We clarify the procedure for expressing the Friedmann equation in terms of directly measurable cosmological scalars constructed out of higher derivatives of the scale factor. We carry out this procedure for pure dust, Chaplygin gas and generalised Chaplygin gas energy-momentum tensors. In each case it leads to a constraint on the scalars thus giving rise to a test of General Relativity. We also discuss a formulation of the Friedmann equation as unparametrised geodesic motion and its connection with the Lagrangian treatment of perfect fluids coupled to gravity.
We obtain a constraint on cosmological scalars for the FRW metric with a pure radiation fluid source and positive cosmological constant. We demonstrate that this constraint is conformally invariant in the context of Penrose's Conformal Cyclic Cosmology proposal, where the metrics of the late stages of the previous aeon and the early stages of the present aeon are described by FRW cosmologies.
Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of…
We derive the expression for the jerk parameter in $f(R)$ gravity. We use the Palatini variational principle and the field equations in the Einstein conformal gauge. For the particular case $f(R)=R-\frac{α^2}{3R}$, the predicted value of the jerk parameter agrees with the SNLS SNIa and X-ray galaxy cluster distance data but does not with the SNIa gold sample data.
In order to study if the anisotropy of the spacetime may induce differences in the cosmic shear or in deceleration parameter we investigate in Bianchi I Universe the most general expression for the cosmic shear and we study the connections between deceleration parameter and cosmic shear. We also consider a shear parametric approach to measure the transition from decelerating to an accelerating Universe. We also study the connection between jerk parameter and ellipsoidal Universe.
The relativistic jerk, snap and all higher-order kinematical D-vectors are defined for the motion of a massive particle in a D-dimensional Minkowski spacetime. We illustrate the formalism with stationary motions, for which we provide a new, Lorentz covariant, classification. We generalize some cases to branes, explaining the relevance to uniform motion in a heat bath. We also consider some non-stationary motions, including motion with constant proper jerk, and free fall into a black hole as viewed from a GEMS perspective.
We derive the expression for the snap parameter in f(R) gravity. We use the Palatini variational principle to obtain the field equations and regard the Einstein conformal frame as physical. We predict the present-day value of the snap parameter for the particular case f(R)=R-const/R, which is the simplest f(R) model explaining the current acceleration of the universe.
In this paper, we have examined the recently proposed modified symmetric teleparallel gravity, in which gravitational Lagrangian is given by an arbitrary function of non-metricity scalar $Q$. We have considered a constant jerk parameter to express the Hubble rate. Moreover, we have used 31 points of OHD datasets and 1701 points of Pantheon+ datasets to constraint our model parameters by means of the Markov Chain Monte Carlo analysis. The mean values and the best fit obtained give a consistent Hubble rate and deceleration parameter compared to the observation values. In order to study the curre…
We calculate the Bogolubov coefficients for a metric which describes the snapping of a cosmic string. If we insist on a matching condition for all times {\it and} a particle interpretation, we find no particle creation.
A Friedmann-Robertson-Walker cosmological model dominated by tachyonic -- faster-than-light -- dark matter can exhibit features similar to those of a standard dark energy/dark matter or $Lambda$CDM model. It can undergo expansion which decelerates to a minimum rate, passes through a "cosmic jerk," then accelerates. But some features of a tachyon-dominated model are sufficiently distinct from those of the standard model that the two possibilities might be distinguished observationally. As a demonstration of concept, the distance-redshift relation of such a model is compared here with some obser…
We discuss in Minkowski spacetime the differences between the concepts of constant proper $n$-acceleration and of vanishing $(n+1)$-acceleration. By $n$-acceleration we essentially mean the higher order time derivatives of the position vector of the trajectory of a point particle, adapted to Minkowski spacetime or eventually to curved spacetime. The $2$-acceleration is known as the Jerk, the $3$-acceleration as the Snap, etc. As for the concept of {\sl proper} $n$-acceleration we give a specific definition involving the instantaneous comoving frame of the observer and we discuss, in such frame…
We study the possibility that the universe is subjected to a deformation, besides its expansion described by Friedmann's equations. The concept of smooth deformation of a riemannian manifolds associated with the extrinsic curvature is applied the standard FLRW cosmology. Starting from the resulting modified Friedman's equation we study two possible solutions with six models for each one in low redshift. In other to constrain the models, we calculate deceleration, jerk and Hubble parameters and compare with different data as the latest BAO/CMB + SNIa constraints, SNLS SNIa, x-ray galaxy cluster…
A dynamical scalar field represents the simplest generalization of a pure Cosmological Constant as a candidate to explain the recent evidence in favour of the accelerated cosmic expansion. We review the dynamical properties of such a component, and argue that, even if the background expectation value of this field is fixed and the equation of state is the same as a Cosmological Constant, scalar field fluctuations can still be used to distinguish the two components. We compare predicted spectra of Cosmic Microvave Background (CMB) anisotropies in tracking scalar field cosmologies with the prese…
We study unimodular gravity in the context of cosmology, particularly some interesting consequences that might be able to describe the background cosmology and the late cosmic acceleration. We focus our attention on the hypothesis of \textit{non conservation of the energy momentum tensor}. This characteristic has an interesting outcome: we can obtain a modified Friedmann equation along with the acceleration equation and also new fluid equations related to a third order derivative of the scale factor, known in cosmography as the jerk parameter. As a consequence of this theory, it seems that rad…
We argue for a ``parametrized post-Friedmanian'' approach to linear cosmology, where the history of expansion and perturbation growth is measured without assuming that the Einstein Field Equations hold. As an illustration, a model-independent analysis of 92 type Ia supernovae demonstrates that the curve giving the expansion history has the wrong shape to be explained without some form of dark energy or modified gravity. We discuss how upcoming lensing, galaxy clustering, cosmic microwave background and Lyman alpha forest observations can be combined to pursue this program, which generalizes th…
Axion-photon mixing has been proposed as an alternative to acceleration as the explanation for supernovae dimming. We point out that the loss of photons due to this mixing will induce a strong asymmetry between the luminosity, d_L(z), and angular-diameter distance, d_A(z), since the latter is unaffected by mixing. In a first search for such an asymmetry we introduce a dimensionless mixing amplitude lambda so that lambda=0 if no photons are lost and lambda = 1 if axion-photon mixing occurs. The best-fit to SNIa and radio galaxy data is lambda = -0.3^{+0.6}_{-0.4} (95% CL), corresponding to an u…
We have considered flat Friedmann-Robertson-Walker (FRW) model of the universe and reviewed the modified Chaplygin gas as the fluid source. Associated with the scalar field model, we have determined the Hubble parameter as a generating function in terms of the scalar field. Instead of hyperbolic function, we have taken Jacobi elliptic function and Abel function in the generating function and obtained modified Chaplygin-Jacobi gas (MCJG) and modified Chaplygin-Abel gas (MCAG) equation of states, respectively. Next, we have assumed that the universe filled in dark matter, radiation, and dark ene…
We study $f(T)$ cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial $f(T)$ model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular $f(T)$ models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-$σ$ confidence level, emphasizing the fa…
