Friedmann-Robertson-Walker Research Articles

Particle production and density fluctuations of nonclassical inflaton in coherent squeezed vacuum state of flat FRW universe

In this paper, we study nonclassical inflaton, which is minimally coupled to the semi-classical gravity in FRW universe in Coherent Squeezed Vacuum State (CSVS). We have determined the Oscillatory phase of inflaton, power-law expansion, scale factor, density fluctuations, quantum fluctuations and particle production for CSVS. We have obtained an estimated leading solution of scale factor in CSVS and found it proportional to [Formula: see text] and showing similar diversification as demonstrated by Semi-classical Einstein Equation (SCEE) of gravity in matter dominated universe. We have also studied the validity of SCEE in CSVS. We have computed validity of uncertainty relation for FRW Universe by determining the quantum fluctuation for CSVS. Our results show that Quantum fluctuations don’t depend on coherent parameter [Formula: see text] as the uncertainty relation doesn’t effect by the displacement of [Formula: see text] in phase space. We have also studied the production of particles in CSVS for oscillating massive inflaton in flat FRW universe.

Dynamical systems of modified Gauss–Bonnet gravity: cosmological implications

In this paper, we derive the field equations of modified Gauss–Bonnet gravity termed as f(R, G) gravity for the non-flat Friedmann–Robertson–Walker (FRW) spacetime. We utilize the dynamical system approach to study the cosmic dynamics of two different class of f(R, G) models composed of radiation and matter (cold dark matter and baryonic matter). The linear perturbations around the fixed points are studied to explore the corresponding stability of points. The cosmological implications are studied in f(R,G)=f0RnG1-n and f(R,G)=f0Rα+f1Gβ models to identify the qualitative evolution of universe with the flat-FRW spacetime. The qualitative differences between the considered class of models are discussed in detail. The fixed points corresponding to the late-time accelerated and radiation phase of the universe will exist in the model but, the existence of fixed point corresponding to the matter dominated phase will depend on the functional form of f(R, G). Furthermore, the autonomous systems are utilized to study the cosmographic parameters along with the statefinder diagnostic.

Cosmological dynamics of FRW universe in presence of tachyonic field

Cosmological dynamics of FRW universe in presence of tachyonic field

3+1 formalism of the minimally extended varying speed of light model

Abstract The $3+1$ formalism provides a structured approach to analyzing spacetime by separating it into spatial and temporal components. When applied to the Robertson-Walker metric, it simplifies the analysis of cosmological evolution by dividing the Einstein field equations into constraint and evolution equations. It introduces the lapse function $N$ and the shift vector $N^i$, which control how time and spatial coordinates evolve between hypersurfaces. In standard model cosmology, $N = 1$ and $N^i = 0$ for the Robertson-Walker metric. However, the $N$ becomes a function of time when we apply the metric to the minimally extended varying speed of light model. This approach allows for a more direct examination of the evolution of spatial geometry and offers flexibility in handling scenarios where the lapse function and shift vector vary. In this manuscript, we derive the model's $N$, $N^i$, along with the constraint and evolution equations, and demonstrate their consistency with the existing Einstein equations. We have shown in a previous paper that the possibility of changes in the speed of light in the Robertson-Walker metric is due to cosmological time dilation. Through the $3+1$ formalism, we can make the physical significance more explicit and demonstrate that it can be interpreted as the lapse function. From this, we show that the minimally extended varying speed of light model is consistent.

Non-flat Friedmann-Lemaitre-Robertson-Walker universe with Barrow holographic dark energy

In this paper, we study a non-flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with cold dark matter and Barrow holographic dark energy. We assume the Hubble horizon as IR cutoff and the scale factor to obey a hybrid expansion law to construct a cosmological model within the framework of General Relativity. The physical and geometrical properties of the model are discussed by studying the evolution of various parameters of cosmological importance. The behaviour of the dark energy equation of state parameter wDE is also studied for both interacting and non-interacting Barrow holographic dark energy. We observe that the Barrow exponent ∆ significantly affects the dark energy equation of state parameter which in turn exhibits the behaviour of quintessence and phantom dark energy. The evolution of the jerk parameter is also studied.

