Torsional instanton effects in quantum gravity

Abstract

We show that, in the first order gravity theory coupled to axions, the instanton number of the

What if? Exploring the multiverse through Euclidean wormholes

“…Please notice that our solution generalises the Giddings-Strominger instanton [4], even though the two solutions have a completely different origin (for further applications of this instanton, see e.g. [49]). In our solution, constructed in the framework of the third quantization, the appearance of a term in the Friedmann equation that scales as a −6 is due to the quantization scheme, while in the Giddings-Strominger instanton, which is supported by an axion whose field strength tensor is defined through a rank-three anti-symmetric tensor H µνλ , a similar term appears in the Friedmann equation by the fact that H µνλ , which contributes quadratically to the action, is subjected to the constraint dH = 0 [4].…”

Dark energy from the gravity vacuum

“…As elucidated in [11], this theory admits the Giddings-Strominger wormholes as classical solutions. To see this, let us adopt the Giddings-Strominger ansatz:…”

“…We begin our discussion by writing down the first order Lagrangian density for (Euclidean) axionic gravity, following [11]:…”

“…In what follows next, we briefly review the essential details of the torsional instanton and the η-vacuum in quantum gravity [11], before going into the main content of this article.…”

“…In the effective Lagrangian, this appears as the coupling constant multiplying the Nieh-Yan topological density [3,4,16]. To emphasize, the work in [11] provides, for the first time, a clear demonstration of the fact that there exists an exact similarity between gauge theories with the famous θ-vacuum and gravity theory with the hitherto unexplored η-vacuum.…”