Horizon Problem Research Articles

There is no electroweak horizon problem

Contrary to a recent assertion, there is no electroweak horizon problem.

Centenary of Alexander Friedmann’s Prediction of the Universe Expansion and the Quantum Vacuum

We review the main scientific pictures of the universe developed from ancient times to Albert Einstein and underline that all of them treated the universe as a stationary system with unchanged physical properties. In contrast to this, 100 years ago Alexander Friedmann predicted that the universe expands starting from the point of infinitely large energy density. We briefly discuss the physical meaning of this prediction and its experimental confirmation consisting of the discovery of redshift in the spectra of remote galaxies and relic radiation. After mentioning the horizon problem in the theory of the hot universe, the inflationary model is considered in connection with the concept of quantum vacuum as an alternative to the inflaton field. The accelerated expansion of the universe is discussed as powered by the cosmological constant originating from the quantum vacuum. The conclusion is made that since Alexander Friedmann’s prediction of the universe expansion radically altered our picture of the world in comparison with the previous epochs, his name should be put on a par with the names of Ptolemy and Copernicus.

Cosmological Perturbations in Bouncing Cosmologies and the Case of the Pre-Big Bang Scenario

Pre-Big Bang cosmology inspired generations of cosmologists in attempts to cure the initial Big Bang singularity using a fundamental length scale as proposed by string theory. The existence of a phase of collapse/inflation with increasing curvature followed by a cosmic bounce has been proposed as an alternative to standard inflation in the solution of the horizon and curvature problems. However, the generation of a nearly scale-invariant spectrum of perturbations is not an automatic prediction of such scenarios. In this paper, I review some general statements about the evolution of perturbations in bouncing cosmologies and some historically significant attempts to reconcile the predicted spectra with the observations. Bouncing cosmologies and, in particular, the pre-Big Bang scenario stand as viable, although more complicated, alternatives to inflation that may still help solve current theoretical and observational tensions.

Analysis of gravitational waves from inflation model with minimal, non-minimal, and non-minimal derivative coupling of scalar field from Horndeski theory

Inflation theory provides solutions for problems in cosmology, such as horizon problem and flatness problem. The study of Gravitational waves production in cosmic inflation era not prove the general inflation theory, but also to differentiate in detail among specific models. In this research, we use inflation model with minimal, non-minimal, and non-minimal derivative coupling of scalar field without potential from Horndeski Theory. From this model, we calculate scalar and tensor perturbation equations and then obtain its equation of gravitational waves, spectral index for each perturbation mode and tensor-to-scalar ratio. Spectral index and tensor-to-scalar ratio nearly scale-invariant and agree with observational data for some Ho, ζ, and ξ. Gravitational waves remain constant during inflation and start oscillates when its modes enter the horizon. Energy of this gravitational waves is scale-invariant for modes that re-enter horizon during radiation dominated era and rises toward lower frequencies.

Approximating Optimal feedback Controllers of Finite Horizon Control Problems Using Hierarchical Tensor Formats

Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the Hamilton-Jacobi-Bellman (HJB) equation are essential. The numerical treatment of these equations poses formidable challenges due to their non-linearity and their (possibly) high-dimensionality. In this paper we consider a finite horizon control system with associated Bellman equation. After a time-discretization, we obtain a sequence of short time horizon problems which we call local optimal control problems. For solving the local optimal control problems we apply two different methods, one being the well-known policy iteration, where a fixed-point iteration is required for every time step. The other algorithm borrows ideas from Model Predictive Control (MPC), by solving the local optimal control problem via open-loop control methods on a short time horizon, allowing us to replace the fixed-point iteration by an adjoint method. For high-dimensional systems we apply low rank hierarchical tensor product approximation/tree-based tensor formats, in particular tensor trains (TT tensors) and multi-polynomials, together with high-dimensional quadrature, e.g. Monte-Carlo. We prove a linear error propagation with respect to the time discretization and give numerical evidence by controlling a diffusion equation with unstable reaction term and an Allen-Kahn equation.

Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress–energy tensor of a quantum field with classical gravity. Here, we consider a free, massless scalar field with general (not necessarily conformal) coupling to curvature. In a cosmological scenario with flat spatial sections for special choices of the initial conditions, we observe a separation of the dynamics of the quantum degrees of freedom from the dynamics of the scale factor, which extends a classical result by Starobinski (1980 Phys. Lett. B 91 99–102) to general coupling. For this new equation of fourth order governing the dynamics of the scale factor, we study numerical solutions. Typical solutions show a radiation-like Big Bang for the early Universe and de Sitter-like expansion for the late Universe. We discuss a specific solution to the cosmological horizon problem that can be produced by tuning parameters in the given equation. Although the model proposed here only contains massless matter, we give a preliminary comparison of the obtained cosmology with the ΛCDM standard model of cosmology and investigate parameter ranges in which the new models, to a certain extent, is capable of assimilating standard cosmology.