Cosmological amplitudes in power-law FRW universe

The correlators of large-scale fluctuations belong to the most important observables in modern cosmology. Recently, there have been considerable efforts in analytically understanding the cosmological correlators and the related wavefunction coefficients, which we collectively call cosmological amplitudes. In this work, we provide a set of simple rules to directly write down analytical answers for arbitrary tree-level amplitudes of conformal scalars with time-dependent interactions in power-law FRW universe. With the recently proposed family-tree decomposition method, we identify an over-complete set of multivariate hypergeometric functions, called family trees, to which all tree-level conformal scalar amplitudes can be easily reduced. Our method yields series expansions and monodromies of family trees in various kinematic limits, together with a large number of functional identities. The family trees are in a sense generalizations of polylogarithms and do reduce to polylogarithmic expressions for the cubic coupling in inflationary limit. We further show that all family trees can be decomposed into linear chains by taking shuffle products of all subfamilies, with which we find simple connection between bulk time integrals and boundary energy integrals.

Thick brane in mimetic-like gravity

We analyze a five-dimensional braneworld governed by a mimetic-like gravity, a plausible candidate for explaining dark matter. Within this scenario, we examine Friedmann-Lemaître-Robertson-Walker (FLRW) branes and find that constant curvature and Minkowskian solutions are possible. We then show that the mimetic model leads to kink-like and lump-like thick brane solutions without the need for spontaneous symmetry breaking. Its stability against small perturbations is also verified.

Gauge theory meets cosmology

We reconsider linear perturbations around general Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom involving only time reparametrizations, we write down classical background solutions analytically, for an arbitrary number of fluid components. We then show that the time evolution of scalar and tensor adiabatic perturbations are governed by Schrödinger-like differential equations of generalized Heun type. After recovering known analytic results for a single-component fluid, we discuss more general situations with two and three different fluid components, with special attention to the combination of radiation, matter and vacuum energy, which is supposed to describe the ΛCDM model. The evolution of linear perturbations of a flat ΛCDM universe is described by a two-transient model, where the transitions from radiation to matter and matter to vacuum energy are governed by a Heun equation and a Hypergeometric equation, respectively. We discuss an analytic approach to the study of the general case, involving generalized Heun equations, that makes use of (quantum) Seiberg-Witten curves for 𝒩 = 2 supersymmetric gauge theories and has proven to be very effective in the analysis of Black-Hole, fuzzball and ECO perturbations.

The generalized second law formulated from the variable equation of state parameter

The generalized second law of thermodynamics (GSLT) is examined in the current work in the backdrop of Friedmann–Robertson–Walker universe. A digression from the standard Bekenstein–Hawking entropy formulation is considered. Two different modified forms of the entropy functions are studied. For the matter component, five well-known parameterizations of the equation of state parameter are taken into consideration. The diagrammatic representations of the rate of change of the entropy functions in the different models are presented. The outcomes suggest that the GSLT is valid in these models for certain choices of the parameters involved.

Inflation and the principle of equivalence

Abstract A formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find – at each location within a curved spacetime – the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature relative to flat spacetime. In this article, we use this theorem to prove that a de Sitter expansion, required during cosmic inflation, does not satisfy this condition and is therefore inconsistent with the PoE. To emphasize the importance – and reality – of this outcome, we contrast it with the analogous derivation for the Schwarzschild metric, which instead satisfies this requirement completely. We point out that this failure by de Sitter results from its incorrect handling of the Friedmann–Lemaître–Robertson–Walker (FLRW) lapse function, g tt {g}_{{\rm{tt}}} . Our conclusion calls into question whether a period of inflated expansion could have even been possible in the context of FLRW cosmologies, and is noteworthy in light of recent, high-precision measurements showing that inflation could not have solved the temperature horizon problem while simultaneously producing the observed primordial power spectrum.

Holographic principle inspired dark energy description of unified early and late universe in viscous mimetic gravity

In this study, we explore the mimetic matter model proposed by Chamseddine and Mukhanov (2013), utilizing the holographic principle to coherently describe both the early and late universe when bulk viscosity is present in the inhomogeneous equation of state. Our examination of the universe’s evolution is based on the generalized infrared-cutoff holographic dark energy model detailed by Nojiri and Odintsov (2017) within the context of the flat FRW model. From a holographic perspective, we derive the energy conservation equation incorporating mimetic matter through a viscous holographic fluid model. Furthermore, we analyze various scenarios of bulk viscosity by assuming a constant equation of state parameter and derive the infrared cut-off expression in terms of the particle horizon. We demonstrate that within the framework of mimetic gravity, there is a class of solutions comparable to those in General Relativity, with an additional contribution from a non-relativistic mimetic matter component. These solutions can effectively describe dark matter.

