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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.

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.

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.

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.

This paper is devoted to study modified Chaplygin gas and cosmological ‘constant’ as candidates of dark energy in the presence of cosmic viscous fluid with reference to the Bianchi type V space-time geometry. To represent a more viable cosmological model, variation of gravitational ‘constant’ is also considered. Precise solutions of equations of field have been acquired, where scale factors expand as monomial functions of cosmic time. Further, by use of graphical representation, behaviours of various parameters are also examined.

This study presents tilted two forms of dark energy in f ( T ) theory of gravity. f T gravity is the generalization of the teleparallel theory of gravity, where T is the torsion scalar. In this work, the tilted model is examined by using forms of dark energy consisting part of quintessence and cosmological constant (Dagwal and Pawar in MPLA 33:185213, 2018). The singular origin and non-singular origin of the models are discussed (Solanke et al. in IJGMMP 18:2150062, 2021). The Hubble parameter H 0 and deceleration parameter q with the help of modern observational data are constrained.The reliability of the resultant model with observational parameter from the point of astrophysical miracle like as look-back time t L , angular-diameter distance d A , distance modulus μ ( z ) , luminosity distance d L and proper distance d ( z ) are explored with SNeIa, H(z), WMAP7 + BAO + H(z) and WMAP7 with observational data (Kumar in MNRAA 422:2532, 2012 and Gumjudpai in MPLA 28:135022, 2013).

Quantum field theory (QFT) and general relativity (GR) are pillars of modern physics, each supported by extensive experimental evidence. QFT operates within Lorentzian spacetime, while GR ensures local Lorentzian geometry. Despite their successes, these frameworks diverge significantly in their estimations of vacuum energy density, leading to the cosmological constant problem—a discrepancy where QFT estimates exceed observed values by 123 orders of magnitude. This paper addresses this inconsistency by tracing the cooling evolution of the universe’s gauge symmetries—from SU(3)×SU(2)×U(1) at high temperatures to SU(3) alone near absolute zero—motivated by the experimental Meissner effect. This symmetry reduction posits that SU(3) forms the fundamental “atoms” of vacuum energy. Our analysis demonstrates that the calculated number of SU(3) vacuum atoms reconciles QFT’s predictions with empirical observations, effectively resolving the cosmological constant problem. The third law of thermodynamics, by preventing the attainment of absolute zero, ensures the stability of SU(3) vacuum atoms, providing a thermodynamic foundation for quark confinement. This stability guarantees a strictly positive mass gap defined by the vacuum energy density and implies a Lorentzian quantum structure of spacetime. Moreover, it offers insights into the origins of both gravity/gauge duality and gravity/superconductor duality.

In this article, we consider the 4 + n dimensional spacetimes among which one is the four dimensional physical Universe and the other is an n-dimensional sphere with constant radius in the framework of Lanczos-Lovelock gravity. We find that the curvature of extra dimensional sphere contributes a huge but negative energy density provided that its radius is sufficiently small, such as the scale of Planck length. Therefore, the huge positive vacuum energy, i.e., the large positive cosmological constant is exactly cancelled out by the curvature of extra sphere. In the mean time the higher order of Lanczos-Lovelock term contributes an observations-allowed small cosmological constant if the number of extra dimensions is sufficiently large, such as n ≈ 69.