Geometry of the Universe and Its Relation to Entropy and Information

Robertson–Walker solution is presented in terms of gauge fields in a de Sitter gauge theory of gravity (Chamseddine and Mukhanov, J High Energy Phys 3:033, 2010). For a vanishing torsion analogous (Zet et al., Int J Mod Phys C15(7):1031, 2004) we present the field strength tensor and the scalar analogous of the Ricci scalar. Following the noncommutative generalization (Chamseddine, Phys Lett B504:33, 2001) for the de Sitter gauge theory of gravity we study how the noncommutativity of space-time deform, through noncommutative parameters, the homogeneous isotropic solution of the commutative gauge theory of gravity. The study is realized with special conceived analytical procedures under GRTensorII for Maple that we designed for the specific quantities of the gauge theory of gravity (Babeti (Pretorian), Rom J Phys 57(5–6):785, 2012). Noncommutative deformations are obtained using a star product deformation of space time and the Seiberg–Witten map to express the deformed fields in terms of undeformed ones and noncommutative parameter. We analyze a space-time (Fabi et al., Phys Rev D78:065037, 2008) and a space-space noncommutativity. The gauge fields, the field strength tensor and the noncommutative analogue of the metric tensor, the noncommutative scalar analog to Ricci scalar are followed until second order in noncommutative parameter.

A cosmological model that admits barotropic fluid distribution and a negative energy massless scalar creation field as a source in the presence of bulk viscosity and vacuum energy (Λ) in Friedmann–Robertson–Walker space–time is investigated. It has been shown that the model satisfies observational tests and is thus an alternative to the standard Big Bang model. The model is free from real singularity and particle horizon. The creation field increases with time, which matches Hoyle and Narlikar (Proc. Roy. Soc. A, 282, 178 (1964). doi:10.1098/rspa.1964.0225 ). To get the deterministic results, we have assumed that the coefficient of bulk viscosity, ζαρ1/2, where ρ is the matter density, ρ = 3H2, Λ ∼ H2, where H is the Hubble parameter. The model satisfies the energy conditions (weak, dominant, and strong). The deceleration parameter, q < 0, shows that the model represents an accelerating phase of the universe.

Several relationships describing the distance versus time dependence of the cosmic horizon (Rh) for an expanding universe have been published within the past two decades. Some are based on the special conditions, including a flat universe geometry, and when applied for calculation return significantly different values. We present our derivation beginning with Newtonian world then following the Friedmann model from the viewpoint of an observer located at the origin of an expanding spherical, homogeneously matter-dominated universe; both geometrically flat and allowing space–time curvature. Our derivations for the cosmic horizon at the speed of light allow examination for the effects of matter density and space– time curvature. We also compare the fitness of several current models, including the recently proposed Rh = ct universe against the demands of the 580 Union2.1 Type Ia supernovae distance and redshift data with uncommon, proper attention paid to data transformation and observational errors.

The plethora of recent cosmologically relevant data has indicated that our Universe is very well fitted by a standard Friedmann-Lemaitre-Robertson-Walker (FLRW) model, with Ω M ≈ 0.27 and Ω Λ ≈ 0.73 - or, more generally, by nearly flat FLRW models with parameters close to these values. Additional independent cosmological information, particularly the maximum of the angular-diameter (observer area) distance and the redshift at which it occurs, would improve and confirm these results, once sufficient precise Type Ia supernovae data in the range 1.5 < z < 1.8 become available. We obtain characteristic FLRW-closed functional forms for C = C(z) and M 0 = M 0 (z), the angular-diameter distance and the density per source counted, respectively, when A ≠ 0, analogous to those we have for A = 0. More importantly, we verify that for flat FLRW models z max - as is already known but rarely recognized - the redshift of C max , the maximum of the angular-diameter distance, uniquely gives Ω Λ , the amount of vacuum energy in the universe, independent of H 0 , the Hubble parameter. For non-flat models, determination of both z max and C max gives both Ω Λ and Ω M , the amount of matter in the universe, as long as we know H 0 independently. Finally, determination of C max automatically gives a very simple observational criterion for whether or not the universe is flat - presuming that it is FLRW.

