Power-law Expansion Research Articles

The expansion of the GRB 221009A afterglow

We observed γ-ray burst (GRB) 221009A using very long baseline interferomety (VLBI) with the European VLBI Network (EVN) and the Very Long Baseline Array (VLBA), over a period spanning from 40 to 262 days after the initial GRB. The high angular resolution (mas) of our observations allowed us, for the second time ever, after GRB 030329, to measure the projected size, s, of the relativistic shock caused by the expansion of the GRB ejecta into the surrounding medium. Our observations support the expansion of the shock with a > 4σ-equivalent significance, and confirm its relativistic nature by revealing an apparently superluminal expansion rate. Fitting a power law expansion model, s ∝ ta, to the observed size evolution, we find a slope a = 0.69−0.14+0.13. Fitting the data at each frequency separately, we find different expansion rates, pointing to a frequency-dependent behaviour. We show that the observed size evolution can be reconciled with a reverse shock plus forward shock, provided that the two shocks dominate the emission at different frequencies and, possibly, at different times.

LRS Bianchi Cosmological Model in Saez-Ballester Theory of Gravity with Time Varying Cosmological Constant

The present work deals with the study of a locally rotationally symmetric (LRS) Bianchi type-I cosmological model in the framework of a scalar-tensor theory of gravity formulated by Saez and Ballester with time varying cosmological constant. To obtain the explicit solutions of the Saez-Ballester field equations we assume the average scale factor to obey a power law expansion and the cosmological constant to be proportional to the energy density of the cosmic fluid. The dynamical behaviour of relevant cosmological parameters including the Hubble parameter, the deceleration parameter, the energy density, the pressure, the equation of state parameter, the cosmological constant, the shear scalar, the expansion scalar etc. are investigated graphically by examining their evolution versus the redshift parameter. The validation of the four energy conditions are also checked. We find the outcomes of the constructed model to be in good agreement with the recent observational data.

LRS Bianchi type-I with Hubble’s horizon as IR cut-off in [formula omitted] gravity

we explored the holographic dark energy model using Hubble’s Horizon as the infrared (IR) cut-off in Locally Rotationally Symmetric (LRS) Bianchi type-I, considering the f(R) gravity framework in our analysis. In order to solve the field equations, we assume a relation F∝am and volumetric power law expansion (where m is constant). we have expressed various crucial cosmological parameters in terms of the redshift z and depicted them graphically to enhance our understanding of the expansion and evolution of the universe like holographic dark energy density (ρΛ), holographic dark energy pressure (pΛ), equation of state parameter (ω) , total energy density parameter (Ω) etc. Also, we analyzed the stability of the universe in our model through the squared speed of sound test and its validity by energy conditions. Ultimately, our model indicates that the universe is currently in an expanding phase, exhibiting an accelerating phase, closely approaching a flat geometry, and its behavior resembles that of a quintessence dark energy model.

Koo‐Kleinstreuer‐Li magneto‐nanofluid model for non‐Newtonian micropolar fluid through porous channel

AbstractThe primary concern of writing this article is to study the rheological properties of the micropolar non‐Newtonian nanofluid flowing through the porous medium along with magnetic field effects. In it, the outer boundary of the sheet is heated by applying an external heat source. The insertion of aluminum oxide nanoparticles in water turned it into a nanofluid. Together with the viscous dissipation phenomena, adding a magnetic field has another effect known as a Joule heating impact that is considered in the energy equation. To investigate the impact of viscosity and thermal conductivity on flow patterns, we considered the Koo‐Kleinstreuer‐Li model. A generalized Proudman‐Johnson equation is obtained by using similarity transformation on Navier‐Stokes equations. The well‐known classical shooting method is used to get the numerical solution to the said problem. Graphical results are portrayed for variant rheological parameters lke power law index, Reynolds number, volume fraction, Prandtl number, expansion ratio, and Hartmann number on the velocity and temperature of nanofluids.

Reconstruction of [formula omitted] gravity model via the Raychaudhuri equation

In this work, we investigate for an analytical solution under modified gravity theory, specifically the f(R,T) gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct f(R,T) gravity model, we consider the functional form of f(R,T) as the sum of two independent functions of the Ricci scalar R and the trace of the energy–momentum tensor T, respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe.

