[Paper Review] Big-Bang Nucleosynthesis and neutralino dark matter in modified gravity

Jin U Kang, Grigoris Panotopoulos|arXiv (Cornell University)|Jun 9, 2008

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates Big-Bang Nucleosynthesis (BBN) and neutralino dark matter within $f(R) \sim R^n$ modified gravity, using the power $n$ as a free parameter to constrain $^4$He abundance. It finds that BBN constraints on $n$ then determine the required dark matter annihilation cross section for consistency with cold dark matter, linking gravitational modification to dark matter phenomenology.

ABSTRACT

In the present work the primordial Big-Bang Nucleosynthesis (BBN) and weakly interacting massive particle (WIMP) dark matter are discussed in a certain class of modified gravitational theories, namely $f(R) \sim R^n$ gravity. The new gravitational model is characterized by a single parameter $n$. First we determine the conditions under which the theoretical predictions for the $^{4}$He abundance are in agreement with the observations. More precisely, during BBN the physics is known and all the parameters are known. The only free parameter to be constrained is the power $n$ related to the new gravitational model. After that, for cold dark matter we use the value of $n$ determined from the BBN considerations and determine how the mass of the dark matter particle is related to the annihilation cross section in order for the cold dark matter constraint to be satisfied.

Motivation & Objective

• To examine how $f(R) \sim R^n$ gravity affects primordial nucleosynthesis, particularly $^4$He abundance predictions.
• To constrain the gravitational parameter $n$ using observational data on $^4$He abundance during BBN.
• To determine the required dark matter annihilation cross section for cold dark matter consistency, given $n$ from BBN.
• To establish a connection between modified gravity and weakly interacting massive particle (WIMP) dark matter phenomenology.

Proposed method

• Model the gravitational action as $f(R) = R^n$, introducing $n$ as a single free parameter to describe modified gravity.
• Apply the modified gravity framework to the early universe, solving the relevant cosmological equations during the BBN epoch.
• Use known BBN physics with standard model parameters, varying only $n$ to match observed $^4$He abundance.
• For the determined $n$, compute the required WIMP annihilation cross section to satisfy cold dark matter relic density constraints.
• Relate the dark matter particle mass to the annihilation cross section under the constraints of $n$-dependent gravity.
• Use the consistency of $^4$He abundance and dark matter relic density to constrain the $n$-parameter space.

Experimental results

Research questions

• RQ1 What values of $n$ in $f(R) \sim R^n$ gravity are consistent with observed $^4$He abundance during Big-Bang Nucleosynthesis?
• RQ2 How does the modified gravity parameter $n$ affect the predicted $^4$He yield in the early universe?
• RQ3 Given $n$ constrained by BBN, what is the required dark matter annihilation cross section to satisfy cold dark matter relic density?
• RQ4 What is the relationship between the neutralino mass and annihilation cross section in this modified gravity framework?
• RQ5 Can the $n$-parameter in $f(R) \sim R^n$ gravity simultaneously satisfy both BBN and cold dark matter constraints?

Key findings

• The value of $n$ is constrained by matching theoretical predictions of $^4$He abundance to observational data, fixing the gravitational modification parameter.
• The $n$ value derived from BBN is used as input to determine the required dark matter annihilation cross section for relic density consistency.
• The paper establishes a quantitative link between the $n$-parameter in $f(R) \sim R^n$ gravity and the WIMP annihilation cross section.
• The required dark matter annihilation cross section depends on the $n$-value, implying that modified gravity influences dark matter phenomenology.
• The model shows that $n$-dependent gravity can simultaneously satisfy both BBN and cold dark matter constraints, provided the cross section is tuned accordingly.
• The analysis demonstrates that $f(R) \sim R^n$ gravity offers a unified framework for constraining both primordial nucleosynthesis and dark matter relic density.