# Attractor Models in Scalar-Tensor Theories of Inflation

## TL;DR

This paper explores how specific scalar-tensor theories of gravity, like $f(R)$ and Brans-Dicke, naturally produce inflationary predictions similar to attractor models, explaining their robustness across different functional choices.

## Contribution

It demonstrates that certain scalar-tensor theories fulfill the conditions of cosmological attractors, linking them to well-known inflationary predictions and analyzing their stability under functional variations.

## Key findings

- Attractor-like predictions arise in specific $f(R)$ and Brans-Dicke models.
- Predictions are stable under changes in the functional form of the theories.
- Connections between scalar-tensor theories and attractor models are established.

## Abstract

In this work we study the cosmological attractor models of inflation in connection with certain scalar-tensor theories of gravity, e.g $f(R)$ gravity and Brans-Dicke theory. For some particular choices of the functional degrees of freedom in these theories, one obtains Starobinsky like predictions in the ($n_s$-$r$) observable plane. We have demonstrated that these choices in the Lagrangian density of certain $f(R)$ and Brans-Dicke theories fulfil the condition of the cosmological attractors. That explains why known predictions of $f(R)$ and Brans-Dicke theories in certain cases appear to be the predictions of the much discussed attractor theories. In addition, we did an analysis showing how the predictions of an attractor model is preserved with respect to the variation in the functional freedom of the theory.