Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Gravitational Lensing Effects of Vacuum Strings: Exact Solutions

This paper deals with two broad issues: the formulation of a mathematical framework for concentrated sources in general relativity and its application to strings. We isolate a class of those metrics whose curvature tensors are well defined as distributions. It is shown that shells of matter---but neither point particles nor strings---can be described by metrics in this class. This conclusion is examined in more detail for the case of strings. We estimate the errors inherent in certain determinations of the mass per unit length of a cosmic string, and in certain calculations of the gravitational radiation from such a string.

Strings and other distributional sources in general relativity.

Exact Solutions of Einstein's Field Equations: Notation

We use the local value of the Hubble constant recently measured with 2.4% precision, as well as the latest compilation of cosmic chronometers data, together with standard probes such as Supernovae Type Ia and Baryon Acoustic Oscillation distance measurements, in order to impose constraints on the viable and most used f(T) gravity models, where T is the torsion scalar in teleparallel gravity. In particular, we consider three f(T) models with two parameters, out of which one is independent, and we quantify their deviation from ΛCDM cosmology through a sole parameter. Our analysis reveals that for one of the models a small but non-zero deviation from ΛCDM cosmology is slightly favored, while for the other models the best fit is very close to ΛCDM scenario. Clearly, f(T) gravity is consistent with observations, and it can serve as a candidate for modified gravity.

https://iopscience.iop.org/article/10.1088/1475-7516/2016/08/011/pdf

New observational constraints on f(T) gravity from cosmic chronometers

Dark energy and dark matter constitute 95% of the observable Universe. Yet the physical nature of these two phenomena remains a mystery. Einstein suggested a long-forgotten solution: gravitationally repulsive negative masses, which drive cosmic expansion and cannot coalesce into light-emitting structures. However, contemporary cosmological results are derived upon the reasonable assumption that the Universe only contains positive masses. By reconsidering this assumption, I have constructed a toy model which suggests that both dark phenomena can be unified into a single negative mass fluid. The model is a modified ΛCDM cosmology, and indicates that continuously-created negative masses can resemble the cosmological constant and can flatten the rotation curves of galaxies. The model leads to a cyclic universe with a time-variable Hubble parameter, potentially providing compatibility with the current tension that is emerging in cosmological measurements. In the first three-dimensional N-body simulations of negative mass matter in the scientific literature, this exotic material naturally forms haloes around galaxies that extend to several galactic radii. These haloes are not cuspy. The proposed cosmological model is therefore able to predict the observed distribution of dark matter in galaxies from first principles. The model makes several testable predictions and seems to have the potential to be consistent with observational evidence from distant supernovae, the cosmic microwave background, and galaxy clusters. These findings may imply that negative masses are a real and physical aspect of our Universe, or alternatively may imply the existence of a superseding theory that in some limit can be modelled by effective negative masses. Both cases lead to the surprising conclusion that the compelling puzzle of the dark Universe may have been due to a simple sign error.

/pdf/a-unifying-theory-of-dark-energy-and-dark-matter-negative-izv8za4tb5.pdf

A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework

In a flat Friedmann–Lemaitre–Robertson–Walker (FLRW) geometry, we consider the expansion of the universe powered by the gravitationally induced ‘adiabatic’ matter creation. To demonstrate how matter creation works well with the expanding universe, we have considered a general creation rate and analysed this rate in the framework of dynamical analysis. The dynamical analysis hints the presence of a non-singular universe (without the big bang singularity) with two successive accelerated phases, one at the very early phase of the universe (i.e. inflation), and the other one describes the current accelerating universe, where this early, late accelerated phases are associated with an unstable fixed point (i.e. repeller) and a stable fixed point (attractor), respectively. We have described this phenomena by analytic solutions of the Hubble function and the scale factor of the FLRW universe. Using Jacobi last multiplier method, we have found a Lagrangian for this matter creation rate describing this scenario of the universe. To match with our early physics results, we introduce an equivalent dynamics driven by a single scalar field, discuss the associated observable parameters and compare them with the latest Planck data sets. Finally, introducing the teleparallel modified gravity, we have established an equivalent gravitational theory in the framework of matter creation.

