On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy

This version deposited at arxiv 02-10-12 arXiv:1210.0730v1. Subsequently published in Physical Review D as Phys. Rev. D 87, 063517 (2013) http://link.aps.org/doi/10.1103/PhysRevD.87.063517. Copyright American Physical Society (APS).11 pages11 pages11 pages11 pagesThe problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems may not be compatible with late-time acceleration driven by anything other than a constant term of the form f(0), which acts like a cosmological constant. For theories with f(R)=R^n we find that no known spherically symmetric vacuum solutions can be matched to an expanding FLRW background. This includes the absence of any Einstein-Straus-like embeddings of the Schwarzschild exterior solution in FLRW spacetimes

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

The Method of Images in Cosmology

31 pages, 18 figures31 pages, 18 figuresWe apply the method of images to the exact initial data for cosmological models that contain a number of regularly arranged discrete masses. This allows us to join cosmological regions together by throats, and to construct wormholes in the initial data. These wormholes allow for the removal of the asymptotically flat "flange" regions that would otherwise exist on the far side of black holes. The method of images also provides us with a way to investigate the definition of mass is cosmology, and the cosmological consequences of the gravitational interaction energies between massive objects. We find evidence that the interaction energies within clusters of massive objects do indeed appear to contribute to the total energy budget in the cosmological regions of the space-time

The Conserved MAPK Site in E(spl)-M8, an Effector of Drosophila Notch Signaling, Controls Repressor Activity during Eye Development

The specification of patterned R8 photoreceptors at the onset of eye development depends on timely inhibition of Atonal (Ato) by the Enhancer of split (E(spl) repressors. Repression of Ato by E(spl)-M8 requires the kinase CK2 and is inhibited by the phosphatase PP2A. The region targeted by CK2 harbors additional conserved Ser residues, raising the prospect of regulation via multi-site phosphorylation. Here we investigate one such motif that meets the consensus for modification by MAPK, a well-known effector of Epidermal Growth Factor Receptor (EGFR) signaling. Our studies reveal an important role for the predicted MAPK site of M8 during R8 birth. Ala/Asp mutations reveal that the CK2 and MAPK sites ensure that M8 repression of Ato and the R8 fate occurs in a timely manner and at a specific stage (stage-2/3) of the morphogenetic furrow (MF). M8 repression of Ato is mitigated by halved EGFR dosage, and this effect requires an intact MAPK site. Accordingly, variants with a phosphomimetic Asp at the MAPK site exhibit earlier (inappropriate) activity against Ato even at stage-1 of the MF, where a positive feedback-loop is necessary to raise Ato levels to a threshold sufficient for the R8 fate. Analysis of deletion variants reveals that both kinase sites (CK2 and MAPK) contribute to ‘cis’-inhibition of M8. This key regulation by CK2 and MAPK is bypassed by the E(spl)D mutation encoding the truncated protein M8*, which potently inhibits Ato at stage-1 of R8 birth. We also provide evidence that PP2A likely targets the MAPK site. Thus multi-site phosphorylation controls timely onset of M8 repressor activity in the eye, a regulation that appears to be dispensable in the bristle. The high conservation of the CK2 and MAPK sites in the insect E(spl) proteins M7, M5 and Mγ, and their mammalian homologue HES6, suggest that this mode of regulation may enable E(spl)/HES proteins to orchestrate repression by distinct tissue-specific mechanisms, and is likely to have broader applicability than has been previously recognized

The prevalence of, and factors associated with, paying for sex among men resident in Britain: findings from the third national survey of sexual attitudes and lifestyles (Natsal-3)

Objectives Men who pay for sex (MPS) are considered a bridging population for sexually transmitted infections (STI). However, the extent, characteristics and role of MPS in transmission is poorly understood. We investigate these questions using data from Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3). Methods We performed complex survey analyses of data from 6293 men aged 16–74 years resident in Britain who completed Natsal-3, a probability sample survey undertaken during 2010–2012, using computer-assisted personal interviewing and computer-assisted self-interview. Results 11.0% (95% CI10.1% to 11.9%) of all men reported ever paying for sex. Among MPS, 18.4% (95% CI 18.2% to 18.7%) of their lifetime sexual partners were paid. 3.6% (95% CI 3.1% to 4.2%) of men had paid for sex in the past 5 years. Partners of MPS constitute 14.7% of all reported partners and MPS report 15.6% of all reported STI diagnoses in the past 5 years. Paying for sex in the past 5 years was strongly associated with reporting larger numbers of sexual partners (adjusted OR, AOR for 5+ partners, past 5 years, 31.50, 95% CI 18.69 to 53.09). After adjusting for partner numbers, paying for sex remained strongly associated with reporting new foreign partners outside the UK (AOR 7.96; 95% CI 4.97 to 12.73) and STI diagnosis/es (AOR 2.34; 95% CI 1.44 to 3.81), all in the past 5 years. Among men ever paying for sex, 62.6% (95% CI 58.3% to 66.8%) reported paying for sex outside the UK, most often in Europe and Asia. Conclusions MPS in Britain remain at greater risk of STI acquisition and onward transmission than men who do not. They report high numbers of partners, but the minority are paid partners. They are an important core group in STI transmission

Cosmological solutions with charged black holes

RB aknowledges support from the Higher Education Commission (HEC) of Pakistan, which provided funding to visit QMUL while this work was performed. TC and JD are supported by the STFC

Derivation of regularized field equations for the Einstein-Gauss-Bonnet theory in four dimensions

6 pages + 2 pages with reference

Observational constraints on the regularized 4D Einstein-Gauss-Bonnet theory of gravity

In this paper we study the observational constraints that can be imposed on the coupling parameter, $\hat \alpha$, of the regularized version of the 4-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit, and apply our results to observations of a wide array of physical systems that admit such a description. We find that the LAGEOS satellites are the most constraining, requiring $| \hat \alpha | \lesssim 10^{10} \,{\rm m}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early universe ($t<10^{-3}\, {\rm s}$), or the immediate vicinity of stellar-mass black holes ($M\lesssim100\, M_{\odot}$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and table-top experiments. It is found that early universe inflation prohibits all but the smallest negative values of $\hat \alpha$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0 \lesssim \hat \alpha \lesssim 10^8 \, {\rm m}^2$.Comment: 17 page

Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter

In this work we study static black holes in the regularized 4D Einstein-Gauss-Bonnet theory of gravity; a shift-symmetric scalar-tensor theory that belongs to the Horndeski class. This theory features a simple black hole solution that can be written in closed form, and which we show is the unique static, spherically-symmetric and asymptotically-flat black hole vacuum solution of the theory. We further show that no asymptotically-flat, time-dependent, spherically-symmetric perturbations to this geometry are allowed, which suggests that it may be the only spherically-symmetric vacuum solution that this theory admits (a result analogous to Birkhoff's theorem). Finally, we consider the thermodynamic properties of these black holes, and find that their final state after evaporation is a remnant with a size determined by the coupling constant of the theory. We speculate that remnants of this kind from primordial black holes could act as dark matter, and we constrain the parameter space for their formation mass, as well as the coupling constant of the theory

The 4D Einstein-Gauss-Bonnet theory of gravity: a review

57 pages, 2 figures57 pages, 2 figure