Perspective view of autonomous control in unknown environment: Dual control for exploitation and exploration vs reinforcement learning

This paper overviews and discusses the relationship between Reinforcement Learning (RL) and the recently developed Dual Control for Exploitation and Exploration (DCEE). It is argued that there are two related but quite distinctive approaches, namely, control and machine learning, in tackling intractability arising in optimal decision making/control problems. In the control approach, the original problems (of an infinite horizon) are approximated by finite horizon problems and solved online by taking advantage of the availability of computing power. In the machine learning approach, the optimal solutions are approximated through iterations, or (offline) training through trials when models are not available. When dealing with unknown environments, DCEE as a technique developed from the control approach could potentially solve similar problems as RL while offering a number of advantages, most notably, coping with uncertainty in environment/tasks, high efficiency in learning through balancing exploitation and exploration, and potential in establishing its formal properties like stability. The links between DCEE and other relevant methods like dual control, Model Predictive Control and particularly Active Inference in neuroscience are discussed. The latter provides a strong biological endorsement for DCEE. The methods and discussions are illustrated by autonomous source search using a robot. It is concluded that DCEE provides a promising, complementary approach to RL, and more research is required to develop it as a generic theory and fully realise its potential. The relationships revealed in this paper provide insights into these relevant methods and facilitate cross fertilisation between control, machine learning and neuroscience for developing autonomous control under uncertain environments.

CEO origin and stock price crash risk: Insider versus outsider CEOs

AbstractResearch question/issueThe recent market trend in the United States has drawn attention to the fact that new chief executive officers (CEOs) are increasingly being recruited from outside rather than getting promoted from within. This study examines the influence of CEO origin on stock price crash risk.Research findings/insightsUsing a sample of 13,331 firm‐year observations during the 1997–2017 period, we find that CEOs promoted from inside the firm are less likely to trigger stock price crashes than CEOs hired from outside. Further, we show that the negative relation between insider CEOs and stock price crash risk is more pronounced for firms with more conservative accounting policies. Additional analyses document that the difference in stock price crash risk between insider and outsider CEOs is stronger in the early years of their tenure and for CEOs with higher pay‐for‐performance sensitivity and higher turnover risk.Theoretical/academic implicationsOur study contributes to the research on stock price crash risk, especially the recent studies investigating the impact of managerial behavior and traits on stock price skewness. The findings are consistent with the bad news hoarding theory of stock price crashes. Our findings also lend further empirical support to the horizon problem of CEO origin by showing that the relatively short average horizon for outsider CEOs incentivizes them to withhold bad news, leading to higher stock price crash risk.Practitioner/policy implicationsOur study adds to the debate on whether to choose a CEO from inside or outside the firm. The potential higher risk of stock price crashes might help boards of directors rethink their approaches to succession.

Topics in Cosmology—Clearly Explained by Means of Simple Examples

This is a very comprehensible review of some key issues in modern cosmology. Simple mathematical examples and analogies are used, whenever available. The starting point is the well-known Big Bang cosmology (BBC). We deal with the mathematical singularities appearing in this theory and discuss some ways to remove them. Next, and before introducing the inflationary paradigm by means of clear examples, we review the horizon and flatness problems of the old BBC model. We then consider the current cosmic acceleration and, as a procedure to deal with both periods of cosmic acceleration in a unified way, we study quintessential inflation. Finally, the reheating stage of the universe via gravitational particle production, which took place after inflation ended, is discussed in clear mathematical terms, by involving the so-called α-attractors in the context of quintessential inflation.

FBSDEs involving time delays and advancements on infinite horizon and LQ problems with delays

This paper is concerned with a class of coupled forward–backward stochastic differential equations (FBSDEs, for short) involving time delays and time advancements on infinite horizon. By introducing a randomized Lipschitz condition and a randomized monotonicity condition, the unique solvability of FBSDEs is obtained. Then the theoretical result is applied to a linear–quadratic (LQ, for short) problem of a time-delayed system with random coefficients. An explicit expression of the unique optimal control is obtained.

Emergent cosmology from matrix theory

Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. We begin a study of cosmology in the context of matrix theory. Specifically, we show that matrix theory can lead to an emergent non-singular cosmology which, at late times, can be described by an expanding phase of Standard Big Bang cosmology. The horizon problem of Standard Big Bang cosmology is automatically solved. We show that thermal fluctuations in the emergent phase source an approximately scale-invariant spectrum of cosmological perturbations and a scale-invariant spectrum of gravitational waves. Hence, it appears that matrix theory can lead to a successful scenario for the origin of perturbations responsible for the currently observed structure in the universe while providing a consistent UV-complete description.

Risk-sensitive semi-Markov decision problems with discounted cost and general utilities

In this article we consider risk-sensitive control of semi-Markov processes with a discrete state space. We consider general utility functions and discounted cost in the optimization criteria. We consider random finite horizon and infinite horizon problems. Using a state augmentation technique we characterize the value functions and also prescribe optimal controls.

Optimistic planning algorithms for state-constrained optimal control problems

In this work, we study optimistic planning methods to solve some state-constrained optimal control problems in finite horizon. While classical methods for calculating the value function are generally based on a discretization in the state space, optimistic planning algorithms have the advantage of using adaptive discretization in the control space. These approaches are therefore very suitable for control problems where the dimension of the control variable is low and allow to deal with problems where the dimension of the state space can be very high. Our algorithms also have the advantage of providing, for given computing resources, the best control strategy whose performance is as close as possible to optimality while its corresponding trajectory comply with the state constraints up to a given accuracy.

