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Minkowski functionals and Shapefinders shed light on the connectedness of large-scale structure by determining its topology and morphology. We use a sophisticated code, SURFGEN2, to measure the Minkowski functionals and Shapefinders of individual clusters by modelling cluster surfaces using the 'Marching Cube 33' triangulation algorithm. In this paper, we study the morphology of simulated neutral hydrogen (HI) density fields using Shapefinders at various stages of reionization from the excursion set approach. Accompanying the Shapefinders, we also employ the 'largest cluster statistic' (LCS) to understand the percolation process. Percolation curves demonstrate that the non-Gaussianity in the HI field increases as reionization progresses. The large clusters in both the HI overdense and underdense excursion sets possess similar values of "thickness" ($T$), as well as "breadth" ($B$), but their third Shapefinder - "length" ($L$) - becomes almost proportional to their volume. The large clusters in both HI overdense and underdense segments are overwhelmingly filamentary. The 'cross-section' of a filamentary cluster can be estimated using the product of the first two Shapefinders, $T \times B$. Hence the cross sections of the large clusters at the onset of percolation do not vary much with volume and their sizes only differ in terms of their lengths. This feature appears more vividly in HI overdense regions than in underdense regions and is more pronounced at lower redshifts which correspond to an advanced stage of reionization., Comment: 19 pages, 15 figures, 1 table, accepted for publication in MNRAS

It is well known that the inflationary scenario often displays different sets of degeneracies in its predictions for CMB observables. These degeneracies usually arise either because multiple inflationary models predict similar values for the scalar spectral index $n_{_S}$ and the tensor-to-scalar ratio $r$, or because within the same model, the values of $\lbrace n_{_S}, r \rbrace$ are insensitive to some of the model parameters, making it difficult for CMB observations alone to constitute a unique probe of inflationary cosmology. We demonstrate that by taking into account constraints on the post-inflationary reheating parameters such as the duration of reheating $N_{_{\rm re}}$, its temperature $T_{_{\rm re}}$ and especially its equation of state (EOS), $w_{_{\rm re}}$, it is possible to break this degeneracy in certain classes of inflationary models where identical values of $\lbrace n_{_S}, r \rbrace$ can correspond to different reheating $w_{_{\rm re}}$. In particular, we show how reheating constraints can break inflationary degeneracies in the T-model and the E-model $��$-attractors. Non-canonical inflation is also studied. The relic gravitational wave (GW) spectrum provides us with another tool to break inflationary degeneracies. This is because the GW spectrum is sensitive to the post-inflationary EOS of the universe. Indeed a stiff EOS during reheating $(w_{_{\rm re}} > 1/3)$ gives rise to a small scale blue tilt in the spectral index $n_{_{\rm GW}} = \frac{d\log{��_{_{\rm GW}}}}{d\log{k}} > 0$, while a soft EOS $(w_{_{\rm re}} < 1/3)$ results in a red tilt. Relic GWs therefore provide us with valuable information about the post-inflationary epoch, and their spectrum can be used to cure inflationary degeneracies in $\lbrace n_{_S}, r\rbrace$., 41 pages, 13 figures, some clarifications and additional references. Matches published version in JCAP

This chapter examines Glenn Snyder’s original formulation, analyze the genesis of the concept, and explores the most important of his insights. It revisits four India-Pakistan crises since the mid-1980s to see if they yield any evidence of the stability-instability paradox in operation. The chapter analyses beyond the stabilityinstability paradox to examine other pieces in the India-Pakistan instability puzzle. It focuses on such issues as incompatible nuclear doctrines, the difference between status quo and revisionist strategies, the offence-defence balance at different levels of escalation, and the ‘plausible deniability’ inherent in asymmetric warfare. The chapter examines the very different meanings that nuclear weapons have for India and Pakistan and asks what it would take to build a robust deterrence relationship between the two states. Mutual deterrence, in the words of Jervis, ‘can be used as a platform for hostility, coercion, and even limited wars’.

