arXiv subjects

Zachary Slepian

Publications and source records attributed to Zachary Slepian.

78 records · Page 5Linked to original sources

arXiv2015

On the signature of the baryon-dark matter relative velocity in the two and three-point galaxy correlation functions

We develop a configuration-space picture of the relative velocity between baryons and dark matter that clearly explains how it can shift the BAO scale in the galaxy-galaxy correlation function. The shift occurs because the relative velocity is non-zero only within the sound horizon and thus adds to the correlation function asymmetrically about the BAO peak. We further show that in configuration space the relative velocity has a localized, distinctive signature in the three-point galaxy correlation function (3PCF). In particular, we find that a multipole decomposition is a favorable way to isolate the relative velocity in the 3PCF, and that there is a strong signature in the l=1 multipole for triangles with 2 sides around the BAO scale. Finally, we investigate a further compression of the 3PCF to a function of only one triangle side that preserves the localized nature of the relative velocity signature while also nicely separating linear from non-linear bias. We expect that this scheme will substantially lessen the computational burden of finding the relative velocity in the 3PCF. The relative velocity's 3PCF signature can be used to correct the shift induced in the galaxy-galaxy correlation function so that no systematic error due to this effect is introduced into the BAO as used for precision cosmology.

astro-ph.CO↗

arXiv2014

A one-parameter formula for testing slow-roll dark energy: observational prospects

Numerous upcoming observations, such as WFIRST, BOSS, BigBOSS, LSST, Euclid, and Planck, will constrain dark energy (DE)'s equation of state with great precision. They may well find the ratio of pressure to energy density, $w$, is -1, meaning DE is equivalent to a cosmological constant. However, many time-varying DE models have also been proposed. A single parametrization to test a broad class of them and that is itself motivated by a physical picture is therefore desirable. We suggest the simplest model of DE has the same mechanism as inflation, likely a scalar field slowly rolling down its potential. If this is so, DE will have a generic equation of state and the Universe will have a generic dependence of the Hubble constant on redshift independent of the potential's starting value and shape. This equation of state and expression for the Hubble constant offer the desired model-independent but physically motivated parametrization, because they will hold for most of the standard scalar-field models of DE such as quintessence and phantom DE. Up until now two-parameter descriptions of $w$ have been available, but this work finds an additional approximation that leads to a single-parameter model. Using it, we conduct a $χ^2$ analysis and find that experiments in the next seven years should be able to distinguish any of these time-varying DE models on the one hand from a cosmological constant on the other to 73% confidence if $w$ today differs from -1 by 3.5%. In the limit of perfectly accurate measurements of $Ω_m$ and $H_0$, this confidence would rise to 96%. We also include discussion of the current status of DE experiment, a table compiling the techniques each will use, and tables of the precisions of the experiments for which this information was available at the time of publication.

astro-ph.CO↗

arXiv2012

The Average Projected Area Theorem - Generalization to Higher Dimensions

In 3-d the average projected area of a convex solid is 1/4 the surface area, as Cauchy showed in the 19th century. In general, the ratio in n dimensions may be obtained from Cauchy's surface area formula, which is in turn a special case of Kubota's theorem. However, while these latter results are well-known to those working in integral geometry or the theory of convex bodies, the results are largely unknown to the physics community---so much so that even the 3-d result is sometimes said to have first been proven by an astronomer in the early 20th century! This is likely because the standard proofs in the mathematical literature are, by and large, couched in terms of concepts that are may not be familiar to many physicists. Therefore, in this work, we present a simple geometrical method of calculating the ratio of average projected area to surface area for convex bodies in arbitrary dimensions. We focus on a pedagogical, physically intuitive treatment that it is hoped will be useful to those in the physics community. We do discuss the mathematical background of the theorem as well, pointing those who may be interested to sources that offer the proofs that are standard in the fields of integral geometry and the theory of convex bodies. We also provide discussion of the applications of the theorem, especially noting that higher-dimensional ratios may be of use for constructing observational tests of string theory. Finally, we examine the limiting behavior of the ratio with the goal of offering intuition on its behavior by pointing out a suggestive connection with a well-known fact in statistics.

