Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime

A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1)xSU(2)xSU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang-Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb-Ramond fields.Comment: 57 pages; References added, section 2 rewritten and expande

A Novel View on the Physical Origin of E8

We consider a straightforward extension of the 4-dimensional spacetime $M_4$ to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in $M_4$. All those objects can be elegantly represented by the Clifford numbers $X\equiv x^A \gamma_A \equiv x^{a_1 ...a_r} \gamma_{a_1 ...a_r}, r=0,1,2,3,4$. This leads to the concept of the so-called Clifford space ${\cal C}$, a 16-dimensional manifold whose tangent space at every point is the Clifford algebra ${\cal C \ell }(1,3)$. The latter space besides an algebra is also a vector space whose elements can be rotated into each other in two ways: (i) either by the action of the rotation matrices of SO(8,8) on the components $x^A$ or (ii) by the left and right action of the Clifford numbers $R=$exp [\alpha^A \gam_A] and $S=$exp [\beta^A \gam_A] on $X$. In the latter case, one does not recover all possible rotations of the group SO(8,8). This discrepancy between the transformations (i) and (ii) suggests that one should replace the tangent space ${\cal C \ell}(1,3)$ with a vector space $V_{8,8}$ whose basis elements are generators of the Clifford algebra ${\cal C \ell}(8,8)$, which contains the Lie algebra of the exceptional group E$_8$ as a subspace. E$_8$ thus arises from the fact that, just as in the spacetime $M_4$ there are $r$-volumes generated by the tangent vectors of the spacetime, there are $R$-volumes, $R=0,1,2,3,...,16$, in the Clifford space ${\cal C}$, generated by the tangent vectors of ${\cal C}$.Comment: 14 page

AD Leonis: Radial Velocity Signal of Stellar Rotation or Spin–Orbit Resonance?

AD Leonis is a nearby magnetically active M dwarf. We find Doppler variability with a period of 2.23 days, as well as photometric signals: (1) a short-period signal, which is similar to the radial velocity signal, albeit with considerable variability; and (2) a long-term activity cycle of 4070 ± 120 days. We examine the short-term photometric signal in the available All-Sky Automated Survey and Microvariability and Oscillations of STars (MOST) photometry and find that the signal is not consistently present and varies considerably as a function of time. This signal undergoes a phase change of roughly 0.8 rad when considering the first and second halves of the MOST data set, which are separated in median time by 3.38 days. In contrast, the Doppler signal is stable in the combined High-Accuracy Radial velocity Planet Searcher and High Resolution Echelle Spectrometer radial velocities for over 4700 days and does not appear to vary in time in amplitude, phase, period, or as a function of extracted wavelength. We consider a variety of starspot scenarios and find it challenging to simultaneously explain the rapidly varying photometric signal and the stable radial velocity signal as being caused by starspots corotating on the stellar surface. This suggests that the origin of the Doppler periodicity might be the gravitational tug of a planet orbiting the star in spin–orbit resonance. For such a scenario and no spin–orbit misalignment, the measured v sin i indicates an inclination angle of 15°̣5 ± 2°̣5 and a planetary companion mass of 0.237 ± 0.047 M Jup

Rotation of planet-harbouring stars

The rotation rate of a star has important implications for the detectability, characterisation and stability of any planets that may be orbiting it. This chapter gives a brief overview of stellar rotation before describing the methods used to measure the rotation periods of planet host stars, the factors affecting the evolution of a star's rotation rate, stellar age estimates based on rotation, and an overview of the observed trends in the rotation properties of stars with planets.Comment: 16 pages, 4 figures: Invited review to appear in 'Handbook of Exoplanets', Springer Reference Works, edited by Hans J. Deeg and Juan Antonio Belmont

Accretion of Planetary Material onto Host Stars

Accretion of planetary material onto host stars may occur throughout a star's life. Especially prone to accretion, extrasolar planets in short-period orbits, while relatively rare, constitute a significant fraction of the known population, and these planets are subject to dynamical and atmospheric influences that can drive significant mass loss. Theoretical models frame expectations regarding the rates and extent of this planetary accretion. For instance, tidal interactions between planets and stars may drive complete orbital decay during the main sequence. Many planets that survive their stars' main sequence lifetime will still be engulfed when the host stars become red giant stars. There is some observational evidence supporting these predictions, such as a dearth of close-in planets around fast stellar rotators, which is consistent with tidal spin-up and planet accretion. There remains no clear chemical evidence for pollution of the atmospheres of main sequence or red giant stars by planetary materials, but a wealth of evidence points to active accretion by white dwarfs. In this article, we review the current understanding of accretion of planetary material, from the pre- to the post-main sequence and beyond. The review begins with the astrophysical framework for that process and then considers accretion during various phases of a host star's life, during which the details of accretion vary, and the observational evidence for accretion during these phases.Comment: 18 pages, 5 figures (with some redacted), invited revie

Extreme sensitivity in Snowball Earth formation to mountains on PaleoProterozoic supercontinents

During the PaleoProterozoic 2.45 to 2.2 billion years ago, several glaciations may have produced Snowball Earths. These glacial cycles occurred during large environmental change when atmospheric oxygen was increasing, a supercontinent was assembled from numerous landmasses, and collisions between these landmasses formed mountain ranges. Despite uncertainties in the composition of the atmosphere and reconstruction of the landmasses, paleoclimate model simulations can test the sensitivity of the climate to producing a Snowball Earth. Here we present a series of simulations that vary the atmospheric methane concentration and latitudes of west–east-oriented mountain ranges on an idealised supercontinent. For a given methane concentration, the latitudes of mountains control whether a Snowball Earth forms or not. Significantly, mountains in middle latitudes inhibited Snowball Earth formation, and mountains in low latitudes promoted Snowball Earth formation, with the supercontinent with mountains at ±30° being most conducive to forming a Snowball Earth because of reduced albedo at low latitudes. We propose that the extreme sensitivity of a Snowball Earth to reconstructions of the paleogeography and paleoatmospheric composition may explain the observed glaciations, demonstrating the importance of high-quality reconstructions to improved understanding of this early period in Earth’s history

Neighbourhood ethnic density effects on behavioural and cognitive problems among young racial/ethnic minority children in the US and England: a cross-national comparison

Studies on adult racial/ethnic minority populations show that the increased concentration of racial/ethnic minorities in a neighbourhood—a so-called ethnic density effect—is associated with improved health of racial/ethnic minority residents when adjusting for area deprivation. However, this literature has focused mainly on adult populations, individual racial/ethnic groups, and single countries, with no studies focusing on children of different racial/ethnic groups or comparing across nations. This study aims to compare neighbourhood ethnic density effects on young children’s cognitive and behavioural outcomes in the US and in England. We used data from two nationally representative birth cohort studies, the US Early Childhood Longitudinal Study-Birth Cohort and the UK Millennium Cohort Study, to estimate the association between own ethnic density and behavioural and cognitive development at 5 years of age. Findings show substantial heterogeneity in ethnic density effects on child outcomes within and between the two countries, suggesting that ethnic density effects may reflect the wider social and economic context. We argue that researchers should take area deprivation into account when estimating ethnic density effects and when developing policy initiatives targeted at strengthening and improving the health and development of racial and ethnic minority children