decaying particle that dominates the energy density of the universe and then decays with a lifetime $\sim 10^{-1}$ sec into electromagnetically-interacting particles can heat the background electron neutrinos more than the $μ$ and $τ$ neutrinos, resulting in a decrease in the primordial $^4$He abundance. Previous calculations of this effect assumed sudden decoupling of the neutrinos from the electromagnetic plasma. Here we repeat this calculation using an improved (although still approximate) treatment of the energy flow from the blackbody radiation into the various neutrino components. We find that with our improved calculation, the reduction in the primordial $^4$He is not as large as had been previously thought, but it occurs over a larger range in decaying particle lifetime $τ$. The reduction in $^4$He can be as large as $ΔY = -0.01$ for $τ= 0.1 - 0.7$ sec.

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arXiv1995

Constraints on Self-Interacting Dark Matter

We consider the growth of density perturbations in the presence of self--interacting dark matter, SIDM, proposed by Carlson, Machacek and Hall (1992). We determine the range of values for the coupling constant $λ$ and the particle mass $m^\prime$, for which the power spectrum lies in the ``allowed" range based on constraints from the IRAS galaxy survey and damped Lyman--$α$ systems. Our results show that no combination of parameters can meet both limits. We consider constraints on the $\2-2$ scatterings which keep the SIDM particles in pressure equilibrium, and we show that if such interactions maintain pressure equilibrium down to the present, they will be strong enough to disrupt galaxy mergers and may lead to stripping of galaxy halos as galaxies move through the dark matter background of these particles. Hence, we also investigate the evolution of large-scale structure in the SIDM model when the particles drop out of pressure equilibrium at some higher redshift. The resulting free-streaming leads to an additional suppression of small-scale perturbations, but it does not significantly affect our results.

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arXiv1994

When Can Non-Gaussian Density Fields Produce a Gaussian Sachs-Wolfe Effect?

The Sachs-Wolfe temperature fluctuations produced by primordial density perturbations are proportional to the potential field ϕ, which is a weighted integral over the density field δ. Because of the central limit theorem, ϕcan be approximately Gaussian even when δis non-Gaussian. Using the Wold representation for non-Gaussian density fields, δ(\rvec) = \int f(|\rvec - \rvec^\prime|) Δ(\rvec^\prime) d^3 \rvec^\prime, we find conditions on Δand f for which ϕmust have a Gaussian one-point distribution, while δcan be non-Gaussian. Sufficient (but not necessary) conditions are that the density field have a power spectrum (which determines f) of P(k) \propto k^n, with -2 < n \le +1, and that Δ(\rvec) be non-Gaussian with no long-range correlations. Thus, there is an infinite set of non-Gaussian density fields which produce a nearly Gaussian one-point distribution for the Sachs-Wolfe effect.

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arXiv1994

Velocity Differences as a Probe of Non--Gaussian Density Fields

We examine the multi--point velocity field for non--Gaussian models as a probe of non--Gaussian behavior. The two--point velocity correlation is not a useful indicator of a non--Gaussian density field, since it depends only on the power spectrum, even for non--Gaussian models. However, we show that the distribution of velocity differences $\bfv_1 - \bfv_2$, where $\bfv_1$ and $\bfv_2$ are measured at the points $\bfr_1$ and $\bfr_2$, respectively, is a good probe of non--Gaussian behavior, in that $p(\bfv_1 - \bfv_2)$ tends to be non--Gaussian whenever the density field is non--Gaussian. As an example, we examine the behavior of $p(\bfv_1 - \bfv_2)$ for non--Gaussian seed models, in which the density field is the convolution of a distribution of points with a set of density profiles. We apply these results to the global texture model.

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