math.DG↗

arXiv2012

Ruling Out Bosonic Repulsive Dark Matter in Thermal Equilibrium

Self-interacting dark matter (SIDM), especially bosonic, has been considered a promising candidate to replace cold dark matter (CDM) as it resolves some of the problems associated with CDM. Here, we rule out the possibility that dark matter is a repulsive boson in thermal equilibrium. We develop the model first proposed by Goodman (2000) and derive the equation of state at finite temperature. Isothermal spherical halo models indicate a Bose-Einstein condensed core surrounded by a non-degenerate envelope, with an abrupt density drop marking the boundary between the two phases. Comparing this feature with observed rotation curves constrains the interaction strength of our model's DM particle, and Bullet Cluster measurements constrain the scattering cross section. Both ultimately can be cast as constraints on the particle's mass. We find these two constraints cannot be satisfied simultaneously in any realistic halo model---and hence dark matter cannot be a repulsive boson in thermal equilibrium. It is still left open that DM may be a repulsive boson provided it is not in thermal equilibrium; this requires that the mass of the particle be significantly less than a millivolt.

astro-ph.CO↗

arXiv2011

Dark Energy as Double N-Flation--Observational Predictions

We propose a simple model for dark energy useful for comparison with observations. It is based on the idea that dark energy and inflation should be caused by the same physical process. As motivation, we note that Linde's simple chaotic inflation $V=(1/2)m^{2}ϕ^{2}$ produces values of $n_{s}=0.967$ and $r=0.13$, which are consistent with the WMAP 1-sigma error bars. We therefore propose $V=(1/2)m_{2}^{2}ϕ_{2}^{2}+(1/2)m_{1}^{2}ϕ_{1}^{2}$ with $m_{1}\sim10^{-5}$ and $m_{2}\leq10^{-60}$, where $c=1=\hbar$ and the reduced Planck mass is set to unity. The field $ϕ_{1}$ drives inflation and has damped by now ($ϕ_{1,0}=0$), while $ϕ_{2}$ is currently rolling down its potential to produce dark energy. Using this model, we derive the formula $δw(z)\equiv w(z)+1=δw_{0}(H_0/H(z))^2$ via the slow-roll approximation. Our numerical results from exact and self-consistent solution of the equations of motion for $ϕ_2$ and the Friedmann equations support this formula, and it should hold for any slow-roll dark energy. Our potential can be easily realized in N-flation models with many fields, and is easily falsifiable by upcoming experiments -- for example, if Linde's chaotic inflation is ruled out. But if $r$ values consistent with Linde's chaotic inflation are detected then one should take this model seriously indeed.

astro-ph.CO↗

arXiv2011

Chance and Chandra (and repulsive dark matter)

A few examples are given of Chandra's work on statistical and stochastic problems that relate to open questions in astrophysics, in particular his theory of dynamical relaxation in systems with inverse-square interparticle forces. The roles of chaos and integrability in this theory require clarification, especially for systems having a dominant central mass. After this prelude, a hypothetical form of repulsive bosonic dark matter is discussed. The repulsion leads to nontrivial thermodynamic behavior, including superfluidity, and would tend to suppress dynamical friction, greatly reducing the drag exerted on rotating galactic bars. However, this form of dark matter can probably be ruled out, at least for parameters that allow halos to reach thermal equilibria within a Hubble time. One combination of the particle mass and interparticle repulsion determines the minimum core radius of dark halos. Bounds on dark-matter collisionality inferred from the Bullet Cluster constrain a second combination. It is possible to satisfy both constraints only for parameters that predict unacceptable rotation curves outside the halo core.

astro-ph.CO↗