# The origin of Chern-Simons modified gravity from an 11 + 3-dimensional manifold

## TL;DR

This paper proposes that Chern-Simons terms in modified gravity originate from adding a 3D algebraic manifold to an 11D spacetime, creating an 11+3D structure that addresses anomalies and aligns with Big Bang topology.

## Contribution

It introduces a novel geometric framework where Chern-Simons terms arise from an extended 11+3D manifold, explaining anomaly cancellation and topological evolution.

## Key findings

- Chern-Simons terms are generated by an added 3D manifold.
- Anomaly cancellation is achieved through interaction of two 11D manifolds.
- Total topology reduces to a single point, consistent with Big Bang theory.

## Abstract

In this contribution, it is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11 +3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simons fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold between the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up over the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk , we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.