Related papers: Towards the Raychaudhuri Equation Beyond General R…
This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's equation to singularities is reported.…
Modifications to gravity can provide attractive alternatives to the dark components of the standard model of cosmology. These modifications to general relativity (GR) must be hidden at small scales where theory is well tested, and so one…
General Relativity is expected to break down in the high-curvature regime. Beyond an effective field theory treatment with higher-order operators, it is important to identify consistent theories with higher-curvature terms at the…
The objective of this thesis is to present a viable extension of general relativity free from cosmological singularities. A viable cosmology, in this sense, is one that is free from ghosts, tachyons or exotic matter, while staying true to…
Recent study has shown that a non-singular oscillating potential, a feature of Infinite Derivative Gravity (IDG) theories, matches current experimental data better than the standard GR potential. In this work we show that this non-singular…
We show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for…
Under the assumption that General Relativity (GR) correctly describes the phenomenology of our Universe, astronomical observations provide compelling evidence that (1) the dynamics of cosmic structure is dominated by dark matter (DM), an…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
We prove a No-Go theorem for singularity resolution in gravitational collapse: within any analytic gravitational theory, including general relativity and all theories with polynomial actions, quantum corrections introduced solely as…
We consider perturbative modifications of the Friedmann equations in terms of energy density corresponding to modified theories of gravity proposed as an alternative route to comply with the observed accelerated expansion of the universe.…
General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match…
Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\Lambda$CDM model, based on General Relativity and standard…
We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy…
A bouncing Universe avoids the big-bang singularity. Using the time-like and null Raychaudhhuri equations, we explore whether the bounce near the big-bang, within a broad spectrum of modified theories of gravity, allows for cosmologically…
Gravity is a phenomenon which arises due to the space-time geometry. The main equations that describe gravity are the Einstein equations. To understand the consequences of these field equations we need to calculate the free particle…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
We present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time. The singularity occurs in the material pressure and acceleration whilst the scale…
The equation of motion is the important equation for obtain the extra force and Raychaudhuri equation. By considering an explicitly coupling between an arbitrary function of the scalar Gauss-Bonnet, G and the Lagrangian density of matter,…
Geodesic incompleteness is a problem in both general relativity and string theory. The Weyl invariant Standard Model coupled to General Relativity (SM+GR), and a similar treatment of string theory, are improved theories that are…