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The Square Kilometre Array (SKA) is a planned large radio interferometer designed to operate over a wide range of frequencies, and with an order of magnitude greater sensitivity and survey speed than any current radio telescope. The SKA will address many important topics in astronomy, ranging from planet formation to distant galaxies. However, in this work, we consider the perspective of the SKA as a facility for studying physics. We review four areas in which the SKA is expected to make major contributions to our understanding of fundamental physics: cosmic dawn and reionisation; gravity and gravitational radiation; cosmology and dark energy; and dark matter and astroparticle physics. These discussions demonstrate that the SKA will be a spectacular physics machine, which will provide many new breakthroughs and novel insights on matter, energy, and spacetime.
The evolution of neutral hydrogen (HI) across redshifts is a powerful probe of cosmology, large scale structure in the universe and the intergalactic medium. Using a data-driven halo model to describe the distribution of HI in the post-reionization universe (z ∼ 5 to 0), we obtain the best-fitting parameters from a rich sample of observational data: low redshift 21-cm emission line studies, intermediate redshift intensity mapping experiments, and higher redshift Damped Lyman Alpha (DLA) observations. Our model describes the abundance and clustering of neutral hydrogen across redshifts 0 - 5, and is useful for investigating different aspects of galaxy evolution and for comparison with hydrodynamical simulations. The framework can be applied for forecasting future observations with neutral hydrogen, and extended to the case of intensity mapping with molecular and other line transitions at intermediate redshifts.
Bisphenol-A (BPA) is a widely used endocrine-disrupting chemical. Prenatal exposure to BPA is known to affect birth weight, but its impact on the cardiovascular system has not been studied in detail. In this study, we investigated the effects of prenatal BPA treatment and its interaction with postnatal overfeeding on the cardiovascular system. Pregnant sheep were given daily subcutaneous injections of corn oil (control) or BPA (0.5 mg/kg/day in corn oil) from day 30 to day 90 of gestation. A subset of female offspring of these dams were overfed to increase body weight to ~30% over that of normal fed controls. Cardiovascular function was assessed using non-invasive echocardiography and cuff blood pressure (BP) monitoring at 21 months of age. Ventricular tissue was analyzed for gene expression of cardiac markers of hypertrophy and collagen at the end of the observation period. Prenatal BPA exposure had no significant effect on BP or morphometric measures. However, it increased atrial natriuretic peptide gene expression in the ventricles and reduced collagen expression in the right ventricle. Overfeeding produced a marked increase in body weight and BP. There were compensatory increases in left ventricular area and internal diameter. Prenatal BPA treatment produced a significant increase in interventricular septal thickness when animals were overfed. However, it appeared to block the increase in BP and left ventricular area caused by overfeeding. Taken together, these results suggest that prenatal BPA produces intrinsic changes in the heart that are capable of modulating morphological and functional parameters when animals become obese in later life.
Ultra-thin flakes of layered materials have recently been attracting widespread research interest due to their exotic properties. In this work, we study the optoelectronic response of a hybrid of two such materials – graphene and MoS2. Our devices consist of mechanically exfoliated graphene flakes transferred on top of similarly exfoliated MoS2. The electrical response of the hybrid is studied in the presence of white light. We show that the four-point resistance of graphene is modulated in the presence of light. This effect is observed to be a strong function of gate voltage. We have also extended our studies to CVD (chemical vapor deposition) - grown graphene transferred onto MoS2 which show qualitatively similar features, thereby attesting to the scalability of the device architecture.
I describe the conceptual and mathematical basis of an approach which describes gravity as an emergent phenomenon. Combining the principle of equivalence and the principle of general covariance with known properties of local Rindler horizons, perceived by observers accelerated with respect to local inertial frames, one can provide a thermodynamic reinterpretation of the field equations describing gravity in any diffeomorphism-invariant theory. This fact, in turn, leads us to the possibility of deriving the field equations of gravity by maximizing a suitably defined entropy functional, without using the metric tensor as a dynamical variable. The approach synthesizes concepts from quantum theory, thermodynamics and gravity, leading to a fresh perspective on the nature of gravity. The description is presented here in the form of a dialogue, thereby addressing several frequently asked questions.
