Andrew Cottham — Independent Theoretical Physics Researcher
D1 Field Theory is a proposed fundamental field framework investigating whether spacetime, gravitation, cosmology and particle-physics phenomena can emerge from the dynamics of an underlying D1 field.
This repository contains research papers, computational models, numerical experiments and supporting material developed as part of the D1 research programme.
The D1 research programme investigates a number of connected questions in fundamental physics.
Can the observed structure of spacetime and gravitational dynamics emerge from the underlying D1 field?
A major current objective is to investigate whether Einstein’s gravitational equations can be obtained as an effective description of the D1 field.
D1 research investigates the behaviour of the field in the extreme-energy regime associated with gravitational collapse, including possible non-singular descriptions of black-hole interiors.
The D1 cosmological programme investigates the evolution of the universe from the early universe through to the present epoch, including inflation, baryogenesis and cosmic acceleration.
The D1 framework is also being developed as a possible foundation for particle physics, including investigations of composite Higgs models and discrete vacuum structures.
A longer-term objective is to investigate whether the D1 framework can provide a common foundation connecting gravitational and quantum descriptions.
This repository contains computational work supporting investigations within D1 Field Theory.
The current repository contains three principal computational components.
gps_injection_recovery.pyThis script performs a numerical injection-and-recovery test using GPS clock residual data.
A sinusoidal annual signal is injected into the clock residuals and the resulting signal is fitted numerically using nonlinear least-squares optimisation.
The calculation is intended to test whether a periodic signal of known amplitude can be recovered from noisy timing data.
The original input dataset is not currently included in this repository.
The script expects:
../data/gps_G01_2018_2019_monthly.csv
The provenance and complete data-processing pipeline for the original dataset are therefore not yet archived here.
The script should consequently be regarded as research analysis code requiring the original input data before the numerical result can be independently reproduced.
reconstruction.pyThis program performs a numerical scalar-field reconstruction associated with the D1 cosmological model.
The calculation proceeds through:
[ \Omega_{m0},\Omega_{\mathrm{DE},0},w \rightarrow H(a) \rightarrow \Phi_{D1}(a) \rightarrow V(\Phi_{D1}) \rightarrow \epsilon \rightarrow N. ]
The current fiducial parameters are:
[ \Omega_{m0}=0.30, ]
[ \Omega_{\mathrm{DE},0}=0.70, ]
[ w=-0.99. ]
The calculation uses a logarithmically spaced scale-factor grid extending from
[ a=10^{-15} ]
to
[ a=1. ]
The program outputs the calculated inflationary e-fold count.
The numerical result should be interpreted as the output of the specified reconstruction and parameter assumptions. Independent validation requires numerical convergence testing and examination of the theoretical assumptions underlying the reconstruction.
slow_roll_parametersThis calculation evaluates inflationary observables from the output of the cosmological reconstruction.
The quantities calculated include:
[ n_s = 1-6\epsilon+2\eta, ]
[ r=16\epsilon, ]
and
[ \alpha_s=\frac{dn_s}{d\ln a}. ]
The current implementation evaluates
[ \eta=\frac{d\ln\epsilon}{d\ln a}. ]
The precise slow-roll convention used for (\eta) should be compared with the theoretical definitions adopted in the associated research work before the numerical results are interpreted as standard potential slow-roll parameters.
The calculation currently evaluates the observables at a specified numerical position near the end of the selected inflationary region.
Python dependencies are listed in:
requirements.txt
The computational scripts are provided as research code supporting the D1 research programme.
Some calculations depend on external data or on variables generated by preceding calculations. Where this is the case, the dependencies are documented in the relevant source files.
Future versions of the repository will progressively improve:
reconstruction.pyThis script implements a D1 cosmological reconstruction calculation based on the proposed relationship between present-day cosmological parameters and the history of the universe.
The calculation includes the determination of inflationary e-folds from specified model parameters.
This work is associated with the D1 cosmological investigation of whether information about the early universe can be connected to present-day measured quantities.
slow_roll_parametersThis calculation investigates standard inflationary slow-roll quantities within the relevant D1 cosmological framework.
The calculations include quantities such as:
These quantities provide a connection between the theoretical inflationary model and observational cosmology.
The D1 research programme has produced a series of theoretical and computational papers covering cosmology, gravitation, black holes and particle physics.
Research outputs are archived through Zenodo and Figshare.
The complete research archive is available through Zenodo.
Published in the Journal of Theoretical, Experimental, and Applied Physics, Volume 2, Issue 3, 2026.
The paper develops a D1 Composite Higgs framework involving discrete (Z_4) crystalline vacua and investigates its numerical structure and phenomenological implications for LHC physics.
```text D1-Theory/ │ ├── Version_2_November_2025/ │ └── paper 4 v2.2.pdf │ ├── gps_injection_recovery.py ├── reconstruction.py ├── slow_roll_parameters ├── requirement.txt └── README.md