Late time transition of Universe and the hybrid scale factor

In this study, we propose an interacting model to explain the physical mechanism of the late time transition from matter-dominated era to the dark energy-dominated era of the Universe evolution and to obtain a scale factor a(t) representing two eras together. In the present model, we consider a minimal coupling of two scalar fields which correspond to the dark matter and dark energy interacting through a potential based on the FLRW framework. Analytical solution of this model leads to a new scale factor a(t) in the hybrid form $$a(t)=a_{0} (t/t_{0})^{\alpha } e^{ht/t_{0}}$$ a ( t ) = a 0 ( t / t 0 ) α e h t / t 0 . This peculiar result reveals that the scale factor behaving as $$a (t) \propto (t/t_{0})^{\alpha }$$ a ( t ) ∝ ( t / t 0 ) α in the range $$t/t_{0}\le t_{c}$$ t / t 0 ≤ t c corresponds to the matter-dominated era while $$a(t) \propto \exp (ht/t_{0})$$ a ( t ) ∝ exp ( h t / t 0 ) in the range $$t/t_{0}>t_{c}$$ t / t 0 > t c accounts for the dark energy-dominated era, respectively. Surprisingly, we explore that the transition from the power-law to the exponential expansion appears at the crossover time $$t_{0} \approx 9.8$$ t 0 ≈ 9.8 Gyear. We attain that the presented model leads to precisely correct results so that the crossover time $$t_{0}$$ t 0 and $$\alpha $$ α are completely consistent with the exact solution of the FLRW and re-scaled Hubble parameter $$H_{0}$$ H 0 lies within the observed limits given by Planck, CMB and SNIa data (or other combinations), which lead to consistent cosmological quantities such as the dimensionless Hubble parameter h, deceleration parameter q, jerk parameter j and EoS parameter w. We also discuss time dependent behavior of the dark energy and dark matter to show their roles on the time evolution of the universe. Additionally, we observe that all main results completely depend on the structure of the interaction potential when the parameter values are tuned to satisfy the zero energy condition. Finally, we conclude that interactions in the dark sector may play an important role on the time evolution and provides a mechanism to explain the late time transition of the Universe.

Asymptotic Solutions of a Generalized Starobinski Model: Kinetic Dominance, Slow Roll and Separatrices

We consider a generalized Starobinski inflationary model. We present a method for computing solutions as generalized asymptotic expansions, both in the kinetic dominance stage (psi series solutions) and in the slow roll stage (asymptotic expansions of the separatrix solutions). These asymptotic expansions are derived in the framework of the Hamilton-Jacobi formalism where the Hubble parameter is written as a function of the inflaton field. They are applied to determine the values of the inflaton field when the inflation period starts and ends as well as to estimate the corresponding amount of inflation. As a consequence, they can be used to select the appropriate initial conditions for determining a solution with a previously fixed amount of inflation.

New Derivation of Redshift Distance without Using Power Expansions

Here we use the flat Friedmann-Lemaitre-Robertson-Walker metric describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the astrophysical literature. We use the co-moving coordinate re (the subscript e indicates emission) for the place of a galaxy which is emitting photons and ra (the subscript a indicates absorption) for the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the real physical distance - the way of light - is calculated by D = a(t0) ra - a(te) re. Here means a(t0) the today’s (t0) scale parameter and a(te) the scale parameter at the time of emission (te) of the photons. Nobody can doubt this real travel way of light: The photons are emitted on the co-moving coordinate place re and are than traveling to the co-moving coordinate place ra. During this traveling the time is moving from te to t0 (te ≤ t0) and therefore the scale parameter is changing in the meantime from a(te) to a(t0). Using this right way of light we calculate some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics. As one result we get e.g. the today’s Hubble parameter H0a ≈ 62.34 km/(s Mpc). This value is smaller than the Hubble parameter H0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data [12] which is discussed in the literature.