What is it all about?
Harold: For quite some time now, you have been talking about ‘gravity being an emergent phenomenon’ and a ‘thermodynamic perspective on gravity’. This is quite different from the conventional point of view in which gravity is a fundamental interaction and spacetime thermodynamics of, say, black holes is a particular result which can be derived in a specific context. Honestly, while I find your papers fascinating I am not clear about the broad picture you are trying to convey. Maybe you could begin by clarifying what this is all about, before we plunge into the details? What is the roadmap, so to speak?
Me: To begin with, I will show you that the equations of motion describing gravity in any diffeomorphism-invariant theory can be given [2] a suggestive thermodynamic reinterpretation (Sections 2.2, 2.3).
Using a novel in-situ TEM triboprobe holder, nanoscale structures formed from polysilicon MEMS materials have been loaded to characterise the failure mechanisms of reduced scale components. Nanobridges with cross-section dimensions much less than 1μm have been deformed using both single, high displacement indentation and low displacement cyclic fatigue. In both deformation modes, significant residual plastic deformation is measured, occurring and accumulating in the polysilicon. This can be seen as a gradual curvature along the entire crossbeam upon unloading. Where the radius of curvature is very high, fracture of the beams at the centre point was generally also seen. When loading at much lower displacement but under fatigue conditions, localised heating around the moving contact point initiates carbon migration, forming a very strong bond. A high tensile force was needed to severe the contact during unload. Such in-situ techniques demonstrate a range of time dependant failure modes which can be overlooked using post-mortem analysis. In particular, the combined effect of localised frictional heating and contamination on the reliability of components that repeatedly comes into contact with one another.
This chapter introduces the special theory of relativity from a perspective that is appropriate for proceeding to the general theory of relativity later on, from Chapter 4 onwards. Several topics such as the manipulation of tensorial quantities, description of physical systems using action principles, the use of distribution function to describe a collection of particles, etc., are introduced in this chapter in order to develop familiarity with these concepts within the context of special relativity itself. Virtually all the topics developed in this chapter will be generalized to curved spacetime in Chapter 4. The discussion of Lorentz group in Section 1.3.3 and in Section 1.10 is somewhat outside the main theme; the rest of the topics will be used extensively in the future chapters.
The principles of special relativity
To describe any physical process we need to specify the spatial and temporal coordinates of the relevant event. It is convenient to combine these four real numbers – one to denote the time of occurrence of the event and the other three to denote the location in space – into a single entity denoted by the four-component object xi = (x0, x1, x2, x3) ≡ (t, x) ≡ (t, xα). More usefully, we can think of an event P as a point in a four-dimensional space with coordinates xi. We will call the collection of all events as spacetime.
This book can be adapted by readers with varying backgrounds and requirements as well as by teachers handling different courses. The material is presented in a fairly modular fashion and I describe below different sub-units that can be combined for possible courses or for self-study.
1 Advanced special relativity
Chapter 1 along with parts of Chapter 2 (especially Sections 2.2, 2.5, 2.6, 2.10) can form a course in advanced special relativity. No previous familiarity with four-vector notation (in the description of relativistic mechanics or electrodynamics) is required.
2 Classical field theory
Parts of Chapter 1 along with Chapter 2 and Sections 3.2, 3.3 will give a comprehensive exposure to classical field theory. This will require familiarity with special relativity using four-vector notation which can be acquired from specific sections of Chapter 1.
3 Introductory general relativity
Assuming familiarity with special relativity, a basic course in general relativity (GR) can be structured using the following material: Sections 3.5, Chapter 4 (except Sections 4.8, 4.9), Chapter 5 (except Sections 5.2.3, 5.3.3, 5.4.4, 5.5, 5.6), Sections 6.2.5, 6.4.1, 7.2.1, 7.4.1, 7.4.2, 7.5. This can be supplemented with selected topics in Chapters 8 and 9.
4 Relativistic cosmology
Chapter 10 (except Sections 10.6, 10.7) along with Chapter 13 and parts of Sections 14.7 and 14.8 will constitute a course in relativistic cosmology and perturbation theory from a contemporary point of view.
