fix mathjax and hyperlink issues in dark matter

theory/cosmology/dark matter.md

@@ -10,52 +10,55 @@ nav_order: 3
 
 ### Overview
 
-Dark matter is one of the most elusive and mysterious components of our universe, making up about 27% of its total mass-energy content. In comparison, ordinary matter (which includes stars, planets, and galaxies) constitutes only about 5%, while [dark energy](dark%20energy.html)—the force responsible for the accelerated expansion of the universe—accounts for a staggering 68%. Despite its significant influence, dark matter doesn’t interact with electromagnetic radiation (light), making it invisible to [telescopes](../../observation/instruments/telescopes.html). Its existence is inferred from its gravitational effects on visible matter and cosmic structures.
+[Dark matter](#dark-matter) is one of the most elusive and mysterious components of our universe, making up about 27% of its total mass-energy content. In comparison, ordinary matter (which includes stars, planets, and galaxies) constitutes only about 5%, while [dark energy](dark%20energy.html)—the force responsible for the accelerated expansion of the universe—accounts for a staggering 68%. Despite its significant influence, [dark matter](#dark-matter) doesn’t interact with electromagnetic radiation (light), making it invisible to [telescopes](../../observation/instruments/telescopes.html). Its existence is inferred from its gravitational effects on visible matter and cosmic structures.
 
 ### Historical Background
 
-The idea of dark matter was first introduced in 1933 by Swiss astronomer Fritz Zwicky while studying the Coma Cluster, a group of galaxies located approximately 320 million light-years away. Zwicky observed that the galaxies were moving faster than the mass of visible matter could explain, leading him to conclude that some invisible mass—what he called "dunkle Materie" (German for dark matter)—was providing the extra gravitational pull.
+The idea of [dark matter](#dark-matter) was first introduced in 1933 by Swiss astronomer Fritz Zwicky while studying the Coma Cluster, a group of galaxies located approximately 320 million light-years away. Zwicky observed that the galaxies were moving faster than the mass of visible matter could explain, leading him to conclude that some invisible mass—what he called "dunkle Materie" (German for [dark matter](#dark-matter))—was providing the extra gravitational pull.
 
-In the 1970s, American astronomer Vera Rubin studied the rotation curves of galaxies, notably Andromeda. According to Newtonian mechanics, stars farther from the center of a galaxy should orbit more slowly than those closer in. However, Rubin found that stars at the outer edges of galaxies were orbiting at speeds nearly constant with stars closer to the center, contradicting the expected Keplerian decline. This phenomenon, called the "galaxy rotation problem" further confirmed the existence of [dark matter](dark%20matter.html), suggesting that a hidden mass was distributing gravitational forces evenly across galaxies.
+In the 1970s, American astronomer Vera Rubin studied the rotation curves of galaxies, notably Andromeda. According to Newtonian mechanics, stars farther from the center of a galaxy should orbit more slowly than those closer in. However, Rubin found that stars at the outer edges of galaxies were orbiting at speeds nearly constant with stars closer to the center, contradicting the expected Keplerian decline. This phenomenon, called the "galaxy rotation problem" further confirmed the existence of [dark matter](#dark-matter), suggesting that a hidden mass was distributing gravitational forces evenly across galaxies.
 
 ### What is Dark Matter?
 
-Despite its profound impact on the universe, dark matter remains undetectable through any means other than its gravitational influence.
+Despite its profound impact on the universe, [dark matter](#dark-matter) remains undetectable through any means other than its gravitational influence.
 
-The leading candidates for dark matter include:
+The leading candidates for [dark matter](#dark-matter) include:
 
-1. **[WIMPs (Weakly Interacting Massive Particles):](../particle%20physics/WIMPs.html)** Hypothetical particles that could interact with ordinary matter through gravity and the weak nuclear force. If WIMPs exist, they would have a mass between 10 to 1000 times that of a proton, but interact so rarely that they are difficult to detect.
+1. **[WIMPs (Weakly Interacting Massive Particles):](../particle%20physics/WIMPs.html)** Hypothetical particles that could interact with ordinary matter through gravity and the weak nuclear force. If [WIMPs](../particle%20physics/WIMPs.html) exist, they would have a mass between 10 to 1000 times that of a proton, but interact so rarely that they are difficult to detect.
 
-2. **Axions:** Extremely light particles, potentially with a mass of about $10^{-22}$ eV, produced in the early universe. They are considered a strong candidate for dark matter due to their theoretical compatibility with particle physics and cosmology.
+2. **Axions:** Extremely light particles, potentially with a mass of about $$10^{-22}$$ eV, produced in the early universe. They are considered a strong candidate for [dark matter](#dark-matter) due to their theoretical compatibility with [particle physics](../particle%20physics/) and [cosmology](../cosmology).
 