Braneworld models with induced gravity exhibit phantom-like behaviour of the effective equation of state of dark energy. They can, therefore, naturally accommodate higher values of $H_0$, preferred by recent local measurements, while satisfying the CMB constraints. We test the background evolution in such phantom braneworld scenarios with the current observational datasets. We find that the phantom braneworld prefers a higher value of $H_0$ even without the R19 prior, thereby providing a much better fit to the local measurements. Although this braneworld model cannot fully satisfy all combinations of cosmological observables, among existing dark energy candidates the phantom brane provides one of the most compelling explanations of cosmic evolution., 16 pages, 6 figures, matches the published version in ApJ

We investigate constraints on some key cosmological parameters by confronting metastable dark energy models with different combinations of the most recent cosmological observations. Along with the standard $\Lambda$CDM model, two phenomenological metastable dark energy models are considered: (\romannumeral1) DE decays exponentially, (\romannumeral2) DE decays into dark matter. We find that: (1) when considering the most recent supernovae and BAO data, and assuming a fiducial $\Lambda$CDM model, the inconsistency in the estimated value of the $\Omega_{\rm{m,0}}h^2$ parameter obtained by either including or excluding Planck CMB data becomes very much substantial and points to a clear tension~\citep{sahni2014model,zhao2017dynamical}; (2) although the two metastable dark energy models that we study provide greater flexibility in fitting the data, and they indeed fit the SNe Ia+BAO data substantially better than $\Lambda$CDM, they are not able to alleviate this tension significantly when CMB data are included; (3) while local measurements of the Hubble constant are significantly higher relative to the estimated value of $H_0$ in our models (obtained by fitting to SNe Ia and BAO data), the situation seems to be rather complicated with hints of inconsistency among different observational data sets (CMB, SNe Ia+BAO and local $H_0$ measurements). Our results indicate that we might not be able to remove the current tensions among different cosmological observations by considering simple modifications of the standard model or by introducing minimal dark energy models. A complicated form of expansion history, different systematics in different data and/or a non-conventional model of the early Universe might be responsible for these tensions., Comment: 13 pages, 11 figures, accepted for publication in ApJ

Scalar perturbations during inflation can be substantially amplified by tiny features in the inflaton potential. A bump-like feature behaves like a local speed-breaker and lowers the speed of the scalar field, thereby locally enhancing the scalar power spectrum. A bump-like feature emerges naturally if the base inflaton potential $V_b(\phi)$ contains a local correction term such as $V_b(\phi)\left[1+\varepsilon(\phi)\right]$ at $\phi=\phi_0$. The presence of such a localised correction term at $\phi_0$ leads to a large peak in the curvature power spectrum and to an enhanced probability of black hole formation. Remarkably this does not significantly affect the scalar spectral index $n_{_S}$ and tensor to scalar ratio $r$ on CMB scales. Consequently such models can produce higher mass primordial black holes ($M_{\rm PBH}\geq 1 M_{\odot}$) in contrast to models with `near inflection-point potentials' in which generating higher mass black holes severely affects $n_{_S}$ and $r$. With a suitable choice of the base potential - such as the string theory based (KKLT) inflation or the $\alpha$-attractor models - the amplification of primordial scalar power spectrum can be as large as $10^7$ which leads to a significant contribution of primordial black holes (PBHs) to the dark matter density today, $f_{\rm PBH} = \Omega_{0,\rm PBH}/\Omega_{0,\rm DM} \sim O(1)$. Interestingly, our results remain valid if the bump is replaced by a dip. In this case the base inflaton potential $V_b(\phi)$ contains a negative local correction term such as $V_b(\phi)\left[1-\varepsilon(\phi)\right]$ at $\phi=\phi_0$ which leads to an enhanced probability of PBH formation. We conclude that primordial black holes in the mass range $10^{-17} M_{\odot} \leq M_{\rm PBH} \leq 100\, M_{\odot}$ can easily form in single field inflation in the presence of small bump-like and dip-like features in the inflaton potential., Comment: 33 pages, 15 figures, Results extended to include a dip in the potential, Additional comments and references, Accepted for publication in JCAP