Probing singularities in quantum cosmology with curvature scalars

� Societa Italiana di Fisica / Springer-Verlag 2011 Abstract. Magnetic curvature effects, investigated by Barrow and Tsagas (Phys. Rev. D 77, 107302 (2008)), as a mechanism for magnetic field decay in open Friedmann universes ( Λ< 0), are applied to dynamo geometric Ricci flows in 3D curved substrate in laboratory. By simple derivation, a covariant three-dimensional magnetic self-induction equation is obtained. The presence of these curvature effects indicates that de Sitter cosmological constant (Λ ≥ 0) leads to enhancement in the fast kinematic dynamo action which induces a stretching in plasma flows. From the magnetic growth rate, the strong shear case implies an anti-de Sitter case ( Λ< 0) where BT magnetic decaying fields are possible. For weak shear, fast dynamos are possible. The self-induced equation in Ricci flows is similar to the equation derived by BT in the (3 + 1)-spacetime continuum. Lyapunov-de Sitter metric is obtained from Ricci flow eigenvalue problem. In the de Sitter analogue there is a decay rate of γ ≈− Λ ≈− 10 −35 s −2 from the corresponding cosmological constant Λ. This shows that, even in the dynamo case, the magnetic field growth is slower than de Sitter inflation, which renders strongly support to BT result.

We constrain the Friedmann-Robertson-Walker (FRW) model with a “radiation-like” contribution to the Friedmann equation against the astronomical data. We analyze the observational bounds on a (1 + z)4 term from type Ia supernovae (SNIa) data, Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations. We argue that it is not possible to determine the energy densities of individual components scaling like radiation from a kinematic astronomical test. The bounds for the density parameter of the total radiation-like term can be obtained. We find different interpretations of the presence of a scaling-like radiation term: the FRW universe filled with a massless scalar field in a quantum regime (the Casimir effect), the FRW model in a semiclassical approximation of loop quantum gravity, the FRW model in the Randall-Sundrum scenario with dark radiation or a cosmological model with global rotation. In this paper, we mainly concentrate on the Casimir effect arising from quantum effects of a scalar field. This contribution can describe a decaying part of the cosmological constant. We discuss the back-reaction of gravity on the Casimir-type force which is a manifestation of the vacuum fluctuations of the quantum scalar field at low temperature. It is shown that, while the Casimir energy gives rise to the accelerating Universe, the cosmological constant term is still required. We argue that a small negative contribution of a radiation-like term can reconcile the tension between the observed primordial 4He and D abundances. Moreover, the presence of such a contribution can also remove the disagreement between the Hubble parameter H0 values obtained from the SNIa and Wilkinson Microwave Anisotropy Probe (WMAP) satellite data.

We study Hawking-like radiation in a Friedmann–Robertson–Walker (FRW) universe using the quasi-classical WKB/tunneling method, which pictures this process as a "tunneling" of particles from behind the apparent horizon. The correct temperature of the Hawking-like radiation from the FRW space–time is obtained using a canonical invariant tunneling amplitude. In contrast to the usual quantum-mechanical WKB/tunneling problem, where the tunneling amplitude has only a spatial contribution, we find that the tunneling amplitude for FRW space–time (i.e. the imaginary part of the action) has both spatial and temporal contributions. In addition we study backreaction and energy conservation of the radiated particles and find that the tunneling probability and the change in entropy, [Formula: see text], are related by the relationship [Formula: see text], which differs from the standard result, [Formula: see text]. By regarding the whole FRW universe as an isolated adiabatic system, the change in the total entropy is zero. Then, splitting the entropy between the interior and exterior parts of the horizon [Formula: see text], we can explain the origin of the minus sign difference with the usual result: our [Formula: see text] is for the interior region, while the standard result from black hole physics is for the exterior region.

In this paper, we study Friedmann cosmology with time-varying vacuum energy density in the context of Brans–Dicke theory. We consider an isotropic and homogeneous flat space, filled with a matter-dominated perfect fluid and a dynamical cosmological term varLambda (t) , obeying the equation of state of the vacuum. As the exact nature of a possible time-varying vacuum is yet to be found, we explore varLambda (t) given by the phenomenological law varLambda (t)=lambda +sigma H, where lambda and sigma are positive constants. We solve the model and then focus on two different cases varLambda _{H1} and varLambda _{H2} by assuming varLambda =lambda and varLambda =sigma H, respectively. Notice that varLambda _{H1} is the analog of the standard varLambda CDM, but within the Brans–Dicke cosmology. We find the analytical solution of the main cosmological functions such as the Hubble parameter, the scale factor, deceleration and equation of state parameters for these models. In order to test the viability of the cosmological scenarios, we perform two sets of joint observational analyses of the recent Type Ia supernova data (Pantheon), observational measurements of Hubble parameter data, Baryon acoustic oscillation/Cosmic microwave background data and Local Hubble constant for each model. For the sake of comparison, the same data analysis is performed for the varLambda CDM model. Each model shows a transition from decelerated phase to accelerated phase and can be viewed as an effective quintessence behavior. Using the model selection criteria AIC and BIC to distinguish from existing dark energy models, we find that the Brans–Dicke analog of the varLambda -cosmology (i.e. our model varLambda _{H1}) performs at a level comparable to the standard varLambda CDM, whereas varLambda _{H2} is less favoured.

