Statistics of Gravitational Microlensing Magnification. I. Two-Dimensional Lens Distribution

(Abridged) In this paper we refine the theory of microlensing for a planar distribution of point masses. We derive the macroimage magnification distribution P(A) at high magnification (A-1 >> tau^2) for a low optical depth (tau << 1) lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual ``point mass plus weak shear'' lenses. We show that a point mass plus weak shear lens produces an astroid- shaped caustic and that the magnification cross-section obeys a simple scaling property. By convolving this cross-section with the shear distribution, we obtain a caustic-induced feature in P(A) which also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A approx 2/tau. In the low magnification (A-1 << 1) limit, the macroimage consists of a bright primary image and a large number of faint secondary images formed close to each of the point masses. Taking into account the correlations between the primary and secondary images, we derive P(A) for low A. The low-A distribution has a peak of amplitude ~ 1/tau^2 at A-1 ~ tau^2 and matches smoothly to the high-A distribution. We combine the high- and low-A results and obtain a practical semi-analytic expression for P(A). This semi-analytic distribution is in qualitative agreement with previous numerical results, but the latter show stronger caustic-induced features at moderate A for tau as small as 0.1. We resolve this discrepancy by re-examining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approx 1-exp(-8 tau). For tau=0.1, the fraction is surprisingly high: approx 55%. For the purpose of computing P(A) in the manner we did, low optical depth corresponds to tau << 1/8.Comment: 35 pages, including 6 figures; uses AASTeX v4.0 macros; submitted to Ap

Static chaos and scaling behaviour in the spin-glass phase

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed point exponent $\theta$ is very close to $\frac{d-3}{2}$. In both approaches $d=3$ is the lower critical dimension in agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil

Cosmic Acceleration from Causal Backreaction with Recursive Nonlinearities

We revisit the causal backreaction paradigm, in which the need for Dark Energy is eliminated via the generation of an apparent cosmic acceleration from the causal flow of inhomogeneity information coming in towards each observer from distant structure-forming regions. This second-generation formalism incorporates "recursive nonlinearities": the process by which already-established metric perturbations will then act to slow down all future flows of inhomogeneity information. Here, the long-range effects of causal backreaction are now damped, weakening its impact for models that were previously best-fit cosmologies. Nevertheless, we find that causal backreaction can be recovered as a replacement for Dark Energy via the adoption of larger values for the dimensionless `strength' of the clustering evolution functions being modeled -- a change justified by the hierarchical nature of clustering and virialization in the universe, occurring on multiple cosmic length scales simultaneously. With this, and with one new model parameter representing the slowdown of clustering due to astrophysical feedback processes, an alternative cosmic concordance can once again be achieved for a matter-only universe in which the apparent acceleration is generated entirely by causal backreaction effects. One drawback is a new degeneracy which broadens our predicted range for the observed jerk parameter $j_{0}^{\mathrm{Obs}}$, thus removing what had appeared to be a clear signature for distinguishing causal backreaction from Cosmological Constant $\Lambda$CDM. As for the long-term fate of the universe, incorporating recursive nonlinearities appears to make the possibility of an `eternal' acceleration due to causal backreaction far less likely; though this does not take into account gravitational nonlinearities or the large-scale breakdown of cosmological isotropy, effects not easily modeled within this formalism.Comment: 53 pages, 7 figures, 3 tables. This paper is an advancement of previous research on Causal Backreaction; the earlier work is available at arXiv:1109.4686 and arXiv:1109.515

ISW effect as probe of features in the expansion history of the Universe

In this paper, using and implementing a new line of sight CMB code, called CMBAns [1], that allows us to modify H(z) for any given feature at any redshift we study the effect of changes in the expansion history of the Universe on the CMB power spectrum. Motivated by the detailed analytical calculations of the effects of the changes in H(z) on ISW plateau and CMB low multipoles, we study two phenomenological parametric form of the expansion history using WMAP data and through MCMC analysis. Our MCMC analysis shows that the standard LCDM cosmological model is consistent with the CMB data allowing the expansion history of the Universe vary around this model at different redshifts. However, our analysis also shows that a decaying dark energy model proposed in [2] has in fact a marginally better fit than the standard cosmological constant model to CMB data. Concordance of our studies here with the previous analysis showing that Baryon Acoustic Oscillation (BAO) and supernovae data (SN Ia) also prefer mildly this decaying dark energy model to LCDM, makes this finding interesting and worth further investigation.Comment: 20 pages, 11 figures, 2 tables, discussions extended, references added, results unchanged, matches final version published in JCA