Matter growth perturbations and cosmography in modified torsion cosmology

We examine the cosmic evolution of the growth of perturbations with respect to matter content at early and recent past era of the Universe under the framework of non-zero torsion cosmology. Some cosmographic parameters are also discussed. To analyze this cosmic scenario, we formulate the cosmic models with two dark matter considerations and apply spherical collapse formalism. We explore that for model-1 (pressureless matter), the density contrast starts growing in early era of the Universe and with the Universe’s overall expansion, density contrast grows faster for different choices of torsion parameter. In model-2 (matter with non-zero pressure), the density contrast shows enormous growth as compared to overall expansion of the Universe for the perturbed region, which indicates the collapse of the perturbed region and formulation of new large scale matter or galaxy. Further, we analyze the behavior of the growth function for both models with different values of torsion parameter. For model-1, the growth function increases smoothly for different choices of torsion parameter but for the model-2 the behavior of the growth function with nonzero DM and torsion significantly deviates from pressureless DM with zero torsion (Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM). We also investigate different cosmographic parameters for both models and analyze their behavior with different choices of torsion parameter and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM. The results show the power-law expansion rate of the accelerating Universe with respect to redshift function.

Reconstruction of [formula omitted] Lagrangian for various cosmological scenarios

In this paper we explore a reconstruction scheme in the background of the f(T,T) gravity theory for different cosmological scenarios, where T is the scalar torsion and T is the trace of the energy-momentum tensor. Using the reconstruction technique f(T,T) Lagrangian is constructed for different cosmological eras such as dust, ΛCDM, perfect fluid, etc. Both minimal and non-minimal matter coupled models are considered for this purpose. Different cosmological scenarios such as power law expansion, de-Sitter expansion, etc. have been considered, and using them Lagrangian functionals are constructed. Mathematical viabilities of all the constructed functionals have been investigated. The physical implications of the obtained solutions are discussed in detail. To check the cosmological compatibility of the constructed f(T,T) functionals we have generated plots of important parameters like the equation of state parameter and deceleration parameter. It is seen that the reconstructed models are perfectly compatible with the late time accelerated expansion of the universe.

Scalar Field Cosmology with Powerlaw and Hybrid Expansion Law in Symmetric Teleparallel Gravity

Scalar Field Cosmology with Powerlaw and Hybrid Expansion Law in Symmetric Teleparallel Gravity

Examining the physical viability of the f(R) gravity via observational constraints

f(R) gravity is an extension of Einstein's General Relativity derived from relaxing the hypothesis that the Hilbert-Einstein action for the gravitational field is strictly linear in the Ricci curvature scalar R and explains the late-time cosmic acceleration of the Universe. We investigate the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) line element filled with two fluids, with the first being pressureless matter and the second being the Renyi holographic dark energy (RHDE) in this study. In this scenario, the Hubble horizon H acts as an Infrared (IR) cutoff. In this regard, the effects of IR cutoff with the Hubble horizon on the traits of RHDE models have been researched. The volumetric power law expansion and the two models of f(R) i.e. f(R)=R+bRm and f(R)=R−μ4R are taken into consideration for the solution of the field equations. The estimated model parameter values that would best fit and work with current observational datasets. This estimation uses 1048 points from the Pantheon supernovae datasets and 30 points from the Hubble datasets. The likelihood function and Bayesian analysis are integrated with the Markov Chain Monte Carlo (MCMC) method at the 1 σ and 2 σ confidence levels. It is crucial to remember that f(R) is a rising function ofR, demonstrating the model's plausibility. For both models, the equation of state (EoS) value is close to a Quintessence zone. The model behaves in a ΛCDM (ΛCold Dark Matter) like manner, as shown by the fact that the statefinder diagnostic pair falls to(r=1,s=0). The Om(z) parameter shows a discrète behaviour.

Anisotropic Cosmological Model in f (R,T) Theory of Gravity with a Quadratic Function of T

In this paper, we study spatially homogeneous and anisotropic Bianchi type-I space-time filled with perfect fluid within the framework of f(R,T) theory of gravity for the functional form f(R,T)=R+2f(T) with f(T)=αT+βT2, where α and β are constants. Exact solutions of the gravitational field equations are obtained by assuming the average scale factor to obey a hybrid expansion law and some cosmological parameters of the model are derived. Two special cases, leading to the power-law expansion and the exponential expansion, are also considered. We investigate the physical and geometrical properties of the models by studying the evolution graphs of some relevant cosmological parameters such as the Hubble parameter (H), the deceleration parameter ( q) etc.