5 Quantum field theory in curved spacetime
Parts of Chapter 8 (especially Sections 8.2, 8.3, 8.7) and Chapter 14 will constitute a first course in this subject.
In this chapter, we will develop further the mathematical formalism required to understand different aspects of curved spacetime, focusing on the description of spacetime curvature. It uses extensively the concepts developed in Chapter 4, especially the idea of parallel transport. Most of the topics described here will be used in the subsequent chapters, except for the ideas discussed in Section 5.6 related to the classification of spacetime curvature which fall somewhat outside the main theme of development.
Three perspectives on the spacetime curvature
The discussion in the previous chapter used only the fact that the metric tensor depended on the coordinates. This dependence can arise either due to the use of curvilinear coordinates in flat spacetime or due to genuine curvature of the spacetime. The gravitational field generated by matter manifests itself as the curvature of the spacetime and hence, to study the gravitational effects, we need to develop the mathematical machinery capable of describing and analysing the curvature of spacetime. This will be the aim of the current chapter and we shall begin by introducing the concept of spacetime curvature from three different – but closely related – perspectives. At a fundamental level, these three perspectives stem from the same source, viz. behaviour of vectors under parallel transport; however, we will discuss them separately in the next three subsections for greater clarity.
Parallel transport around a closed curve
The first perspective on curvature originates from the changes induced in a vector when it is parallel transported around a small, closed, curve in the spacetime.
We begin this chapter by introducing the action functional for gravity and obtaining Einstein's equations. We then describe the general properties of Einstein's equations and discuss their weak field limit. The action functional and its properties will play a crucial role in Chapters 12, 15 and 16, while the linearized field equations will form the basis of our discussion of gravitational waves in Chapter 9.
Action and gravitational field equations
Let us recall that we studied the scalar and electromagnetic fields in Chapter 2 in two steps. First, in Sections 2.3.1 and 2.4.1, we considered the effect of the field (scalar or electromagnetic) on other physical systems (like material particles). In the second step, in Sections 2.3.2 and 2.7, we studied the dynamics of the field itself, by adding a new term to the action principle. This new term depended on the field and on its first derivatives; by varying the field in the total action we could obtain the dynamical equations governing the field.
In the case of gravity, we have already completed the corresponding first step in the previous two chapters. We have seen that the effect of gravity on any other physical system (particles, fluids, electromagnetic field, …) can be incorporated by modifying the action functional for the physical system by changing d4x to, partial derivatives by covariant derivatives and replacing ηab by gab.
This chapter applies the general theory of relativity to the study of cosmology and the evolution of the universe. Our emphasis will be mostly on the geometrical aspects of the universe rather than on physical cosmology. However, in order to provide a complete picture and to appreciate the interplay between theory and observation, it is necessary to discuss certain aspects of the evolutionary history of the universe. We shall do this in Section 10.6 even though it falls somewhat outside the main theme of development.
The Friedmann spacetime
Observations show that, at sufficiently large scales, the universe is homogeneous and isotropic; that is, the geometrical properties of the three-dimensional space: (i) are the same at all spatial locations and (ii) do not single out any special direction in space.
The geometrical properties of the space are determined by the distribution of matter through Einstein's equations. It follows, therefore, that the matter distribution should also be homogeneous and isotropic. This is certainly not true at small scales in the observed universe, where a significant degree of inhomogeneity exits in the form of galaxies, clusters, etc. We assume that these inhomogeneities can be ignored and the matter distribution may be described by a smoothed out average density in studying the large scale dynamics of the universe.
