Big Bang revisited

Abstract

The Friedmann cosmological solution of the standard Einstein gravitational field equation has a curvature singularity at a moment in time known as the Big Bang. It has been suggested that this Big Bang curvature singularity can be eliminated by use of a degenerate spacetime metric. This proposal was the main topic of our talk at the Workshop, but, here, we also discuss the possible appearance of CPT-conjugated worlds and the conjectured relevance of an extended version of Einstein's field equation.

Figures (5)

• Figure 1: Cosmic scale factor $a(t)$ of the Friedmann solution (\ref{['eq:Friedmann-asol']}) for equation-of-state parameter $w_{M}=1/3$, with $t_{0}=4\,\sqrt{5} \approx 8.944$.
• Figure 2: Cosmic scale factor $a(t)$ of the defect-cosmology solution (\ref{['eq:regularized-Friedmann-asol']}) for $w_{M}=1/3$, with $b=1$ and $t_{0}=4\,\sqrt{5} \approx 8.944$.
• Figure 3: Defect cosmology: Pair-creation scenario. The small double arrows (in red) indicate the direction of the physical, thermodynamic time $\mathcal{T}=|t|$.
• Figure 4: Defect cosmology: Penrose conformal diagram using the same notation as in Fig. 15(ii) of Ref. HawkingEllis1973. A $t$-retarded gravitational wave with emission time $t_\text{em}<0$ and observation time $t_\text{obs}>0$ is shown as the single-arrowed curve going diagonally up and a $t$-advanced gravitational wave emitted at $t_\text{em}<0$ as the double-arrowed curve going diagonally down; see Sec. \ref{['sec:Defect-cosmology']} for further explanations.
• Figure 5: Two sketches of the four-leaf-clover universe. Left: spacetime defects at $t=0$ and $\xi=0$, with exemplary P and CT transformations. Right: two pairs of CPT-conjugated worlds ($W$--$\overline{W}$ and $\mathfrak{w}$--$\overline{\mathfrak{w}}$). See Sec. \ref{['sec:Defect-cosmology-FLC-universe']} for further explanations and references.