The holographic bound in the scalar-tensor and $f(R)$ gravities

TL;DR

This paper extends the holographic bound to scalar-tensor and $f(R)$ gravities, using Noether charge entropy, and applies it to cosmological models to constrain theory parameters, also discussing frame transformations.

Contribution

It introduces the holographic bound in scalar-tensor and $f(R)$ gravities and explores its implications for cosmological models and parameter constraints.

Findings

Holographic bound extended to scalar-tensor and $f(R)$ gravities.

Additional constraints on gravity parameters derived from holographic considerations.

Discussion of frame transformation impacts on the holographic bound.

Abstract

The holographic bound has been extended to the different theory of gravities such as scalar-tensor gravity and $f(R)$ gravity according to the Noether charge definition of the entropy for a black hole surface. We have introduced some popular examples of the flat FRW cosmology in order to investigate holographic bound in scalar-tensor and $f(R)$ gravity. Using the holographic bound, we put an additional constraint on the scalar-tensor gravity and $f(R)$ gravity parameters. We also discuss about the transformation from Jordan frame to Einstein frame.