The evolution of the homogeneous universe was described in Chapter 10. Following up on that, we shall now turn to the study of the formation of structures in the universe. The key idea is that if there were small fluctuations in the energy density in the early universe, then the gravitational instability could amplify them leading – eventually – to structures like galaxies, clusters, etc. The most popular model for generating the initial fluctuations is based on the paradigm that, if the very early universe went through a phase of accelerated expansion (called the inflationary phase), then the quantum fluctuations of the field driving the inflation could lead to fluctuations in the energy density. (We will discuss this idea in detail in Chapter 14.) When the perturbations are small, one can use the linear perturbation theory to study its growth. The observations of cosmic microwave background radiation (CMBR) at z ≃ 103 show that the fractional perturbations in the energy density were quite small (about 10−4–10−5) at z ≈ 1000 when the matter and radiation decoupled. Hence, linear perturbation theory can be used to make clear predictions about the state of the universe at z ≈ 1000 and to study the anisotropies in the CMBR. This will be one key application of the formalism developed in this chapter.
Structure formation and linear perturbation theory
The basic idea behind linear perturbation theory in cosmology is well defined and simple.
In this chapter we will obtain the simplest of the exact solutions to Einstein's equations, which are the ones with spherical symmetry. The chapter also discusses the orbits of particles and photons in these spacetimes and the tests of general relativity. All of this will be used in the study of black holes in the next chapter.
Metric of a spherically symmetric spacetime
One of the simplest – but fortunately very useful – class of solutions to Einstein's equations is obtained when the source Tik and the resulting metric possess spherical symmetry. We shall first obtain the general form of the metric in the spherically symmetric context and then use Einstein's equations to relate the metric to the source. While the form of the spherically symmetric metric (given in Eq. (7.12) below) can be obtained almost ‘by inspection’, we shall perform a rather formal analysis in order to illustrate a useful technique.
If the spacetime exhibits a particular symmetry which can be characterized by the action of an element of a group, then the functional change in the form of the metric under the action of this element of the group should vanish. In the case of spherical symmetry, the relevant group is the group of rotations under which the Cartesian coordinates will change by xa → xa + ξa, where ξa has the components
Here εαβ = −εβα is a set of arbitrary infinitesimal constants (with only three elements being independent due to the antisymmetry) which describe infinitesimal rotations.
Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The 'Foundation' section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications - spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the 'Frontier' section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered in-depth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the reader's understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research.
The description of gravity based on Einstein's general theory of relativity is quite satisfactory in most respects. It has been repeatedly verified experimentally as regards those features which could be directly tested while other parts of it are conceptually very elegant and beautiful. Nevertheless, it is obvious that this theory is fundamentally flawed or – at the least – incomplete.
Such a conclusion emerges from the fact that there exist well defined situations in which the theory is incapable of predicting the future evolution of the dynamical variables owing to the development of singularities. To see this concretely, consider the example of a collapsing sphere of dust described in Chapter 8. An observer comoving along with the dust particle will find that the trajectory of the dust particle hits a singularity (at which the curvature and density diverge) within finite proper time τ as shown by the observer's clock. In other words, the observer can not ascertain beforehand her future evolution for arbitrarily large values of τ using Einstein's theory of gravity. As another example, consider the standard description of our universe in terms of a Friedmann model discussed in Chapter 10. For reasonable values of the parameters of the model at the present moment – which are determined observationally – the theory is incapable of describing the state of the universe, say, 20 billion years ago for any equation of state for high density matter having positive pressure and energy density.
This chapter develops the ideas of classical field theory in the context of special relativity. We use a scalar field and the electromagnetic field as examples of classical fields. The discussion of scalar field theory will allow us to understand concepts that are unique to field theory in a somewhat simpler context than electromagnetism; it will also be useful later on in the study of topics such as inflation, quantum field theory in curved spacetime, etc. As regards electromagnetism, we concentrate on those topics that will have direct relevance in the development of similar ideas in gravity (gauge invariance, Hamilton–Jacobi theory for particle motion, radiation and radiation reaction, etc.).
The ideas developed here will be used in the next chapter to understand why a field theory of gravity – developed along similar lines – runs into difficulties. The concept of an action principle for a field will be extensively used in Chapter 6 in the context of gravity. Other topics will prove to be valuable in studying the effect of gravity on different physical systems.
External fields of force
In non-relativistic mechanics, the effect of an external force field on a particle can be incorporated by adding to the Lagrangian the term −V(t, x), thereby adding to the action the integral of −V dt. Such a modification is, however, not Lorentz invariant and hence cannot be used in a relativistic theory.