In [Phys. Rev. D 80, 123003 (2009)] Schmidt suggested that dynamical dark energy (DDE) propagating on the phantom brane could mimick $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Schmidt went on to derive a phenomenological expression for ${\ensuremath{\rho}}_{\mathrm{DE}}$ which could achieve this. We demonstrate that while Schmidt's central premise is correct, the expression for ${\ensuremath{\rho}}_{\mathrm{DE}}$ derived by [Schmidt, Phys. Rev. D 80, 123003 (2009)] is flawed. We derive the correct expression for ${\ensuremath{\rho}}_{\mathrm{DE}}$ which leads to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$-like expansion on the phantom brane. We also show that DDE on the brane can be associated with a quintessence field and derive a closed form expression for its potential $V(\ensuremath{\phi})$. Interestingly the $\ensuremath{\alpha}$-attractor based potential $V(\ensuremath{\phi})\ensuremath{\propto}{\mathrm{coth}}^{2}\ensuremath{\lambda}\ensuremath{\phi}$ makes braneworld expansion resemble $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. However the two models can easily be distinguished on the basis of density perturbations which grow at different rates on the braneworld and in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$.

We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale., 35 pages, 27 figures, matches the published version in PRD

We derive an analytical expression for the growth rate of matter density perturbations on the phantom brane (which is the normal branch of the Dvali-Gabadadze-Porrati model). This model is characterized by a phantomlike effective equation of state for dark energy at the present epoch. It agrees very well with observations. We demonstrate that the traditional parametrization $f=\Omega_m^\gamma$ with a quasiconstant growth index $\gamma$ is not successful in this case. Based on a power series expansion at large redshifts, we propose a different parametrization for this model: $f=\Omega_m^\gamma\left(1+\frac{b}{\ell H}\right)^\beta$, where $\beta$ and $b$ are constants. Our numerical simulations demonstrate that this new parametrization describes the growth rate with great accuracy - the maximum error being $\leq 0.1\%$ for parameter values consistent with observations., Comment: 21 pages, 5 figures, published version

Using Shapefinders, which are ratios of Minkowski functionals, we study the morphology of neutral hydrogen (HI) density fields, simulated using semi-numerical technique (inside-out), at various stages of reionization. Accompanying the Shapefinders, we also employ the 'largest cluster statistic' (LCS), originally proposed in Klypin and Shandarin (1993), to study the percolation in both neutral and ionized hydrogen. We find that the largest ionized region is percolating below the neutral fraction $x_{HI} \lesssim 0.728$ (or equivalently $z \lesssim 9$). The study of Shapefinders reveals that the largest ionized region starts to become highly filamentary with non-trivial topology near the percolation transition. During the percolation transition, the first two Shapefinders - 'thickness' ($T$) and 'breadth' ($B$) - of the largest ionized region do not vary much, while the third Shapefinder - 'length' ($L$) - abruptly increases. Consequently, the largest ionized region tends to be highly filamentary and topologically quite complex. The product of the first two Shapefinders, $T\times B$, provides a measure of the 'cross-section' of a filament-like ionized region. We find that, near percolation, the value of $T\times B$ for the largest ionized region remains stable at $\sim 7$ Mpc$^2$ (in comoving scale) while its length increases with time. Interestingly all large ionized regions have similar cross-sections. However their length shows a power-law dependence on their volume, $L\propto V^{0.72}$, at the onset of percolation., Comment: 10 pages, 9 figures, matches published version in MNRAS

We propose a new class of metastable dark energy (DE) phenomenological models in which the DE decay rate does not depend on external parameters such as the scale factor or the curvature of the Universe. Instead, the DE decay rate is assumed to be a constant depending only on intrinsic properties of DE and the type of a decay channel, similar to case of the radioactive decay of unstable particles and nuclei. As a consequence, the DE energy density becomes a function of the proper time elapsed since its formation, presumably in the very early Universe. Such a natural type of DE decay can profoundly affect the expansion history of the Universe and its age. Metastable DE can decay in three distinct ways: (i) exponentially, (ii) into dark matter, (iii) into dark radiation. Testing metastable DE models with observational data we find that the decay half-life must be many times larger than the age of the Universe. Models in which dark energy decays into dark matter lead to lower values of the Hubble parameter at large redshifts relative to $\Lambda$CDM. Consequently these models provide a better fit to cosmological BAO data (especially data from from high redshift quasars) than concordance ($\Lambda$CDM) cosmology., Comment: 12 pages, 8 figures, 2 tables, matches the final version published in MNRAS

Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $\alpha$-attractors. The $\alpha$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $\alpha$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the $\alpha$-attractors, which we call $\alpha$-dark matter ($\alpha$DM), shares many of the attractive features of fuzzy dark matter, with $V(\varphi) = \frac{1}{2}m^2\varphi^2$, while having none of its drawbacks. Like fuzzy dark matter, $\alpha$DM can have a large Jeans length which could resolve the cusp-core and substructure problems faced by standard cold dark matter. $\alpha$DM also has an appealing tracker property which enables it to converge to the late-time dark matter asymptote, $\langle w\rangle \simeq 0$, from a wide range of initial conditions. It thus avoids the enormous fine-tuning problems faced by the $m^2\varphi^2$ potential in describing dark matter., Comment: 43 pages, 22 figures, Some clarifications and an additional reference. Main results unchanged. Accepted for publication in JCAP

We describe a new class of dark energy (DE) models which behave like cosmological trackers at early times. These models are based on the $\alpha$-attractor set of potentials, originally discussed in the context of inflation. The new models allow the current acceleration of the universe to be reached from a wide class of initial conditions. Prominent examples of this class of models are the potentials $\coth\varphi$ and $\cosh\varphi$. A remarkable feature of this new class of models is that they lead to large enough negative values of the equation of state at the present epoch, consistent with the observations of accelerated expansion of the universe, from a very large initial basin of attraction. They therefore avoid the fine tuning problem which afflicts many models of DE., Comment: 24 pages, 16 figures, matches published version in JCAP

Achilles tendon injuries are common but complex in nature. Healing occurs via scar tissue formation leading to poor patient outcomes. Currently surgical and non-surgical treatment leads to suboptimal tendon healing and has complications. Tissue engineering is an advancing field that can either augment surgical repair or provide an alternative method for Achilles tendon repair. This article will explore the principles behind tissue engineering in Achilles tendon repair. Furthermore it will describe the current literature regarding the different types of stem cells used in Achilles tendon repair, how different growth factors augment tendon repair, as well as the role of biomaterials in tissue engineering.

The phantom brane has several important distinctive features: (i) Its equation of state is phantom-like, but there is no future `big rip' singularity, (ii) the effective cosmological constant on the brane is dynamically screened, because of which the expansion rate is {\em smaller} than that in $\Lambda$CDM at high redshifts. In this paper, we constrain the Phantom braneworld using distance measures such as Type Ia supernovae (SNeIa), Baryon Acoustic Oscillations (BAO), and the compressed Cosmic Microwave Background (CMB) data. We find that the simplest braneworld models provide a good fit to the data. For instance, BAO +SNeIa data can be accommodated by the braneworld for a large region in parameter space $0 < \Omega_l < 0.3$ at $1\sigma$. The Hubble parameter can be as high as $H_0 < 78$ km/s/Mpc, and the effective equation of state at present can show phantom-like behaviour with $w_0 < -1.2$ at $1\sigma$. We note a correlation between $H_0$ and $w_0$, with higher values of $H_0$ leading to a lower, and more phantom-like, value of $w_0$. Inclusion of CMB data provides tighter constraints $\Omega_l < 0.1$. (Here $\Omega_l$ encodes the ratio of the five and four dimensional Planck mass.) The Hubble parameter in this case is more tightly constrained to $H_0 < 71$ km/s/Mpc, and the effective equation of state to $w_0 < -1.1$. Interestingly, we find that the universe is allowed be closed or open, with $-0.5 < \Omega_{\kappa} < 0.5$, even on including the compressed CMB data. There appears to be some tension in the low and high $z$ BAO data which may either be resolved by future data, or act as a pointer to interesting new cosmology., Comment: 16 pages, 10 figures. Constraints on effective equation of state w_0 added, correlation between w_0 and H_0 noted. Accepted for publication in PRD