A class of five-dimensional space–times that contain four-dimensional hypersurfaces whose intrinsic metrics are Friedman–Robertson–Walker (FRW) metrics is examined (the four-dimensional intrinsic Lorentzian metrics are both spatially homogeneous and isotropic). The five-dimensional vacuum field equations, 5Gij=0, are shown to induce four-dimensional perfect-fluid FRW field equations, 4Gij=4Tij, and thus these FRW cosmological models may be interpreted as being purely geometrical in origin.

The models represent expanding and shearing universe and both models start with Big Bang initially and the expansion stops for large time. The spatial volume increases with time representing inflationary scenario. The shear is zero for large value of time representing isotropization of universe. The Hubble parameter determines the age of the universe. The expression for Hubble parameter matches with FRW model.

Recently a new time-evolution picture of the Dirac quantum mechanics was defined in charts with spatially flat Robertson–Walker metrics, under the name of Schrödinger picture (I. I. Cotăescu, Mod. Phys. Lett. A22, 2965 (2007)). In the present paper, new Dirac quantum modes are found in moving charts of the de Sitter space–time using the technical advantages offered by this picture. The principal result is a new set of energy eigenspinors which behave as polarized plane waves and form a complete system of orthonormalized solutions of the free Dirac equation.

In this paper, we study the viscous extended cosmic Chaplygin gas whose equation of state reduces to extended Chaplygin gas in the limit $$\omega \rightarrow 0$$ with varying cosmological constant in flat FRW universe. In this framework, we assume the bulk viscosity $$\zeta $$ and cosmological constant $$\Lambda $$ as a linear combination of two terms, one is constant and other is a function of dark energy density $$\rho $$. We obtain generalized Friedmann equations due to bulk viscosity, cosmological constant and extended cosmic Chaplygin gas. We calculate the time-dependent dark energy density $$\rho $$ for various values of n and $$\alpha = 1/2$$ both analytically and numerically. We analyse the behaviour of scale factor, Hubble expansion parameter and deceleration parameter graphically and discuss the stability of the model by using square of speed of sound.

In the framework of a spherically symmetric Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime, we construct a quintessence model driven by a nonlinear, massless spinor field in an open-universe scenario. The model parameters are constrained using recent cosmological observations, including the distance modulus from type Ia supernovae (binned Pantheon sample), Hubble parameter measurements from cosmic chronometers (CC) and the Sloan Digital Sky Survey (SDSS), and baryon acoustic oscillation (BAO) data. A comprehensive Markov chain Monte Carlo (MCMC) analysis yields best-fit estimates for a relatively lower present-day Hubble constant, and the equation-of-state parameter. The best-fit theoretical predictions are compared with observational data for both the Hubble parameter and the distance modulus. Furthermore, the deceleration parameter and the statefinder pair $$\{r, s\}$$ { r , s } are evaluated to demonstrate the model’s effectiveness in describing the universe’s late-time acceleration. The resulting lower value of $$H_{0}=66.9~\text {km}\,\text {s}^{-1}\,\text {Mpc}^{-1}$$ H 0 = 66.9 km s - 1 Mpc - 1 is consistent with the Planck cosmic microwave background (CMB) measurements and suggests a possible route toward alleviating the current Hubble tension. Overall, the spinor field quintessence model with $$w_{\textrm{de}}=-0.814$$ w de = - 0.814 and $$\Omega _{m0} = 0.264$$ Ω m 0 = 0.264 emerges as a statistically viable and physically consistent alternative to the standard $$\Lambda $$ Λ CDM cosmology and conventional scalar-field quintessence frameworks.

The accelerating expansion of the universe has motivated the exploration of alternative gravity theories beyond General Relativity (GR). In this study, we investigate the cosmological implications of [Formula: see text] gravity, an extension of [Formula: see text] gravity that incorporates additional torsional scalar [Formula: see text], within a homogeneous and isotropic Friedmann–Robertson–Walker (FRW) metric. We derive the field equations and analyze the cosmic expansion, energy density, isotropic pressure, and equation of state parameter. To ensure observational consistency, we constrain the model parameters using Hubble parameter [Formula: see text] measurements and the Pantheon+ Type Ia supernovae dataset through a Markov Chain Monte Carlo (MCMC) analysis. Our findings indicate that this model naturally explains cosmic acceleration without requiring a cosmological constant, with results closely aligning with Planck data. The study further examines the energy conditions and the stability. The violation of the strong energy condition at late times supports the observed acceleration, consistent with other modified gravity frameworks. This work highlights the potential of [Formula: see text] gravity in explaining dark energy phenomena and motivates further theoretical and observational investigations.