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Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified Rényi entropy is applied to Padmanabhan’s ‘holographic equipartition law’, by regarding the Bekenstein–Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original Rényi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropic, and spatially flat universe. When a specific condition is mathematically satisfied, the extra driving term is found to be constant-like as if it is a cosmological constant. Interestingly, the order of the constant-like term is naturally consistent with the order of the cosmological constant measured by observations, because the specific condition constrains the value of the constant-like term.

Persisting tensions between high-redshift and low-redshift cosmological observations suggest the dark energy sector of the Universe might be more complex than the positive cosmological constant of the Λ CDM model. Motivated by string theory, wherein symmetry considerations make consistent AdS backgrounds (i.e., maximally-symmetric spacetimes with a negative cosmological constant) ubiquitous, we explore a scenario where the dark energy sector consists of two components: a negative cosmological constant, with a dark energy component with equation of state w ϕ on top. We test the consistency of the model against low-redshift baryon acoustic oscillation and Type Ia supernovae distance measurements, assessing two alternative choices of distance anchors: the sound horizon at baryon drag determined by the Planck collaboration and the Hubble constant determined by the SH0ES program. We find no evidence for a negative cosmological constant and mild indications for an effective phantom dark energy component on top. A model comparison analysis reveals that the Λ CDM model is favoured over our negative cosmological constant model. While our results are inconclusive, should low-redshift tensions persist with future data, it would be worth reconsidering and further refining our toy negative cosmological constant model by considering realistic string constructions.

In this work, we discuss a simple toy model in which the nonlinear and stochastic terms typical of dynamical collapse models are added to the Wheeler-DeWitt equation of gravity and a perfect fluid once a clock coordinate is fixed. We see that the addition of these terms allows us to explain the emergence of a single well-defined cosmological constant, starting from a superposition of different values of the latter.

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found.

Cosmic inflation in LRS Bianchi Type I space-time under effect of the bulk viscosity and time dependent cosmological constant in C-field cosmology is investigated. To find the deterministic result of the field equations, we assumed R where H0 is the Hubble parameter and t is cosmic time. It has been observed that the C-field effect increases with cosmic time, and the obtained result resembles the evidence in HN theory. The real singularity does not exist in the derived model and Particle horizon exists in the model. The spatial volume increases in exponentially manner with proper time favorable to the expansion of the universe. The negative deceleration (q 0) indicates the accelerated phase of the universe and the de-sitter cosmos is investigated. The bulk viscosity coefficient is found to be constant and vacuum energy density found to be negatively in exponential manner with cosmic time which shows that the decay of the energy component transfers energy in a continuous way to the material component.The volume of cosmos varies as exponentially way to proper time along with hubble parameter. The geometrical and dynamical properties of physical parameter are investigated in rigorous manner. The behavior of the model under different physical conditions is also discussed.

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations.

In this study, a variable cosmological constant model is created for anisotropic star structures, which satisfies the remaining physical requirements, and validates the required energy conditions (Ecs), and TOV equations. First, the Finch-Skea spacetime solution is taken into account as a static spherically symmetric metric. Moreover, external Schwarzschild geometry is taken into account to correlate our internal stellar structure and determine the values of the constants used in the Finch-Skea spacetime solution. Finally, in this paper, multiple aspects are discussed, such as the radius, compactness, stresses, stability, density profile, and masses under the variable cosmological constant model in f ( R , T ) gravity for various stars.

We review selected aspects of unimodular gravity and we discuss its viability as a solution of the old cosmological constant problem. In unimodular gravity, the cosmological constant is promoted to a global degree of freedom. We highlight the importance of correctly setting up its initial data in order to achieve a resolution of the cosmological constant problem on a semi-classical level. We review recent path integral analysis of quantum aspects of unimodular gravity to note that the semi-classical findings carry over to the quantum level as well. We point out that a resolution of the problem inherently relies on a global constraint on the spacetime four-volume. This makes the theory closely related to the vacuum energy sequester, which operates in a similar way. We discuss possible avenues of extending unimodular gravity that preserve the resolution of the cosmological constant problem.

Recently Chung and Hassanabadi proposed a higher order general uncertainty principle (GUP∗) that predicts a minimal length as well as possesses a upper bound momentum limit. In this article, we have discussed an ideal gas system and its thermal properties using that deformed canonical algebra introduced by them. Moreover, we examined blackbody radiation spectrum and the cosmological constant in the presence of the GUP∗. After a comparison with the existing literature, we concluded that the given formalism of Chung and Hassanabadi yields more accurate results.

This paper explores and analyzes a set of solutions describing the interior structure of relativistic compact stellar structures with variable cosmological constant Λ(r). We consider the solution of Krori–Barua space-time to a static spherical symmetric metric. Furthermore, we match our interior stellar structure with the exterior Schwarzschild geometry to determine the values of the constants used in the solution of the Krori–Barua space-time. The numerical values of these constants were determined for a set of different compact stars, and using these constants in our solutions, we have studied the viability of matter content, stability, TOV equations, and surface red-shift; and we predicted some physical aspects like central and surface densities, stresses, masses, and radii.