We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\rm eff} < -1$, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in $\Lambda$CDM. Additionally, the gravitational potentials $\Phi$ and $\Psi$ evolve differently on the brane than in $\Lambda$CDM, for which $\Phi = \Psi$. On the brane, by contrast, the ratio $\Phi/\Psi$ exceeds unity during the late matter-dominated epoch ($z \lesssim 50$). These features emerge as "smoking gun" tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure., Comment: Matches published version

Investigation of dark energy (DE) properties using the largest existing Constitution supernovae sample including recent CfA data for small redshifts and omitting the assumption of a constant equation of state w for DE reveals a slight inconsistency (more than 1σ) with the standard spatially flat LCDM model. The effect which is most clearly seen using the recently introduced Om diagnostic corresponds to an increase of both this diagnostic and w at redshifts z

This talk briefly reviews the different approaches which have been used to reconstruct the properties of dark energy from observations. It is based on the review article [V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. D 15 (2006), 2105; astro-ph/0610026] to which the reader is referred for more details of cosmological reconstruction.

Six propositions drive this article. First, India's relations with the great powers as they evolve over the next two decades are going to be conditioned by India's own emergence as a great power. Second, it will take at least 15 to 20 years for a balance to re-emerge in the contemporary hegemonic system; hence, India's emergence will be simultaneous with the relative decline of the United States (US). Third, Indian policy makers and analysts need to think structurally about India's external relations, especially with the US and China. Fourth, India's relations with the great powers are inseparable from the broader issue of emerging Asian balances and security architectures. Fifth, India needs to keep a keen eye on other major powers, among whom Russia, Japan, the European Union (EU) and Brazil will be particularly important. Finally, while building its capabilities along a broad spectrum, India must not lose sight of the normative component that is inherent in great power status.

In explaining the eight key factors that drive contemporary Indian foreign policy, the article provides the context for looking at India's engagement with the continent, an issue addressed in different ways by other articles in this volume. It also looks at the non‐drivers, some of which may surprise observers who may have thought them to be crucial elements of the country's foreign policy.

It is generally believed that a cosmological arrow of time must be associated with entropy production. Indeed, in his seminal work on cyclic cosmology, Tolman introduced a viscous fluid in order to make successive expansion/contraction cycles larger than previous ones, thereby generating an arrow of time. However, as we demonstrate in this letter, the production of entropy is not the only means by which a cosmological arrow of time may emerge. Remarkably, systems which are dissipationless may nevertheless demonstrate a preferred direction of time provided they possess attractors. An example of a system with well defined attractors is scalar-field driven cosmology. In this case, for a wide class of potentials (especially those responsible for inflation), the attractor equation of state during expansion can have the form $p \simeq -\rho$, and during contraction $p \simeq \rho$. If the resulting cosmology is cyclic, then the presence of cosmological hysteresis, $\oint p~dV \neq 0$ during successive cycles, causes an arrow of time to emerge in a system which is formally dissipationless. An important analogy is drawn between the arrow of time in cyclic cosmology and an arrow of time in an $N$-body system of gravitationally interacting particles. We find that, like the $N$-body system, a cyclic universe can evolve from a single past into two futures with oppositely directed arrows of time., Comment: 19 pages, 6 figures. Matches published version in Class. Quantum Grav. 32 (2015) 182001 (Fast Track Communication)

We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value., Comment: 19 pages, 3 figures, text slightly improved and references added. Accepted for publication in Classical and Quantum Gravity

By building robust political and economic links with both China and the United States, India could end up playing an important catalytic role in bringing both countries together in a new cooperative Asia.