A numerical solution of Schrödinger equation for the dynamics of early universe

Artificial neural networks (ANNs) have attained widespread success across varied disciplines. This study is designated for looking into an application of an integrated intelligent computing paradigm concerning dynamics in the early Universe through numerical solutions to the Schrödinger equation. To arrive at this we leverage the Levenberg–Marquardt backpropagation networks (LMBNs) to probe cosmic evolution in the early Universe with the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric for a flat minisuperspace model of the Universe in the background. This leads to bridging quantum mechanics and inflationary Universe dynamics conducing to quantum cosmology within the standard model. Wheeler–DeWitt equation corresponds to the time-independent Schrödinger equation obtained from the equations of motion for a single scalar field in flat spacetime with FLRW metric. Utilizing the ntstool the whole computing process is operated for simulation. To evaluate the accuracy and efficiency of the proposed scheme a comparative analysis is carried out. To construct continuous neural network mappings we employ the explicit Runge–Kutta method as the target parameter for generating datasets. To determine the solution datasets of different scenarios, the training, testing, and validation processes are employed to take advantage of these in the learning of neural network models established upon the backpropagation technique of Levenberg–Marquardt. By varying related parameters we develop three scenarios that produce nine cases, three for each. The data plots of performance, training state, error histogram, regression, time-series response, and error autocorrelation represent the visualization of the results. These plots show a complete case description by displaying all the necessary data values. The analysis of these plots is presented to validate all the cases. Performing the analysis by mean square error (MSE) validates the achieved accuracy of the results by validating and verifying neural networks. This work is motivated by the compelling need to develop innovative computational methods for solving complex cosmological questions to untangle the conundrums of the early universe. The attractive numerical solutions of the Schrödinger equation for the early Universe heralds a step towards quantum cosmology based on the interplay of the Wheeler–DeWitt equation and time-independent Schrödinger equation. There is an increasing trend to use computational methods to solve ordinary and partial differential equations with the help of code development in Matlab. For this purpose feed-forward artificial neural network is used for investigating the Schrödinger equation.

Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy

According to the quantum deformation approach to quantum gravity, the thermodynamical entropy of a quantum-deformed (q-deformed) black hole with horizon area A established by Jalalzadeh is expressed as S=πsinA8GN/sinπ2N, where N=Lq2/Lp2 is the q-deformation parameter, Lp denotes the Planck length, and Lq denotes the quantum-deformed cosmic apparent horizon distance. In this paper, assuming that the q-deformed entropy is associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) universe, we derive the modified Friedmann equation from the unified first law of thermodynamics, dE=TdS+WdV. And this one obtained is in line with the modified Friedmann equation derived from the law of emergence proposed by Padmanabhan. It clearly shows the connection between the law of emergence and thermodynamics. We further investigate the constraints of entropy maximization in the framework of the q-deformed horizon entropy, and the results demonstrate the consistency of the law of emergence with the maximization of the q-deformed horizon entropy.

Mimetic Weyl geometric gravity

We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space–time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained by starting from a conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and an effective matter term, respectively. After linearizing the action in the Weyl scalar by introducing an auxiliary scalar field, we include the mimetic field, constructed from the same auxiliary scalar field used to linearize the action, via a Lagrange multiplier. The conformal invariance of the action is maintained by imposing the trace condition on the effective matter energy–momentum tensor, built up from the ordinary matter Lagrangian, and some specific functions of the Weyl vector, and the scalar field, respectively, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the Mimetic Weyl geometric gravity by considering the dynamics of an isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker FLRW Universe. The generalized Friedmann equations of the model are derived, and their solutions are obtained numerically for a dust filled Universe. Moreover, we perform a detailed comparison of the predictions of the considered model with a set of observational data for the Hubble function, and with the results of the ΛCDM standard paradigm. Our results indicate that the present model give a good description of the observational data, and they reproduce almost exactly the predictions of the ΛCDM scenario. Hence, Mimetic Weyl geometric gravity can be considered a viable alternative to the standard approaches to cosmology, and to the gravitational phenomena.

On the convergence of cosmographic expansions in Lemaître–Tolman–Bondi models

Abstract We study cosmographic expansions of the luminosity distance for a variety of Lemaître–Tolman–Bondi (LTB) models which we specify inspired by local large-scale structures of the Universe. We consider cosmographic expansions valid for general spacetimes and compare to the Friedmann–Lemaître–Robertson–Walker (FLRW) limit of the expansions as well as to its naive isotropic extrapolation to an inhomogeneous Universe. The FLRW expansions are often poor near the observer but become better at higher redshifts, where the light rays have reached the FLRW background. In line with this we find that the effective Hubble, deceleration and jerk parameters of the general cosmographic expansion are often very different from the global ΛCDM values, with deviations up to several orders of magnitude. By comparing with the naive isotropic extrapolation of the FLRW expansion, we assess that these large deviations are mainly due to gradients of the shear. Very close to the observer, the general cosmographic expansion is always best and becomes more precise when more expansion terms are included. However, we find that the convergence radius of the general cosmographic expansion is small for all studied models and observers and the general cosmographic expansion becomes poor for most of the studied observers already before a single LTB structure has been traversed. The small radius of convergence of the general cosmographic expansion has also been indicated by earlier work and may need careful attention before we can safely apply the general cosmographic expansion to real data.

Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP

In this paper, we explore the phase transition, critical behavior and microstructure of the FRW in the framework of a new higher order generalized uncertainty principle (GUP). Our initial step involves deriving the equation of state by defining the work density W from GUP corrected Friedmann equations as the thermodynamic pressure P. Based on the modified equation of state, we conduct an analysis of the P−V phase transition in the FRW universe. Subsequently, we obtain the critical exponents and coexistence curves for the small and large phases of the FRW universe around the critical point. Finally, employing Ruppeiner geometry, we derive the thermodynamic curvature scalar RN, investigating its sign-changing curve and spinodal curve. The results reveal distinctive thermodynamic properties for FRW universes with positive and negative GUP parameters β. In the case of β>0, the phase transition, critical behavior and microstructure of FRW universe are like those of Van der Waals system and charged AdS. Conversely, for β<0, the results resemble those obtained through effective scalar field theory. These findings underscore the capacity of quantum gravity to induce phase transitions in the universe, warranting further in-depth exploration.

McVittie–Plummer Spacetime: Plummer Sphere Immersed in the FLRW Universe

The McVittie–Plummer spacetime is a spherically symmetric inhomogeneous cosmological model that represents a spherical star system embedded in a standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model. We study the main physical properties of this gravitational field. Regarding the interplay between the physics of the local system and the expanding background, we employ the Misner–Sharp mass–energy function to show that there is a relatively weak time-dependent general relativistic coupling between the astrophysical system and the background FLRW cosmological model. The coupling term is proportional to the inverse of the scale factor and decreases as the Universe expands.

Spectrum of primordial gravitational waves in the presence of a cosmic string

In this paper we consider an inflating universe with long straight cosmic string along z-axis. We demonstrate that cosmic string's effect can be treated as a perturbation on the background of FRW metric. By performing cosmological perturbations on this inflating cosmic string background, we derived the linearized Einstein field equations. We show that at leading order (neglecting the mixing terms of cosmic string perturbations with gravitational tensor perturbations), the cosmic string appears as an inhomogeneous term on the right hand side of wave equation for tensor perturbations. Finally, by finding analytical solution of the wave equation for slow-roll inflation, we illustrate its impact on the spectrum of primordial gravitational waves.

Thermal chaos of quantum-corrected-AdS black hole in the extended phase space

We briefly analyzed the equation of state and critical points of the quantum-corrected-AdS black hole and used the Melnikov method to study its thermal chaotic behavior in the extended phase space of flat, closed, and open universes. The results show that the black hole’s thermodynamic behavior is similar to that of the Van der Waals system. Although the critical ratios at the critical points in the three types of universes differ, they are all independent of the quantum correction parameter. Only an open universe can attain the critical ratio of 38 corresponding to the Van der Waals system, while in the other two universes, the critical ratio is always greater than this value. For chaos, time perturbations will lead to chaotic behavior when their amplitude exceeds a critical value that depends on the quantum correction parameter and the radius of the dust sphere in the FRW model. Based on this, we found that the chaotic behavior of the black hole varies across different universes depending on the quantum correction parameter, but this parameter always makes chaos more likely. Using the value of the quantum correction parameter determined by Meissner, chaos is always more difficult to occur in an open universe compared to the other two types of universes. Which universe is most prone to chaos depends on the radius of the dust sphere. Finally, chaotic behavior is always present under spatial perturbations.

Evolution of the Universe with quintessence model in Rastall gravity

Abstract We investigate the Universe’s evolution within the framework of Rastall gravity, which is an extension of the standard ΛCDM model. Utilizing a linear parametrization of the Equation of State (EoS) in a Friedmann-Lemaître-Robertson-Walker (FLRW) background, we constrain the model parameters through analysis of cosmic chronometers (CC), Pantheon, Gold, Gamma Ray Burst (GRB), and Baryon Acoustic Oscillations (BAO) datasets, as well as their joint analysis, under 1σ and 2σ confidence levels, considering the Rastall parameter λ. The constrained parameters are then used to compare our model with the standard ΛCDM model. Our findings include a detailed examination of the model’s physical interpretations and demonstrate the potential for an accelerating universe expansion in later times, aligning with the observed behavior of dark energy.