A Constructive Treatment to Elemental Life Forms through Mathematical Philosophy

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation.

Extracting the astrophysics of reionization from the Lyα forest power spectrum: a first forecast

ABSTRACT The impact of cosmic reionization on the Lyα forest power spectrum has recently been shown to be significant even at low redshifts (z ∼ 2). This memory of reionization survives cosmological time-scales because high-entropy mean-density gas is heated to ∼3 × 104 K by reionization, which is inhomogeneous, and subsequent shocks from denser regions. In the near future, the first measurements of the Lyα forest 3D power spectrum will be very likely achieved by upcoming observational efforts such as the Dark Energy Spectroscopic Instrument (DESI). In addition to abundant cosmological information, these observations have the potential to extract the astrophysics of reionization from the Lyα forest. We forecast, for the first time, the accuracy with which the measurements of Lyα forest 3D power spectrum can place constraints on the reionization parameters with DESI. Specifically, we demonstrate that the constraints on the ionization efficiency, ζ, and the threshold mass for haloes that host ionizing sources, mturn, will have the 1σ error at the level of ζ = 25.0 ± 11.6 and $\log _{10} (m_{\rm turn}/{\rm M}_\odot) = 8.7^{+0.36}_{-0.70}$, respectively. The Lyα forest 3D power spectrum will thus provide an independent probe of reionization, probably even earlier in detection with DESI, with a sensitivity only slightly worse than the upcoming 21-cm power spectrum measurement with the Hydrogen Epoch of Reionization Array (HERA), i.e. σDESI/σHERA ≈ 1.5 for ζ and σDESI/σHERA ≈ 2.0 for log10(mturn/M⊙). Nevertheless, the Lyα forest constraint will be improved about three times tighter than the current constraint from reionization observations with high-z galaxy priors, i.e. σDESI/σcurrent ≈ 1/3 for ζ.

Analytical Solution to FRW Metric with Variable Speed of Light

<p>According to the principle of general covariance, the laws of physics are the same in all reference frames. The controversial theory of the Varying Speed of Light (VSL) contradicts the principle of general covariance. Fortunately the VLS theory explains some crucial issues in cosmology such as Lorentz variance, biometric theories, locally Lorentz variance, cosmological constant problem, horizon<em> </em>and flatness<em> </em>problems. Also, recent astronomical observations from quasar show that the fine structural constant depends on redshift and therefore, varies with cosmological time. In other to harness this fascinating and published knowledge, two models where used in this work. 1. Cosmology with variables c; here the Friedmann-Robertson-Walker (FRW) is used in the Einstein field equation with variable c and Λ terms to obtain the scale factor, which shows the continuous exponential expansion of the universe. 2. Variation of the speed of light as a function of the scale factor of the universe; here we obtained: a good approximation to estimate the current age of the universe. The scale factor of the universe depends its content given by the equation of state parameter ω. We obtained the deceleration parameter in terms of the Hubble parameter. We arrived at a conclusion that the universe was decelerating at ω = 1, accelerating at ω = 1/3 and the Hubble parameter diverges at the beginning and end of the universe.</p>

Stealth decaying spin-1 dark matter

We consider models of decaying spin-1 dark matter whose dominant coupling to the standard model sector is through a dark-Higgs Yukawa portal connecting a TeV-scale vector-like lepton to the standard model (right-handed) electron. Below the electron-positron threshold, dark matter has very slow, loop-suppressed decays to photons and (electron) neutrinos, and is stable on cosmological time-scale for sufficiently small gauge coupling values. Its relic abundance is set by in-equilibrium dark lepton decays, through the freeze-in mechanism. We show that this model accommodates the observed dark matter abundance for natural values of its parameters and a dark matter mass in the ∼ 5 keV to 1 MeV range, while evading constraints from direct detection, indirect detection, stellar cooling and cosmology. We also consider the possibility of a nonzero gauge kinetic mixing with the standard model hypercharge field, which is found to yield a mild impact on the model’s phenomenology.

Cosmological time crystals from Einstein-cubic gravities

By including appropriate Riemann-cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the two vacua with the same scale factor a, but opposite $${\dot{a}}$$ a ˙ . The tunneling from one vacuum to the other provides a robust mechanism for bounce universes; it always occurs for systems with positive energy density. For a suitable matter energy-momentum tensor we also construct cyclic universes. Cosmological solutions that resemble the classical time crystals can be constructed in massive gravity.

Cosmological Time

This chapter examines the role of Islamic temporal cosmology in villagers’ lives. It focuses on how moments of daily prayer, fasting, and worship are entwined with the materials of temporal textures, in particular in their calendric and time-measuring forms. These entwinements co-constitute villagers’ religious experience, and offer improvised techniques for making meaning and organizing social life. This chapter argues that any study of secular temporal orientations needs to be viewed in parallel with the modes of temporal reasoning and practice that are derived from Islamic temporal conceptions.