In this article, we view India not as a unitary rational actor—the conventional conceptualisation in strategic studies—but rather as a liberal democratic polis composed of the three arenas of civil society, political society and the state. We seek answers to two related questions. The first pertains to the changes that are currently underway in Indian state and society. What is the probable impact of these internal dynamics upon strategic stability in the region? We restrict our analysis to the four most important factors in each of the three political arenas. The answer we arrive at is that the majority of factors making up the internal dynamics of contemporary India either enhance regional stability or, at best, have a mixed impact upon it. Our second concern is to discern the sources of strategic surprises from an Indian perspective. Are the stimuli for strategic surprises from the Indian perspective more internal or external? We conclude that the two India–Pakistan crises since overt nucleari...

We reconstruct the equation of state $w(z)$ of dark energy (DE) using a recently released data set containing 172 type Ia supernovae without assuming the prior $w(z) \geq -1$ (in contrast to previous studies). We find that dark energy evolves rapidly and metamorphoses from dust-like behaviour at high $z$ ($w \simeq 0$ at $z \sim 1$) to a strongly negative equation of state at present ($w \lleq -1$ at $z \simeq 0$). Dark energy metamorphosis appears to be a robust phenomenon which manifests for a large variety of SNe data samples provided one does not invoke the weak energy prior $\rho + p \geq 0$. Invoking this prior considerably weakens the rate of growth of $w(z)$. These results demonstrate that dark energy with an evolving equation of state provides a compelling alternative to a cosmological constant if data are analysed in a prior-free manner and the weak energy condition is not imposed by hand., Comment: 20 pages, 21 figures. Discussions enhanced. Appendix added on error propagation with new figures. References updated. Main results unchanged. Accepted for publication in MNRAS

Traditionally, higher-dimensional cosmological models have sought to provide a description of the fundamental forces in terms of a unifying geometrical construction. In this essay we discuss how, in their present incarnation, higher-dimensional `braneworld' models might provide answers to a number of cosmological puzzles including the issue of dark energy and the nature of the big-bang singularity., Honorable mention in the 2002 Essay Competition of the Gravity Research Foundation. 10 pages, 2 figures

Solar models suggest that four billion years ago the young Sun was about 25% fainter than it is today, rendering Earth's oceans frozen and lifeless. However, there is ample geophysical evidence that Earth had a liquid ocean teeming with life 4 Gyr ago. Since ${\cal L_\odot} \propto G^7M_\odot^5$, the Sun's luminosity ${\cal L_\odot}$ is exceedingly sensitive to small changes in the gravitational constant $G$. We show that a percent-level increase in $G$ in the past would have prevented Earth's oceans from freezing, resolving the faint young Sun paradox. Such small changes in $G$ are consistent with observational bounds on ${\Delta G}/G$. Since ${\cal L}_{\rm SNIa} \propto G^{-3/2}$, an increase in $G$ leads to fainter supernovae, creating tension between standard candle and standard ruler probes of dark energy. Precisely such a tension has recently been reported by the Planck team., Comment: 9 pages, 1 figure. Typo's corrected, acknowledgement added. Main results unchanged. Matches published version in IJMPD

Platelet Rich Plasma (PRP) and growth factors have had encouraging results in several surgical specialties. Their use in orthopaedics is increasing and has been trialed in fracture management, spinal fusion and tendon and ligament healing. Anterior cruciate ligament (ACL) injuries are a significant economic burden and often require surgical reconstruction. This review article used laboratory and clinical studies to evaluate the effectiveness of PRP and growth factors as an adjunct to ACL reconstruction. Overall, the results of studies to date have been disappointing especially given the success in other specialties. PRP has been relatively successful in improving vascularization within the tibial tunnel but less so in the femoral tunnels. The targeting of specific growth factors seems to show more promise than generic PRP injections with vascular endothelial growth factor (VEGF), platelet derived growth factor (PDGF) and transforming growth factor-beta (TGF-β) showing the most significant results in graft healing. Further trials are still required before a definitive conclusion can be reached.