Evolution and dynamics of a matter creation model

If we live on the weak brane with zero effective cosmological constant in a warped 5D bulk spacetime, gravitational waves and brane fluctuations can be generated by a part of the 5D Weyl tensor and carries information of the gravitational field outside the brane. We consider on a cylindrical symmetric warped FLRW background a U(1) self-gravitating scalar field coupled to a gauge field without bulk matter. It turns out that brane fluctuations can be formed dynamically, due to the modified energy–momentum tensor components of the scalar-gauge field (“cosmic string”). As a result, we find that the late-time behavior could significantly deviate from the standard evolution of the universe. The effect is triggered by the time-dependent warpfactor with two branches of the form $$\frac{\pm 1}{\sqrt{\tau r}}\sqrt{(c_1e^{\sqrt{2\tau } t}+c_2e^{-\sqrt{2\tau } t})(c_3e^{\sqrt{2\tau } r}+c_4e^{-\sqrt{2\tau } r})}$$
 ( with $$\tau , c_i$$
 constants) and the modified brane equations comparable with a dark energy effect. This is a brane-world mechanism, not present in standard 4D FLRW, where the large disturbances are rapidly damped as the expansion proceed. Because gravity can propagate in the bulk, the cosmic string can build up a huge angle deficit (or mass per unit length) by the warpfactor and can induce massive KK-modes felt on the brane. Disturbances in the spatial components of the stress-energy tensor cause cylindrical symmetric waves, amplified due to the presence of the bulk space and warpfactor. They could survive the natural damping due to the expansion of the universe. It turns out that one of the metric components becomes singular at the moment the warp factor develops an extremum. This behavior could have influence on the possibility of a transition from acceleration to deceleration or vice versa.

A New Fate of a Warped 5D FLRW Model with a U(1) Scalar Gauge Field

Time evolution and matching conditions of spinning gauge strings

The dilatonic Ernst solution describing a Schwarzschild black hole immersed in a background magnetic field is generalized by including a Liouville-type potential in the action principle. We prove that the thermodynamic properties of this new black hole dilaton solution are unaffected by an external magnetic field passing through it.

On ernst black holes with a dilaton potential

We find a emergent azimuthal-angle dependency of the Nielsen-Olesen vortices in the general relativistic situation just after the symmetry breaking at GUT-scale. Using a high-frequency perturbation method, we obtain in the first and second order perturbation equations $\varphi$-dependent terms left over after the phase transition of the Higgs field. Vortices with high multiplicity decay into a lattice with entangled Abrikosov vortices. The stability of this lattice of correlated flux $n=1$ vortices with preferred azimuthal-angle is guaranteed by the contribution from the bulk spacetime by means of the warp factor: the cosmic string becomes super-massive for some time during the evolution and initiates the excitations of the vortices to high multiplicity. The correlation will not fade away during the expansion by the warp factor. We used this azimuthal-angle correlation for the explanation of the recently observed alignment of polarization axes of quasars in large quasar groups. The detailed behavior of this alignment can be explained with our model. The two different orientations perpendicular to each other in quasars groups of less richness could be a second order effect in our model. There is a striking similarity between this phase transition of the gauged Higgs field and the temporarily breaking of the axially symmetry of self-gravitating cosmic string, by the appearance of non-diagonal energy-momentum tensor components. The eccentricity of the ellipsoid can be seen as order parameter. Recovery to SO(2) symmetry induces emission of gravitational and electro-magnetic radiation. More data of high-redshift quasars will be needed in order to test the second order effect predicted in our model.

Reinoud Jan Slagter

Papers

Evolution and dynamics of a matter creation model

A New Fate of a Warped 5D FLRW Model with a U(1) Scalar Gauge Field

Time evolution and matching conditions of spinning gauge strings

On ernst black holes with a dilaton potential

Evidence of cosmic strings by the observation of the alignment of quasar polarization axes on Mpc scale