Speaker
Description
From the action formalism, the Ricci scalar $R$ in the Einstein-Hilbert action can be decomposed into a bulk term $\mathcal{G}$ and a boundary term $\mathcal{B}$. A recent modified theory of gravity is the so-called $f(\mathcal{G})$ gravity, which arises from the action after removing its boundary term $\mathcal{B}$ from the Ricci scalar $R$ while mapping the remaining bulk term $\mathcal{G}$ to $f(\mathcal{G})$. We will begin by examining linearised $f(\mathcal{G})$ gravity and several of its interesting aspects.
Firstly, there is a correspondence between the linearised $\mathcal{G}$ and the Fierz-Pauli Lagrangian which governs the field theory of the (rank-2 tensor) graviton. Secondly, we discover that one can recover the field equations with the cosmological term from the linearised $f(\mathcal{G})$ field equations by a specific choice of $f(\mathcal{G})$. Third, we investigate a trial solution of the form $f(\mathcal{G}) = c_{1/2} \sqrt{\mathcal{G}} + \mathcal{G} + c_{3/2} \mathcal{G}^{3/2} + c_2 \mathcal{G}^2 \cdots$. We show that this solution is unphysical when expanding from the Minkowski background and discuss the numerical solution of its background Friedmann equation when expanding from the flat FLRW background.
| Topic | Modified theories of gravity, gravitational waves |
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