## Honors Theses

#### Date of Award

Fall 5-1-2021

#### Document Type

Undergraduate Thesis

#### Department

Physics and Astronomy

#### First Advisor

Luca Bombelli

#### Second Advisor

Cecille Labuda

#### Third Advisor

Benjamin Pilgrim

#### Relational Format

Dissertation/Thesis

#### Abstract

Causal Set theory is an approach to quantum gravity. In this approach, the spacetime continuum is assumed to be discrete rather than continuous. The discrete points in a causal set can be seen as a continuum spacetime if they can be embedded in a manifold such that the causal structure is preserved. In this regard, a manifold can be constructed by embedding a causal set preserving causal information between the neighboring points. In this thesis, some of the fundamental properties of causal sets are discussed and the curvature and dimension information of Minkowski, de Sitter, and Anti-de Sitter spaces is approximated using chain length distributions. The accuracy of the results is compared with the continuum manifold and the feasibility of such an approach is discussed. In the first chapter, the need for quantizing gravity is addressed and the concept of spacetime and Lorentz boosts is delineated at length. The second chapter begins with a formal definition of a causal set and delves deep into how points can be sprinkled on a causal manifold. In the third chapter, the chain distribution on different manifolds is calculated computationally and the result is compared with the theoretical approximation. The fourth chapter is devoted to analyzing the curvature information of a manifold using causal set theory. The Dimension of such manifold is calculated using the Myrheim-Meyer relation and the computational error is discussed if any. In the conclusion, the action of a causal set and the possible future work are discussed.

#### Recommended Citation

Dhital, Ayush, "Curved Spacetime in the Causal Set approach to Quantum Gravity" (2021). *Honors Theses*. 1901.

https://egrove.olemiss.edu/hon_thesis/1901

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### Included in

Elementary Particles and Fields and String Theory Commons, Other Physics Commons, Quantum Physics Commons