Bias of the Hubble Constant Value Caused by Errors in Galactic Distance Indicators

The bias in the determination of the Hubble parameter and the Hubble constant in the modern Universe is discussed. It could appear due to the statistical processing of data on the redshifts of galaxies and the estimated distances based on some statistical relations with limited accuracy. This causes a number of effects leading to either underestimation or overestimation of the Hubble parameter when using any methods of statistical processing, primarily the least squares method (LSM). The value of the Hubble constant is underestimated when processing a whole sample; when the sample is constrained by distance, especially when constrained from above. Moreover, it is significantly overestimated due to the data selection. The bias significantly exceeds the values of the erro ofr the Hubble constant calculated by the LSM formulae. These effects are demonstrated both analytically and using Monte Carlo simulations, which introduce deviations in the velocities and estimated distances to the original dataset described by the Hubble law. The characteristics of the deviations are similar to real observations. Errors in the estimated distances are up to 20%. They lead to the fact that, when processing the same mock sample using LSM, it is possible to obtain an estimate of the Hubble constant from 96% of the true value when processing the entire sample to 110% when processing the subsample with distances limited from above. The impact of these effects can lead to a bias in the Hubble constant obtained from real data and an overestimation of the accuracy of determining this value. This may call into question the accuracy of determining the Hubble constant and can significantly reduce the tension between the values obtained from the observations in the early and modern Universes, which were actively discussed during the last year.

The nonlinear patterns of the cosmic anisotropy: the spatially flat perfect fluid universes.

In this manuscript, we investigate the patterns of the cosmological anisotropy in the spatially flat Bianchi models filled with a perfect fluid. We analyse the factor 1 + ∆R, the ratio of the Hubble parameter in the anisotropic model over its isotropic counterpart. In general, ∆R starts to deviate significantly from zero at a specific redshift zA, which depends on the type of the fluid and the value of the anisotropy magnitude. We also show that the deceleration and the jerk along the principal directions of the expansion tensor are constrained by simple algebraic equations that do not depend on the type of matter present. These characteristic patterns form a valuable framework to probe the cosmological anisotropy in the late-time universe.

Observational cosmology

The main strands of observation in cosmology are presented. These are redshift surveys using standard candles; galaxy distributions; age estimates drawing on a number of strands of evidence; and the CMB radiation. The chapter begins with a discussion of systemtic and statistical error in measurements, and explains the terminology of “Lambda CDM” model. Observations are combined with the Friedman equation in order to constrain the density parameters in a LCDM model. Data from supernova surveys are used to obtain the Hubble parameter and the deceleration parameter, and hence evidence of an accelerating expansion. Evidence of the BAO process is deduced from sky surveys, and used to constrain the spatial curvature. The CMB radiation is discussed at length. The Sachs-Wolfe effect is obtained by a simple calculation,. The method to deduce spatial curvature from the position of the acoustic peaks is outlined. Further features such as spectal index and polarization are briefly discussed.

String excitation by initial singularity of inflation

We discuss excitation of string oscillation modes by an initial singularity of inflation. The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and hence it is not clear that stringy effects become significant around it. With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak’s classification. We demonstrate that the initial singularities of Starobinsky and hill top inflation, assuming the slow roll inflation to the past infinity, are strong. Hence stringy corrections are inevitable in the very early stage of these inflation models. We also find that the initial singularity of the hill top inflation could be weak for non-slow roll case.

Friedmann cosmology with decaying vacuum density in Brans–Dicke theory

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 $$\varLambda (t) $$ Λ ( 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 $$\varLambda (t)$$ Λ ( t ) given by the phenomenological law $$\varLambda (t)=\lambda +\sigma H$$ Λ ( t ) = λ + σ H , where $$\lambda $$ λ and $$\sigma $$ σ are positive constants. We solve the model and then focus on two different cases $$\varLambda _{H1}$$ Λ H 1 and $$\varLambda _{H2}$$ Λ H 2 by assuming $$\varLambda =\lambda $$ Λ = λ and $$\varLambda =\sigma H$$ Λ = σ H , respectively. Notice that $$\varLambda _{H1}$$ Λ H 1 is the analog of the standard $$\varLambda $$ Λ 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 $$\varLambda $$ Λ 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 $$\varLambda $$ Λ -cosmology (i.e. our model $$\varLambda _{H1}$$ Λ H 1 ) performs at a level comparable to the standard $$\varLambda $$ Λ CDM, whereas $$\varLambda _{H2}$$ Λ H 2 is less favoured.

Statefinder and Om Diagnostics for New Generalized Chaplygin Gas Model

We explore a unified model of dark matter and dark energy. This new model is a generalization of the generalized Chaplygin gas model and is known as a new generalized Chaplygin gas (NGCG) model. We study the evolutions of the Hubble parameter and the distance modulus for the model under consideration and the standard ΛCDM model and compare that with the observational datasets. Furthermore, we demonstrate two geometric diagnostics analyses including the statefinder (r,s) and Om(z) to the discriminant NGCG model from the standard ΛCDM model. The trajectories of evolution for (r,s) and Om(z) diagnostic planes are shown to understand the geometrical behavior of the NGCG model by using different observational data points.