Robertson Walker Universe Research Articles

Cosmology of the generalized model of LQG

In this paper, we study the main cosmological properties of the classical Friedmann equations in the case of homogeneous and isotropic Friedmann–Robertson–Walker Universe and we also generalized the expression of the Friedmann equation in the case of Loop Quantum Cosmology (LQC). Considering the [Formula: see text]-model, we found the solutions of the equations considered for two particular cases, i.e. [Formula: see text] (i.e. the de Sitter solution) and [Formula: see text]. Moreover, we considered and studied two exact cosmological solutions of the [Formula: see text]-model, in particular the power-law and the exponential ones. Moreover, we also considered a third more complicated case and we derived the solution for an arbitrary function of the time [Formula: see text]. A scalar field description of the model is presented by constructing its self-interacting potential.

Effective theories for a nonrelativistic field in an expanding universe: Induced self-interaction, pressure, sound speed, and viscosity

A massive, nonrelativistic scalar field in an expanding spacetime is usually approximated by a pressureless perfect fluid, which leads to the standard conclusion that such a field can play the role of cold dark matter. In this paper, we systematically study these approximations, incorporating subleading corrections. We provide two equivalent effective descriptions of the system, each of which offers its own advantages and insights: (i) A nonrelativistic effective field theory (EFT) with which we show that the relativistic corrections induce an effective self-interaction for the nonrelativistic field. As a byproduct, our EFT also allows one to construct the exact solution, including oscillatory behavior, which is often difficult to achieve from the exact equations. (ii) An effective (imperfect) fluid description, with which we demonstrate that, for a perturbed Friedmann-Lemaître- Robertson-Walker (FLRW) universe: (a) The pressure is small but nonzero (and positive), even for a free theory with no tree-level self-interactions. (b) The sound speed of small fluctuations is also nonzero (and positive), reproducing already known leading-order results, correcting a subdominant term, and identifying a new contribution that had been omitted in previous analyses. (c) The fluctuations experience a negative effective bulk viscosity. The positive sound speed and the negative bulk viscosity act in favor of and against the growth of overdensities, respectively. The net effect may be considered a smoking gun for ultra-light dark matter.

Casimir effect and Stefan–Boltzmann law at finite temperature in a Friedmann–Robertson–Walker universe

A spatially flat Friedmann–Robertson–Walker background with a general scale factor is considered. In this spacetime, the energy–momentum tensor of the scalar field with a general curvature coupling parameter is obtained. Using the Thermo Field Dynamics (TFD) formalism, the Stefan–Boltzmann law and the Casimir effect at finite temperature are calculated. The Casimir effect at zero temperature is also considered. The expansion of the universe changes these effects. A discussion of these modifications is presented.

Density fluctuations and single-mode thermal states in the FRW universe

Using single-mode squeezed and coherent thermal states formalism, we analyzed the validity of the semiclassical Einstein equation (SCEE) in the flat Friedmann–Robertson–Walker universe by analyzing the density fluctuations in terms of a massive inflaton. In a single-mode squeezed thermal states the density fluctuations are too large; consequently, the semiclassical theory of gravity (SCTG) does not hold good, for squeezing parameter greater than unity, i.e., $$r_{s}>1$$; however, the theory is valid when this related squeezing parameter is smaller than the unity, i.e., $$r_{s}<<1$$ and $$r_{s}<1$$. Also, it is noted that the SCEE is dependable on coherent thermal state formalism. The current study provides a description of the density fluctuations as a result of the quantum and thermal effects in the SCTG.

A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes

We report a symmetry property of the Einstein–Friedmann equations for spatially flat Friedmann–Lemaître–Robertson–Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a one-parameter Abelian group.

Similarity solutions for the Wheeler\u2013DeWitt equation in fleft( Rright) -cosmology

In the case of a spatially flat Friedmann–Lemaître–Robertson–Walker Universe in fleft( Rright) -gravity we write the Wheeler–DeWitt equation of quantum cosmology. The equation depends upon the functional form of fleft( Rright) . We choose to work with four specific functions of fleft( Rright) in which the field equations for the classical models are integrable and solvable through quadratures. For these models we determine similarity solutions for the Wheeler–DeWitt equation by determining Lie–Bäcklund transformations. In addition we show how the classical limit is recovered by the similarity solutions of the Wheeler–DeWitt equation.

Optimal estimation of parameters for scalar field in an expanding spacetime exhibiting Lorentz invariance violation

We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson–Walker universe exhibiting Lorentz invariance violation (LIV). We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision.

Particle Creation in Friedmann–Robertson–Walker Universe

Using variable gravitational and cosmological constants, the mechanism of particle creation in the universe is studied for Friedmann–Robertson–Walker (FRW) space-times at high dimensions to explain the early deceleration and present accelerating phases. To investigate the dynamics of these phases, we consider two scale factor of the forms $$a(t)=\sqrt{t^\alpha{e^t}}$$ and $$a(t)=\sqrt[m]{{\rm{sin}}h(kt)}$$, which yield two different time-dependent deceleration parameters. Firstly, we modify the d-dimensional time-dependent field equations, including the general formulation of particle creation and entropy generation mechanisms. Then, we investigate the time dependence of a few quantities such as the particle creation rate ψ, the entropy S, the gravitational constant G, the cosmological constant Λ, the energy density ρ, the deceleration parameter q, etc. We show that all constants and quantities, except the gravitational constant G and the entropy S, characteristically decrease with time for two kinds of scale factors in all dimensions. However, the gravitational constant G and the entropy S increase with time. Additionally, we show that the cosmological constant Λ is unexpectedly independent of the particle creation mechanism, unlike G.

