To illustrate the remark that there is no unique form of auxiliary field that observes (22.5) let us take (22.6) where is raised to the power This brings the conformal scalar into the form (22.7) A…

What would be the properties of a universe with only one spatial dimension and one time dimension? General relativity in 1+1 dimensions is unique since the two curvature terms in the Einstein field equations cancel. This makes the Einstein field equations algebraic rather than differential equations. This special feature can make 1+1 dimensionality attractive as an instructional tool to simplify the mathematics that many beginners find opaque. We explore the implications and features of the Einstein field equations in 1+1 dimensions and find they provide a surprisingly rich and interesting model. We then study an alternate theory and its implications for a potentially stable wormhole solution.

Big Bang Nucleosynthesis (BBN) is very sensitive to the cosmological expansion rate. If the gravitational constant $G$ took a different value during the nucleosynthesis epoch than today, the primordial abundances of light elements would be affected. In this work, we improve the bounds on this variation using recent determinations of the primordial element abundances, updated nuclear and weak reaction rates and observations of the Cosmic Microwave Background (CMB). When combining the measured abundances and the baryon density from CMB observations by Planck, we find $G_\mathrm{BBN}/G_0 = 0.99^{+0.06}_{-0.05}$ at $2σ$ confidence level. If the variation of $G$ is linear in time, we find $\dot{G}/G_0 = 0.7^{+3.8}_{-4.3}\times 10^{-12} \, \mathrm{yr}^{-1}$, again at $2σ$. These bounds are significantly stronger than those from previous primordial nucleosynthesis studies, and are comparable and complementary to CMB, stellar, solar system, lunar laser ranging, pulsar timing and gravitational wave constraints.

This just proves that if and are fixed as constant, then through the equation of motion for the conformal scalar (22.1), is also fixed as constant thereby, showing consistency in the full spacetime…

There are revisions in the title as well as in the abstract, while (23.20) has been put in its formal form.

The draft has been updated up to page 12. In this updated version, we have included subsection 3.3, wherein we show some short details in arriving at an extremal form (23.5) of the (1 + 1)-dim EH a…

The draft has been updated up to page 12. In this updated version, we have included subsection 3.3, wherein we show some short details in arriving at an extremal form (23.5) of the (1 + 1)-dim EH a…