Form Invariance of Differential Equations in General Relativity

Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second order nonlinear ordinary differential equation $\ddot{y}+\alpha f(y)\dot{y}+\beta f(y)\int{f(y) dy}+\gamma f(y)=0$. Also, it appears in the generalized statistical mechanics for the most interesting value q=-1. The invariant form of this equation is imposed and the corresponding nonlocal transformation is obtained. The linearization of that equation for any $\alpha, \beta$ and $\gamma$ is presented and for the important case $f=by^n+k$ with $\beta=\alpha ^2 (n+1)/((n+2)^2)$ its explicit general solution is found. Moreover, the form invariance is applied to yield exact solutions of same other differential equations.Comment: 22 pages, RevTeX; to appear in J. Math. Phy

Persistence pays: how viruses promote host group survival.

Recently, we have realized that viruses numerically dominate all life. Although viruses are known to affect host survival in populations, this has not been previously evaluated in the context of host group selection. Group selection per se is not a currently accepted idea and its apparent occurrence is explained by statistical gene frequency models of kin selection. Viruses were not considered in such models. Prevalent views associate viruses and disease. Yet many viruses establish species-specific persistent, inapparent infections that are stable on an evolutionary time scale. Such persistent infections can have large effects on relative reproductive fitness of competing host populations. In this essay, I present arguments on how persistent infections can promote population survival. Mouse hepatitis virus is used as well studied examplar to re-evaluate the theoretical basis of the mouse haystack model of M Smith. This virus-centric re-examination concludes that viruses can indeed affect and promote relative group selection

Interacting fluids generating identical, dual and phantom cosmologies

We find the group of symmetry transformations generated by interacting fluids in spatially flat Friedmann-Robertson-Walker (FRW) spacetime which links cosmologies with the same scale factor {\it (identity)} or with scale factors $a$ and $a^{-1}$ {\it (duality)}. There exists a duality between contracting and superaccelerated expanding scenarios associated with {\it (phantom)} cosmologies. We investigate the action of this symmetry group on self-interacting minimally(conformally) coupled quintessence and $k$-essence cosmologies.Comment: 5 pages, revised version accepted for publication in PL

Linear and nonlinear interactions in the dark sector

We investigate models of interacting dark matter and dark energy for the universe in a spatially flat Friedmann-Robertson-Walker (FRW) space-time. We find the "source equation" for the total energy density and determine the energy density of each dark component. We introduce an effective one-fluid description to evidence that interacting and unified models are related with each other, analyze the effective model and obtain the attractor solutions. We study linear and nonlinear interactions, the former comprises a linear combination of the dark matter and dark energy densities, their first derivatives, the total energy density, its first and second derivatives and a function of the scale factor. The latter is a possible generalization of the linear interaction consisting of an aggregate of the above linear combination and a significant nonlinear term built with a rational function of the dark matter and dark energy densities homogeneous of degree one. We solve the evolution equations of the dark components for both interactions and examine exhaustively several examples. There exist cases where the effective one-fluid description produces different alternatives to the \LaCDM model and cases where the problem of coincidence is alleviated. In addition, we find that some nonlinear interactions yield an effective one-fluid model with a Chaplygin gas equation of state, whereas others generate cosmological models with de Sitter and power-law expansions. We show that a generic nonlinear interaction induces an effective equation of state which depends on the scale factor in the same way that the variable modified Chaplygin gas model, giving rise to the "relaxed Chaplygin gas model".Comment: Accepted for publication in PR

Exactly solved models of interacting dark matter and dark energy

We introduce an effective one-fluid description of the interacting dark sector in a spatially flat Friedmann-Robertson-Walker space-time and investigate the stability of the power-law solutions. We find the "source equation" for the total energy density and determine the energy density of each dark component. We study linear and nonlinear interactions which depend on the dark matter and dark energy densities, their first derivatives, the total energy density with its derivatives up to second order and the scale factor. We solve the evolution equations of the dark components for both interactions, examine exhaustively several examples and show cases where the problem of the coincidence is alleviated. We show that a generic nonlinear interaction gives rise to the "relaxed Chaplygin gas model" whose effective equation of state includes the variable modified Chaplygin gas model while some others nonlinear interactions yield de Sitter and power-law scenarios.Comment: To appear in the proceedings of the CosmoSul conference, held in Rio de Janeiro, Brazil, 01-05 august of 2011. References adde

Force for ancient and recent life: viral and stem-loop RNA consortia promote life.

Lytic viruses were thought to kill the most numerous host (i.e., kill the winner). But persisting viruses/defectives can also protect against viruses, especially in a ubiquitous virosphere. In 1991, Yarmolinsky et al. discovered the addiction modules of P1 phage, in which opposing toxic and protective functions stabilize persistence. Subsequently, I proposed that lytic and persisting cryptic virus also provide addiction modules that promote group identity. In eukaryotes (and the RNA world), a distinct RNA virus-host relationship exists. Retrovirurses/retroposons are major contributors to eukaryotic genomes. Eukaryotic complexity appears to be mostly mediated by regulatory complexity involving noncoding retroposon-derived RNA. RNA viruses evolve via quasispecies, which contain cooperating, minority, and even opposing RNA types. Quasispecies can also demonstrate group preclusion (e.g., hepatitis C). Stem-loop RNA domains are found in long terminal repeats (and viral RNA) and mediate viral regulation/identity. Thus, stem-loop RNAs may be ancestral regulators. I consider the RNA (ribozyme) world scenario from the perspective of addiction modules and cooperating quasispecies (i.e., subfunctional agents that establish group identity). Such an RNA collective resembles a "gang" but requires the simultaneous emergence of endonuclease, ligase, cooperative catalysis, group identity, and history markers (RNA). I call such a collective a gangen (pathway to gang) needed for life to emerge

Radio Continuum Sources Associated with AB Aur

We present high angular resolution, high-sensitivity Very Large Array observations at 3.6 cm of the Herbig Ae star AB Aur. This star is of interest since its circumstellar disk exhibits characteristics that have been attributed to the presence of an undetected low mass companion or giant gas planet. Our image confirms the continuum emission known to exist in association with the star, and detects a faint protuberance that extends about $0\rlap.{''}3$ to its SE. Previous theoretical considerations and observational results are consistent with the presence of a companion to AB Aur with the separation and position angle derived from our radio data. We also determine the proper motion of AB Aur by comparing our new observations with data taken about 17 years ago and find values consistent with those found by Hipparcos.Comment: 6 pages, 1 figur