Abstract:
Weyl invariant gravity has been investigated as the fundamental theory of the vector inflation. Accordingly, we consider a Weyl invariant extension of Dirac-Born-Infeld type gravity. We find that an appropriate choice of the metric removes the scalar degree of freedom which is at the first sight required by the local scale invariance of the action, and then a vector field acquires mass. Then non-minimal couplings of the vector field and curvatures are induced. We find that the Dirac-Born-Infeld type gravity is a suitable theory to the vector inflation scenario.

We consider f(R,T) theory of gravity, where R is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case, f(R,T)=R+2f(T) and two expressions are assumed for the function f(T),(a_{1}T^{n}+b_{1})/(a_{2}T^{n}+b_{2}) and a_{3}In^{q}(b_{
}

At the fundamental level, the 4-dimensional space-time of our direct experience might not be a continuum and discrete quantum entities might “collectively” rule its dynamics. Henceforth, it seems natural to think that in the “low-energy” regimesome of its distinctive quantum attributes could, in principle, manifest themselves even at macroscopically large scales. Indeed, when confronted with Nature, classical gravitational dynamics of spinning astrophysical bodies is known to lead to paradoxes: to untangle them, dark matter or modifications to the classical law of gravity are openly considered. In this article, the hypothesis of a fluctuating space-time acquiring “at large distances” the properties of a Bose-Einstein condensate is pushed forward: firstly, it is shown that a natural outcome of this picture is the production of monopoles, dyons, and vortex lines of “quantized” gravitomagnetic—or gyrogravitational—flux along the transition phase; the minimal supported “charge” (and multiples of it) being directly linked with a nonzero (minimal) vacuum energy. Thus, a world of vibrating, spinning, interacting strings whose only elements in their construction are our topological concepts of space and time is envisioned, and they are proposed as tracers of the superfluid features of the space-time: the archetypal embodiment of these physical processes being set by the “gravitational roton”, an analogue of Landau’s classic higher-energy excitation used to explain the superfluid properties of helium II. The far and the near field asymptotics of string line solutions are presented and used to deduce their pair-interaction energy. Remarkably, it is found that two stationary, axis-aligned, quantum space-time vortices with the same sense of spin not only exhibit zones of repulsion but also of attraction, depending on their relative geodetic distance.

Abstract:
We start with a formulation of a modified “Poisson” equation from Poissons and Will as of 2014, and then use the Padmanabhan inter relationship between an inflaton and an early universe potential system. Then from there, we come up with a quadratic equation for a minimum radius, for producing a “massive graviton” value. We then close with observations as to what this implies as to gravitational physics.

Abstract:
We find that having the scale factor close to zero due to a given magnetic field value, an early universe magnetic field affects how we would interpret Mukhanov’s chapter on “self reproduction of the universe”. We extend such arguments, and refer to the possibility of modified gravity. We hope that some of the issues raised by Kobayashi and Seto as to allowed inflation models may be addressed, once further refinement of these preliminary results commences. We close with statements as to the value of α in a gravitational potential proportional to r^{？α} and how this adjustment affects the 3 body problem.

Abstract:
We suggest to consider the spacetime as a non-equilibrium system with a long-term stationary state that possess as a spatio-temporally fluctuating quantity ？ . These systems can be described by a superposition of several statistics, “superstatistics”. We propose a Gamma distribution for f( ？) that depends on a parameter ρ1. By means of it the corresponding entropy is calculated, ρ1 is identified with the probability corresponding to this model. A generalized Newton’s law of gravitation is then obtained following the entropic force formulation. We discuss some of the difficulties to try to get an associated theory of gravity.

We consider FLRW cosmological models for perfect fluid (with ρ as the energy density) in the frame work of the f(ρ) modified theory of gravity [V. N. Tunyak, Russ. Phys. J. 21, 1221 (1978); J. R. Ray, L. L. Smalley, Phys. Rev. D. 26, 2615 (1982)]. This theory, with total Lagrangian R-f(ρ), can be considered as a cousin of the F(R) theory of gravity with total Lagrangian F(R)-ρ. We can pick proper function forms f(ρ) to achieve, as the F(R) theory does, the following 4 specific goals, 1) producing a non-singular cosmological model (Ricci scalar and

Starting from the classical Newton inverse square law of gravitation we
arrive at a modified Newtonian gravity in the spirit of the work of Milgrom-Bekenstein
pioneering work. This is achieved by injecting the needed quantum mechanical
dissection of special relativity into Newton’s law via the modified energy mass
relationship which transforms Einstein’s famous formula from a smooth four dimensional space to a
rugged fractal-like spacetime manifold. The confidence in the present result
stems not only from the consistency of the mathematical scheme but also from
agreement with the general direction of cosmological measurements and
observations.

Abstract:
We examine the weak version of the third law of black hole thermodynamics inthe n-dimensional Einstein–Gauss–Bonnet system with a negative cosmological constant.To see whether the extreme black hole solution with zero temperature is formed, weinvestigate the motion of the thin shell that has the equal mass to the extreme black holein the background described by the non-GR branch solutions. The interior of the shell isempty. Our analysis using the generalized Israel's junction condition shows that the shellcan contract beyond a certain radius and the degenerate horizon is formed for same range ofparameters. Hence, this model can be a counterexample of the third law.

Abstract:
A bulk viscosity is introduced in the formalism of modified gravity. It is shownthat, based on a natural scaling law for the viscosity, a simple solution can be found forquantities such as the Hubble parameter and the energy density. These solutions mayincorporate a viscosity-induced Big Rip singularity. By introducing a phase transition inthe cosmic fluid, the future singularity can nevertheless in principle be avoided.