The Lambert W Function: A Newcomer in the Cosmology Class?

Abstract We propose a novel equation of state (EoS) which explains the evolutionary history of a flat Friedmann–Lemaitre–Robertson–Walker universe. The uniqueness of this EoS lies in the fact that it incorporates the Lambert W function in a special fashion. It is explicitly demonstrated that with observationally relevant values of the unknown parameters ϑ 1 and ϑ 2, all the evolutionary phases of the universe can be reproduced. Moreover, it also shows that the initial singularity is unavoidable and asserts that the late-time acceleration of the universe would continue forever.

Using Spatial Curvature with H ii Galaxies and Cosmic Chronometers to Explore the Tension in H0

Abstract We present a model-independent measurement of spatial curvature Ω k in the Friedmann–Lemaître–Robertson–Walker universe, based on observations of the Hubble parameter H(z) using cosmic chronometers, and a Gaussian process (GP) reconstruction of the H ii galaxy Hubble diagram. We show that the imposition of spatial flatness (i.e., Ω k = 0) easily distinguishes between the Hubble constant measured with Planck and that based on the local distance ladder. We find an optimized curvature parameter when using the former (i.e., ), and for the latter ( ). The quoted uncertainties are extracted by Monte Carlo sampling, taking into consideration the covariances between the function and its derivative reconstructed by GP. These data therefore reveal that the condition of spatial flatness favors the Planck measurement, while ruling out the locally inferred Hubble constant as a true measure of the large-scale cosmic expansion rate at a confidence level of ∼3σ.

Quantum Cosmologies under Geometrical Unification of Gravity and Dark Energy

A Friedmann–Robertson–Walker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann–Robertson–Walker–quintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the quintessence scalar field, as well as a (first order) constraint equation. Our approach naturally unified gravity and dark energy, as it was obtained that the Lagrangian and the equations of motion are those of a relativistic particle moving on a two-dimensional, conformally flat spacetime. The conformal metric factor was related to the dark energy scalar field potential. We proceeded to quantize the system in three different schemes. First, we assumed the Universe was a spinless particle (as it is common in literature), obtaining a quantum theory for a Universe described by the Klein–Gordon equation. Second, we pushed the quantization scheme further, assuming the Universe as a Dirac particle, and therefore constructing its corresponding Dirac and Majorana theories. With the different theories, we calculated the expected values for the scale factor of the Universe. They depend on the type of quantization scheme used. The differences between the Dirac and Majorana schemes are highlighted here. The implications of the different quantization procedures are discussed. Finally, the possible consequences for a multiverse theory of the Dirac and Majorana quantized Universe are briefly considered.

Critical Robertson–Walker universes

The integral of the mass-energy density m of a closed Robertson–Walker (RW) spacetime with source a perfect fluid and cosmological constant Λ gives rise to an action functional on the space of scale functions of RW spacetime metrics. This paper studies closed RW spacetimes which are critical for this functional, subject to volume-preserving variations (m-critical RW universes). A complete classification of m-critical RW universes is given and explicit solutions in terms of Weierstrass elliptic functions and their degenerate forms are computed. The standard energy conditions (weak, dominant, and strong) as well as the cyclic property of m-critical RW universes are discussed.

Local existence of scalar wave equation on the Robertson-Walker universe as a background with k = 0

In this paper, we study about the wellposedness of scalar wave equation on Robertson-Walker universe as a background with zero spatial curvature, k = 0. We start from non-minimal Lagrangian for scalar field on curved background with potential turned on. Then we derive the equations of motion and tensor energy-momentum. After that we specify our case to k = 0. Finally, we prove the local existence and uniqueness of the solution of the equation of motion.

Some interactions of spherically symmetric massive scalar field with Brans–Dicke scalar field in Robertson–Walker universe

Here in this work, we investigated the possible cosmological consequences of the interaction of Brans–Dicke scalar field and massive scalar field by considering spherically symmetric Robertson–Walker metric. The present problem can also be treated as an extension work of [K. Priyokumar et al., Interaction of gravitational field and Brans–Dicke field, Res. Astron. Astrophys. 16(4) (2016) 64; K. Priyokumar and M. Dewri, Interaction of electromagnetic field and Brans–Dicke field, Chinease J. Phys. 54 (2016) 845]. The exact solutions of the field equations are obtained with seven different cases. The behavior of the model and their contribution to the process of the evolution are examined in detail from some explicit and reasonable values of free parameter. We also presented the variations of certain physical parameters versus cosmic time graphically to compare our solutions with the present observational findings. When we studied further, it is found that the cosmological term [Formula: see text] takes a great role in the accelerating expansion of our universe when both scalar fields are exponentially increasing functions of time, while the cosmological term will not appear in the case when both the scalar fields are exponentially decreasing functions of time. Also, the scalar field is seen to have a tendency to increase the expansion of the universe, thereby flattening the universe.

