String duality transformations in $f(R)$ gravity from Noether symmetry approach

Abstract

We select $f(R)$ gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the tree-level dilaton-graviton string effective action into $f(R)$ gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based $f(R)$ Lagrangians are shown in cases where the duality transformation becomes a parity inversion.

v1: 13 pages; v2: minor rephrasings, published version

References in corpus (5)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Spherical symmetry in $f(R)$-gravity
• Connecting early and late universe by $f(R)$ gravity

Cited by in corpus (17)

• Noether Symmetry Approach in $f(\mathcal{G},T)$ Gravity
• Phase transition of charged black holes in massive gravity through new methods
• Classification of the Horndeski cosmologies via Noether Symmetries
• Swampland conjecture in $f(R)$ gravity by the Noether Symmetry Approach
• Early and late time cosmology: the $f(R)$ gravity perspective
• Equivalence of non-minimally coupled cosmologies by Noether symmetries
• Non-Local Curvature and Gauss-Bonnet Cosmologies by Noether Symmetries
• Exact Solutions in Higher-Dimensional Lovelock and $Ad{S}_5$ Chern-Simons Gravity
• Noether symmetries and duality transformations in cosmology
• Noether Symmetries and Some Exact Solutions in $f(R,T^2)$ Theory
• Brane inflation and the robustness of the Starobinsky inflationary model
• Duality transformation and conformal equivalent scalar-tensor theories
• Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether's approach
• Thermal stability of a special class of black hole solutions in F(R) gravity
• Spinning (A)dS Black Holes with Slow-Rotation Approximation in Dynamical Chern-Simons Modified Gravity
• Causal properties of nonlinear gravitational waves in modified gravity
• Unified first law for traversable wormholes in non-minimal coupling of curvature and matter