Brans–Dicke cosmology with cosmological term [formula omitted

In this paper, we study the dynamics of a flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model by considering varying vacuum energy density (VED) in Brans–Dicke (BD) cosmology. For this purpose, we consider the well-motivated VED of the form Λ(H)=c0+3νH2, where c0 and ν are dimensionless constants. We first adopt a theoretical method to find the exact solutions for various cosmological parameters of two models, namely ΛRG1 and ΛRG2. In ΛRG1 model, the scale factor evolves as a power-law expansion which gives the deceleration parameter a constant value. Hence, this type of model does not show the transition phase. The second model ΛRG2 describes the transition phase from deceleration to acceleration. In the second part, we perform two joint likelihood analysis in order to find the constrain on the main free parameters of the ΛRG2 model using the latest observational data sets including SNe Pantheon, H(z) data, BAO/CMB data and local H0 by SH0ES. Performing the two different combination of datasets, we find that the model shows prior decelerated epoch followed by late time accelerated epoch. We also compare the decaying VED with traditional Λ cosmology, which help us to define the evolution of the VED model. The results show that varying VED model in BD theory is consistent with data and the cosmic evolutions are in good agreement with the concordance ΛCDM and BD with constant Λ models. The AIC and BIC selection criteria are also discussed.

Observational constraints in modified Chaplygin gas cosmological model

Bianchi type-V cosmological model with modified Chaplygin gas having the equation of state p=γρ−Cρα, where C is a positive constant and 0≤α,γ≤1, has been investigated. To find the deterministic solution, we have considered power-law and intermediate expansions which predicts the decelerating and accelerating phases of expansion of the Universe. Here, we have also constructed cosmographic parameters like H,j,l,s∗ and studied their evolution in the background of Bianchi type-V Universe with modified Chaplygin gas. The geometric diagnostics, the state-finder (r,s) in our cosmological model to discriminate from the ΛCDM model are studied. We have performed the statistical analysis and obtained best fit values of the parameters using MCMC technique for intermediate model. We have also compared our models with observed Hubble data for both scenarios. We have noted some new and interesting cosmological solutions which is relevant for the model building, including present accelerating phase of the Universe.

Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels

The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ε of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ε, with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ε of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit ε≪1. The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ε exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

Interspecific and intraspecific Taylor's laws for frog skin microbes

Amphibians are known to have an abundance of microorganisms colonizing their skin, and these symbionts often protect the host from disease. There are now many comprehensive studies on amphibian skin microbes, but the interspecific and intraspecific abundance distributions (or abundance heterogeneity) of amphibian skin microbes remain unclear. Furthermore, we have a very limited understanding of how the abundance and heterogeneity of microbial communities relate to the body size (or more specifically, skin surface area) of amphibian hosts. In this study, we evaluated the interspecific and intraspecific abundance distribution patterns of amphibian skin microbes and evaluated whether the symbiotic skin microbes of different anuran species share a fundamental heterogeneity scaling parameter. If scaling invariance exists, we hypothesize that a fundamental heterogeneity scaling value also exists. A total of 358 specimens of 10 amphibian host species were collected, and we used Type-I and III Taylor’s power law expansions (TPLE) to assess amphibian skin microbial heterogeneity at the community and mixed-species population levels, respectively. The obtained results showed that, at the community scale, a high aggregation of the microbial abundance distribution on the skin barely changed with host size. In a mixed-species population (i.e., a community context), the abundance distribution pattern of mixed microbial species populations also does not change with host size and always remains highly aggregated. These findings suggest that while amphibian skin microbiomes located in different hosts may have different environmental conditions, they share a fundamental heterogeneity scaling parameter, and thus, scale invariance exists. Finally, we found that microhabitat area provided by the host skin is vital to the stability of the symbiotic microbial community.

Unimodular f(𝒢,T) gravity

In this study, unimodular [Formula: see text] gravity is proposed as an alternative theory of gravity. Field equations of unimodular [Formula: see text] gravity are suggested. The field equation and their solutions are obtained for exponential expansion and power-law expansion models. Energy conditions of unimodular [Formula: see text] gravity are defined by using Raychaudhuri equations. Energy conditions for exponential expansion and power-law expansion models are investigated. Hubble parameter and deceleration parameter are calculated by considering power-law expansion model and obtained solutions. It has been shown that both deceleration parameter and Hubble parameter are compatible with the current observational data.