Spatially overlapped partners in quantum field theory

In quantum field theory particles are physically defined as what Unruh–De Witt particle detectors observe. By detecting a particle mode A, a reduced density operator for a quantum state of A is constructed. Even if the entire quantum state of the quantum field is pure, the state of A is not pure but mixed due to entanglement between other subsystems. The partner mode B of the field is defined as a purification partner of A such that the AB system in a pure state. We show that, without any fine-tuning of the particle detector design of A, the weighting function of partner B has spatial overlap of that of A. We show a general formula of partner B associated with arbitrarily fixed A of a free field in a general Gaussian state. We demonstrate an example of memory effects in an expanding Freedman–Robertson–Walker universe.

Thermal stability of Tsallis holographic dark energy in nonflat universe

We consider a nonflat Friedmann–Robertson–Walker universe filled by a pressureless dark matter and Tsallis holographic dark energy (THDE) whose IR cutoff is the apparent horizon. We also consider both noninteracting and interacting cases in which a mutual interaction between the two dark sectors of cosmos is taken into account. For the noninteracting case, the density, equation of state (EoS) and the deceleration parameters show a satisfactory behavior by themselves, and the phantom line is not crossed. In this manner, unlike the flat case for THDE (Tavayef et al. in Phys Lett B 781:195, 2018), where the squared of sound speed is always negative, the squared of sound speed is negative and approaches zero at future. In the interacting case, the phantom line is crossed by EoS parameter, the squared of the sound speed is always negative and the density and deceleration parameters have acceptable behavior. Finally, by studying the thermodynamic parameters, namely the heat capacities and the compressibility criterions, the thermal stability of both cases are discussed which reveals that both models are thermodynamically unstable.

Robertson-Walker evreninde kütleli spin-1 parçacıklarının yaratılması

Robertson-Walker evreninde kütleli spin-1 parçacıklarının yaratılması

Impact of Collisional Matter on the Late-Time Dynamics of f(R,T) Gravity

We study the cosmic evolution of non-minimally coupled f ( R , T ) gravity in the presence of matter fluids consisting of collisional self-interacting dark matter and radiation. We study the cosmic evolution in the presence of collisional matter, and we compare the results with those corresponding to non-collisional matter and the Λ -cold-dark-matter ( Λ CDM) model. Particularly, for a flat Friedmann–Lema i ^ tre–Robertson–Walker Universe, we study two non-minimally coupled f ( R , T ) gravity models and we focus our study on the late-time dynamical evolution of the model. Our study is focused on the late-time behavior of the effective equation of the state parameter ω e f f and of the deceleration parameter q as functions of the redshift for a Universe containing collisional and non-collisional dark matter fluids, and we compare both models with the Λ CDM model. As we demonstrate, the resulting picture is well accommodated to the latest observational data on the basis of physical parameters.

Thermodynamics of event horizon with modified Hawking temperature in scalar-tensor gravity

In recent past, Hawking temperature has been modified for the validity of thermodynamical laws at the event horizon in general relativity context. This lead to the introduction of modified Hawking temperature and it has been found that the modified Hawking temperature is more realistic on the event horizon. With this motivation, here we investigate the thermodynamical consistency of scalar-tensor gravity based models by examining the validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) at the event horizon. In order to attain our goal, we consider a spatially flat Friedman–Robertson–Walker Universe filled with ordinary matter and the boundary of the Universe bounded by the event horizon that is in thermal equilibrium with modified Hawking temperature. Next, we calculate the general expressions for the GSLT and TE using modified Hawking temperature in the context of the more general action of scalar-tensor gravity where there is a non-minimally coupling between the scalar field and matter Lagrangian (as the chameleon field). From the general expression of GSLT, we find that the null energy condition must hold for a viable scalar-tensor model of the Universe dominated by a perfect fluid. Furthermore, in order to better understand these complicated general expressions of GSLT and TE, we explore the validity of the GSLT and TE for two viable models of scalar-tensor gravity namely Brans–Dicke gravity with a self-interacting potential and Chameleon gravity at the event horizon using special cosmological solutions. Finally, some graphical representation of the GSLT and TE have been presented. From the graphical analysis, we found that the power-law forms of the scale factor and scalar field is much favourable for the study of universal thermodynamics as compared to other choices of the scalar field and the analytic function.

Third Quantization and Emergence of the Quasiclassical Wave Function of the Universe

Quantized solutions of the Wheeler–DeWitt (WDW) equation describing a closed Friedmann–Robertson–Walker universe with a $$\Lambda $$ term and a set of massless scalar fields are studied. It is shown that when $$\Lambda \ll 1$$ units and the standard in-vacuum state is considered, the wave function of the universe $$\Psi $$ behaves as a random quasiclassical field at rather large a, namely, $$1 \ll a \ll {{e}^{{\frac{2}{{3\Lambda }}}}}$$ [1].