We propose a novel approach to the problem of cosmological perturbations in a braneworld model with induced gravity, which leads to a closed system of equations on the brane. We focus on a spatially closed brane that bounds the interior four-ball of the bulk space. The background cosmological evolution on the brane is now described by the normal branch, and the boundary conditions in the bulk become the regularity conditions for the metric everywhere inside the four-ball. In this approach, there is no spatial infinity or any other boundary in the bulk space since the spatial section is compact, hence, we term this setup as a no-boundary proposal. Assuming that the bulk cosmological constant is absent and employing the Mukohyama master variable, we argue that the effects of nonlocality on brane perturbations may be ignored if the brane is marginally closed. In this case, there arises a relation that closes the system of equations for perturbations on the brane. Perturbations of pressureless matter and dark radiation can now be described by a system of coupled second-order differential equations. Remarkably, this system can be exactly solved in the matter-dominated and de Sitter regimes. In this case, apart from the usual growing and decaying modes, we find two additional modes that behave monotonically on super-Hubble spatial scales and exhibit rapid oscillations with decaying amplitude on sub-Hubble spatial scales., 28 pages, 1 figure

Purpose The introduction of patient-specific instruments (PSI) for guiding bone cuts could increase the incidence of malalignment in primary total knee arthroplasty. The purpose of this study was to assess the agreement between one type of patient-specific instrumentation (Zimmer PSI) and the pre-operative plan with respect to bone cuts and component alignment during TKR using imageless computer navigation.MethodsA consecutive series of 30 femoral and tibial guides were assessed in-theatre by the same surgeon using computer navigation. Following surgical exposure, the PSI cutting guides were placed on the joint surface and alignment assessed using the navigation tracker. The difference between in-theatre data and the pre-operative plan was recorded and analysed.ResultsThe error between in-theatre measurements and pre-operative plan for the femoral and tibial components exceeded 3° for 3 and 17 % of the sample, respectively, while the error for total coronal alignment exceeded 3° for 27 % of the sample.ConclusionThe present results indicate that alignment with Zimmer PSI cutting blocks, assessed by imageless navigation, does not match the pre-operative plan in a proportion of cases. To prevent unnecessary increases in the incidence of malalignment in primary TKR, it is recommended that these devices should not be used without objective verification of alignment, either in real-time or with post-operative imaging. Further work is required to identify the source of discrepancies and validate these devices prior to routine use.Level of evidenceII.

Ya.B. Zeldovich was a pre-eminent Soviet physicist whose seminal contributions spanned many fields ranging from physical chemistry to nuclear and particle physics, and finally astrophysics and cosmology. March 8, 2014 marks Zeldovich's birth centenary, and this article attempts to convey the zest with which Zeldovich did science, and the important role he played in fostering and mentoring a whole generation of talented Scientists., Comment: 23 pages, 4 figures. Originally written for the Indian popular science journal Resonance

This talk presents a brief overview of recent results pertaining to the cosmological constant ‘A’. I summarize the observational situation focussing on observations of high redshift Type Ia supernovae which suggest A > 0. Observations of small angular anisotropies in the cosmic microwave background complement Type Ia supernovae observations and both CMB and Sn can be combined to place strong constraints on the value of A. The presence of a small A-term increases the age of the universe and slows down the formation of large scale structure. I also review recent theoretical attempts to generate a small A-term at the current epoch and a model independent approach for determining the cosmic equation of state.

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Lambda-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Lambda-term. We discuss the current observational situation focusing on cosmological tests of Lambda including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Lambda: the generation of Lambda in models with spontaneous symmetry breaking and through quantum vacuum polarization effects -- mechanisms which are known to give rise to alarge value of Lambda hence leading to the `cosmological constant problem'. More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modeling a dynamical Lambda-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small cosmological constant are briefly reviewed. A comprehensive bibliography of recent work on Lambda is provided.

I present a short overview of current observational results and theoretical models for a cosmological constant. The main motivation for invoking a small cosmological constant (or A-term) at the present epoch has to do with observations of high redshift Type Ia supernovae which suggest an accelerating universe. A flat accelerating universe is strongly favoured by combining supernovae observations with observations of CMB anisotropies on degree scales which give the ‘best-fit’ values ΘA ⋍ 0.7 and Θ m ⋍ 0.3. A time dependent cosmological A-term can be generated by scalar field models with exponential and power law potentials. Some of these models can alleviate the ‘fine tuning’ problem which faces the cosmological constant.

