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The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence…
Quantum theory, general relativity, the standard model of particle physics, and the $\Lambda$CDM model of cosmology have all been spectacularly successful within their respective regimes of applicability, but many central problems remain…
The cosmological constant $\Lambda$ can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e. $\Omega_{m}$ and $\Omega_{k}$,…
In this article, our goal is to investigate the cosmological dynamics and structure formation in a modified cosmological framework inspired by a generalized mass-to-horizon entropy relation and consistent with the Clausius relation.…
The cosmological constant, i.e., the energy density stored in the true vacuum state of all existing fields in the Universe, is the simplest and the most natural possibility to describe the current cosmic acceleration. However, despite its…
The cosmological constant if considered as a fundamental constant, provides an information treatment for gravitation problems, both cosmological and of black holes. The efficiency of that approach is shown via gedanken experiments for the…
This paper investigates anthropic bounds on the vacuum energy $\Lambda$. We first consider the possibility of cosmic observers existing at any random time (including the future) for constant $\Lambda$, and take into account the suppression…
I propose an observationally and theoretically consistent resolution of the cosmological constant problem: $\Lambda$ is a counterterm -- with a running coupling -- that balances the monopole celestial sky average of the kinetic energy of…
We investigate the role of the cosmological constant in the holographic description of a radiation-dominated universe $C_2/R^4$ with a positive cosmological constant $\Lambda$. In order to understand the nature of cosmological term, we…
The cosmological constant is normally introduced as an additional term entering the Einstein-Hilbert (EH) action. In this letter we demonstrate that instead, it appears naturally from the standard EH action as an invariant term emerging…
We study the effects of a generalized uncertainty principle on the classical and quantum cosmology of a closed Friedmann Universe whose matter content is either a dust or a radiation fluid. More concretely, assuming the existence of a…
After reviewing the cosmological constant problem - why is Lambda not huge? - I outline the two basic approaches that had emerged by the late 1980s, and note that each made a clear prediction. Precision cosmological experiments now indicate…
A theory of the cosmological constant Lambda is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the…
Entropy bounds render quantum corrections to the cosmological constant $\Lambda$ finite. Under certain assumptions, the natural value of $\Lambda$ is of order the observed dark energy density $\sim 10^{-10} {\rm eV}^4$, thereby resolving…
We consider a dynamical approach to the cosmological constant. There is a scalar field with a potential whose minimum occurs at a generic, but negative, value for the vacuum energy, and it has a non-standard kinetic term whose coefficient…
The extended black hole thermodynamics in which the cosmological constant plays the role of pressure significantly enriches the phase structure of the theory. In order to understand the extended black hole thermodynamics more precisely, we…
Using the holographic entropy proposal for a closed universe by Verlinde, a bound on equations of state for different stages of the universe is obtained. Further exploring this bound, we find that an inflationary universe naturally emerges…
We present a new mechanism for addressing the cosmological constant problem based on global constraints arising from a lapse function in a higher-dimensional gravitational theory. Inspired by Horava-Lifshitz gravity, we consider a 5d…
The causal entropic principle has been proposed as a superior alternative to the anthropic principle for understanding the magnitude of the cosmological constant. In this approach, the probability to create observers is assumed to be…
We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant $G$ and the speed of light $c$. Three different approaches to the formulation of the field equations are…