Squeezed Number State Representation of the Inflaton and Particle Production in the FRW Universe

In this study, we use a single-mode squeezed thermal vacuum state formalism and examine the nature of a massive homogeneous scalar field, minimally coupled to the gravity in the framework of semiclassical gravity in the Bianchi type-I universe. We have obtained an estimate leading solution to the semiclassical Einstein equation for the Bianchi type-I universe shows, each scale factor in its respective direction obeys t^(2/3) power-law expansion. The mechanism of the nonclassical thermal cosmological particle production is also analyzed in the Bianchi type-I universe.

Quantum field simulator for dynamics in curved spacetime.

In most cosmological models, rapid expansion of space marks the first moments of the Universe and leads to the amplification of quantum fluctuations1. The description of subsequent dynamics and related questions in cosmology requires an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge2-5, and thus a quantum field simulator can lead to insights. Here we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap6,7 and adjustable interaction strength to implement this model system. We explicitly show the realization of spacetimes with positive and negative spatial curvature by wave-packet propagation and observe particle-pair production in controlled power-law expansion of space, using Sakharov oscillations to extract amplitude and phase information of the produced state. We find quantitative agreement with analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulatorof a new class. In the future, straightforward upgrades offer the possibility to enter unexplored regimes that give further insight into relativistic quantum field dynamics.

-gravity in the context of dark energy with power law expansion and energy conditions* *G.M. and A.P. acknowledge the DSTB, Government of West Bengal, India for financial support through the Grants No.: 322(Sanc.)/ST/P/S&T/16G-3/2018 dated 06.03.2019. S.R. is thankful to the authority of IUCAA, Pune for providing Visiting Associateship under which a part of this work has been done

The objective of this work is to generate a general formalism of gravity in the context of dark energy under the framework of K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where is the familiar Ricci scalar, is the DBI type non-canonical Lagrangian with , and ϕ is the K-essence scalar field. The emergent gravity metric () and the well known gravitational metric () are not conformally equivalent. We have constructed a modified field equation using the metric formalism in -gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric, which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of the modified Friedmann equations have been deduced for the specific choice of , which is of Starobinsky-type, using the power law expansion method. The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of the dark energy density as , which indicates that the present universe is dark-energy dominated. Graphical plots for the energy density (ρ), pressure (p), and equation of state parameter () with respect to (w.r.t.) time (t) based on parametric values are interestingly consistent with the dark energy domination theory, and hence the accelerating features. We also highlight the corresponding energy conditions and constraints of the theory with a basic example.

Hybrid expansion law in viscous braneworld gravity with Gauss–Bonnet terms

The cosmological model executing hybrid expansion law (HEL) of scale factor in Randall–Sundrum type II (RS) braneworld gravity with Gauss–Bonnet terms in the presence of bulk viscosity described by Eckart theory, Truncated Israel–Stewart (TIS) theory, Full Israel–Stewart (FIS) theory and nonlinear Israel–Stewart (nIS) theory is studied. In the hybrid expansion law, the scale factor of the universe is described by the product of power-law and exponential expansions. In the HEL model, the early inflation and its transition from deceleration phase to present accelerated phase of expansion can be explored. The constraints of hybrid expansion law model parameters are determined using the recent observational data. Thereafter, the estimated parameters are considered to explore the present value of deceleration parameter, jerk parameter and transition epoch from early deceleration to the present accelerating phase.

A study on exact solutions of einstein’s field equations in different cosmological models

The paper deals with the exact solutions of the Einstein’s field equations in various cosmo-logical models based on Lyra’s geometry: (i) Bianchi type III cosmological model in a perfect fluid by considering the Equation of State (EoS) of the type p = αρ 2 − ρ, where α > 0 is constant (ii) Spatially flat FRW model with constant deceleration parameter q and time dependent displacement field vector β for the specific choice of particle creation function (iii) FRW model with variable β and time dependent q. The conditions for attaining an accelerated power-law expansion of the universe in the matter dominated era have also been discussed.