We apply Shapefinders, statistical measures of `shape' constructed from two dimensional partial Minkowski functionals, to study the degree of filamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski functionals characterise the morphology of an object, they are: its perimeter (L), area (S), and genus. Out of L and S a single dimensionless Shapefinder Statistic, F can be constructed (0, Accepted for publication in ApJ

I briefly review the observational evidence for a small cosmological constant at the present epoch. This evidence mainly comes from high redshift observations of Type 1a supernovae, which, when combined with CMB observations strongly support a flat Universe with . Theoretically a cosmological constant can arise from zero point vacuum fluctuations. In addition ultra-light scalar fields could also give rise to a Universe which is accelerating driven by a time de- pendent -term induced by the scalar field potential. Finally a dominated Universe also finds support from observations of galaxy clustering and the age of the Universe. The cosmological constant was introduced into cosmology by Einstein in 1917. Ein- stein, under the influence of Mach's principle, constructed a Universe which was static and closed - a configuration that could only arise under the joint influence of both mat- ter and a cosmological constant. Subsequently Friedmann derived expanding solutions to the Einstein equations and Einstein acknowledged that the introduction of was probably unnecessary, particularly in view of Hubble's discovery that the Universe was expanding. However, interest in the cosmological constant remained, partly due to the rich variety of new solutions which arise in the Einstein equations with a cosmological constant includ- ing: the static Einstein Universe, singularity free 'bouncing' models, quasi-static 'loitering' models etc. Interest in was reignited in the late 1960's, when it was felt than an excess of QSO's was being observed at redshift 1.95. This observation was difficult to explain in the framework of standard FRW cosmology, but easier to account for if the Universe loitered at that redshift. More recently a large cosmological constant at an early epoch is the basis of the inflationary model, and a much smaller cosmological constant at a much later epoch is suggested by current observations.

We consider the geometrical properties of a distribution of matter evolving under gravitational clustering. Such a distribution can be studied using standard statistical indicators such as the correlation function as well as geometrical descriptors sensitive to ‘connectedness’ such as percolation analysis and Minkowski functionals. Applying these methods to N-body simulations and galaxy catalogues we find that the filling factor at the percolation threshold is usually very small reflecting the fact that the Universe consists of a network of filaments and pancakes, the latter being statistically more prominent.

The close relationship between the cosmological constant and the vacuum has been emphasized in the past by Zeldovich amongst others. We briefly discuss different approaches to the cosmological constant issue including the possibility that Λ could be generated by vacuum polarization in a static universe. Fresh possibilities occur in an expanding universe. An inflationary universe generically leads to particle creation from the vacuum, the nature and extent of particle production depending upon the mass of the field and its coupling to gravity. For ultra-light, non-minimally coupled scalar fields, particle production can be large and the resulting vacuum energy–momentum tensor will have the form of an effective cosmological constant. The inflationary scenario therefore, could give rise to a universe that is both flat andΛ-dominated, in agreement with observations.

We explore shapes of clusters and superclusters in the IRAS 1.2 Jy redshift survey with three reconstructions spanning the range \beta = 0.1, 0.5, 1.0, where \beta = \Omega^{0.6}/b, b is the bias factor and \Omega the present value of the dimensionless matter density. Comparing our results to Gaussian randomized reconstructions of the IRAS catalogue, we find structures having both planar and filamentary properties. For \beta = 0.5, 1.0 the largest structures in the survey have a distinct tendency to be filament-like} in general agreement with the results of N-body simulations.

We study a class of Friedmann-Robertson-Walker spacetimes with a nonminimally coupled light massive scalar field. Values of the coupling parameter {xi}{lt}0 enhance long range power in the vacuum expectation value of the energy-momentum tensor {l_angle}T{sub {mu}{nu}}{r_angle} and fundamentally alter the nature of inflationary particle production: the energy density of created particles behaves like an effective cosmological constant, leading generically to {Omega}{sub m}{lt}1 in clustered matter and providing a possible resolution of the {open_quotes}{Omega} problem{close_quotes} for low density cosmological models. {copyright} {ital 1998} {ital The American Physical Society }