Earnings Management, Horizon Problem, and Advisor Posts for Retiring CEOs

Earnings Management, Horizon Problem, and Advisor Posts for Retiring CEOs

On Director Jia Zhangke's Style from the Perspective of Cinemetrics

Driven by the trend of big data technology and digital humanities, quantitative research methods combining metrology, statistics and theory of film study have emerged in the world.The emergence of cinemetrics not only breaks the problem of narrow research horizon, but also provides a more accurate, more systematic, and more objective film analysis model, which brings a new paradigm to the traditional film and television research. With the help of “ysjl”, a film and television measurement and analysis tool developed by the team of film and television quantitative analysis of the School of Humanities of Tiangong University, the author visualized the data of recent film works directed by Jia Zhangke, and analyzed their style characteristics, rhythm changes and spatial feature. combined with relevant film theories.

Risk-sensitive optimal stopping with unbounded terminal cost function

In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have multiple solutions and we give a probabilistic interpretation for the minimal and the maximal one. Also, we show how to approximate them using finite time horizon problems. The analysis, covering both discrete and continuous time case, is supported with illustrative examples.

Capital as common-pool resource: Horizon problem, financial sustainability and reserves in worker cooperatives

• Collective capital reserves are considered as common-pool resources in cooperative enterprises. • The problem of undercapitalization due to the members’ truncated temporal horizon and capital variability is reconsidered. • A new layered system of divisible and indivisible reserve funds is proposed as possible solution to under-investment. • Inner or indivisible layers correspond to stability and strength of patrimony. •Outer or divisible layers correspond to performance and members’ financial involvement. In most countries, self-financed accumulation of capital in cooperative enterprises makes substantial (but variable) use of indivisible reserves, which can be understood as common-pool capital resources, since they are characterized by rivalry and non-excludability in utilization among the members of the cooperative. The paper is structured in two main parts. The first part deals with dynamic inefficiency in investments and the problem of undercapitalization due to the members’ truncated temporal horizon in worker cooperatives. The conjugation of different types of reserves, divisible and indivisible, is envisaged as possible solution to under-investment. In the second part, a new layered system of reserve funds, both divisible and indivisible, is discussed, showing that each different layer has distinctive functions in facing the stability vs performance trade-off: stability and strength of patrimony are adjudicated to the indivisible layers, while efficient allocation of reinvested funds and members’ financial involvement require divisible reserve layers.

On the viability of the evolution of the universe with Geometric Inflation

We perform a general analysis of the cosmological viability of Geometric Inflation. We show that the evolution of the universe, from inflation to the present day, can be seen from the addition of an infinite tower of curvature invariants into the Hilbert-Einstein action. The main epochs of the Universe can be reproduced: Inflation, Big Bang Nucleosynthesis, and Late-time acceleration driven by the cosmological constant. The slow-roll condition is a robust prediction of the theory. Inflation possesses a graceful exit with enough number of $e-$folds between the limit imposed by the Planck density and the exit of the exponential expansion to solve the horizon problem and the absence of topological defects. We also provide some scenarios where the energy scale of the theory can be calibrated.

Post‐CEO retirement appointments and financial accounting—Evidence from CEO turnovers

AbstractPrior research has shown that when boards seek to appoint CEOs as outside directors, the director labor market rewards CEOs' accounting performance. This study examines whether the external labor market's assessment of the accounting performance is moderated by CEOs' past exercise of financial reporting discretion in the form of accruals and real earnings management and financial statement readability. Our results show a positive association between post‐CEO board opportunities and within‐GAAP accruals management as well as to more readable financial statements. Earnings restatements are associated with fewer board positions and director pay. However, the director labor market appears to punish R&D expenditure above the industry median, suggesting that boards view overinvestment as a risky avenue for growth. Finally, the results suggest that for CEOs with planned retirement, the director labor market provides some mitigating effect on the horizon problem.

Interaction of fermionic matter and ECSK black hole leading to bouncing universe

The interactions between the spin of fermionic matter and torsion in the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity provides a repulsive gravitational potential at the very dense states of fermionic matter, which prevents the formation of black hole singularities inside the deeper horizon. While the fermionic matter in the black hole is attracted by the black hole at the beginning, after a critical point it is repelled to bounce at a critical high density and then expand into other side of the horizon as a newly created space, which may be considered as a nonsingular, closed universe. We constructed the action of these fermions in a black hole with torsion in the framework of ECSK theory of gravity from which the free Dirac action is inferred to obtain the interaction potential. The creation of a bouncing universe with the extremely repulsive potential may be related to the running vacuum and the modified Friedmann equations yield the consistent cosmological parameters with present FRW universe. Finally, this scenario naturally solves the flatness and horizon problems of cosmology without introducing finely tuned scalar fields, or more complicated functions of the Ricci Scalar R in the gravitational action.