-3. **Sterile Neutrinos:** A type of neutrino that doesn’t interact via the weak force but could still contribute to dark matter. Their mass is thought to be in the range of keV (kilo-electron volts), much higher than that of regular neutrinos.
+3. **Sterile Neutrinos:** A type of neutrino that doesn’t interact via the weak force but could still contribute to [dark matter](#dark-matter). Their mass is thought to be in the range of keV (kilo-electron volts), much higher than that of regular neutrinos.
 
-4. **MACHOs (Massive Compact Halo Objects):** These are large, dense objects like [black holes](../special%20stars/black%20holes.html), [neutron stars](../special%20stars/neutron%20stars.html), or [brown dwarfs](../special%20stars/dwarf%20stars.html) that could contribute to dark matter’s mass, but are insufficient to account for all of it. Observations suggest that MACHOs make up less than 20% of the total dark matter.
+4. **MACHOs (Massive Compact Halo Objects):** These are large, dense objects like [black holes](../special%20stars/black%20holes.html), [neutron stars](../special%20stars/neutron%20stars.html), or [brown dwarfs](../special%20stars/dwarf%20stars.html) that could contribute to [dark matter](#dark-matter)’s mass, but are insufficient to account for all of it. Observations suggest that MACHOs make up less than 20% of the total [dark matter](#dark-matter).
 
 ### Gravitational Lensing and Dark Matter
 
-One of the most effective methods to detect dark matter is through gravitational lensing. According to Einstein's general theory of relativity, massive objects, including dark matter, bend the path of light. The Einstein radius (\theta_E​) quantifies the angle of deflection:
+One of the most effective methods to detect [dark matter](#dark-matter) is through gravitational lensing. According to Einstein's general theory of relativity, massive objects, including [dark matter](#dark-matter), bend the path of light. The Einstein radius $$(\theta_E​)$$ quantifies the angle of deflection:
 
-$$ \theta_E = \sqrt{\frac{4GM}{c^2} \cdot \frac{D_{ls}}{D_l D_s}}​ $$
+$$ \theta*E = \sqrt{\frac{4GM}{c^2} \cdot \frac{D*{ls}}{D_l D_s}}​ $$
 
 where:
-   - $G$ is the gravitational constant,
-   - $M$ is the mass of the lensing object,
-   - $c$ is the speed of light,
-   - $D_{ls}$, $D_l$, and $D_s$ are the angular diameter distances between the observer and the source, the observer and the lens, and the lens and the source, respectively.
-By analyzing the distortions in light from distant galaxies, astronomers can map out dark matter in galaxy clusters and cosmic structures.
+
+- $$G$$ is the gravitational constant,
+- $$M$$ is the mass of the lensing object,
+- $$c$$ is the speed of light,
+- $$D_{ls}$$, $$D_l$$, and $$D_s$$ are the angular diameter distances between the observer and the source, the observer and the lens, and the lens and the source, respectively.
+
+By analyzing the distortions in light from distant galaxies, astronomers can map out [dark matter](#dark-matter) in galaxy clusters and cosmic structures.
 
 ### Role in Structure Formation
 
-Dark matter is crucial in the formation of galaxies and cosmic structures. In the early universe, slight density fluctuations in dark matter ($\frac{\delta \rho}{\rho} \approx 10^{-5}$) allowed it to gravitationally attract regular matter, seeding the formation of galaxies. As the universe expanded, these dark matter "halos" pulled in gas and dust, leading to the birth of stars, galaxies, and larger structures. Without [dark matter](dark%20matter.html), models suggest the universe would be too smooth, with too little clumping to form the galaxies we observe today.
+[Dark matter](#dark-matter) is crucial in the formation of galaxies and cosmic structures. In the early universe, slight density fluctuations in [dark matter](#dark-matter) ($$\frac{\delta \rho}{\rho} \approx 10^{-5}$$) allowed it to gravitationally attract regular matter, seeding the formation of galaxies. As the universe expanded, these [dark matter](#dark-matter) "halos" pulled in gas and dust, leading to the birth of stars, galaxies, and larger structures. Without [dark matter](#dark-matter), models suggest the universe would be too smooth, with too little clumping to form the galaxies we observe today.
 
 ### Challenges and Ongoing Research
 
-Detecting dark matter directly remains one of the greatest challenges in physics. Experiments such as the Large Hadron Collider (LHC) and Xenon1T aim to detect dark matter particles by measuring rare interactions between dark matter and ordinary matter, but no definitive results have emerged yet. Underground detectors seek to capture WIMP interactions, but the cross-section (probability) of interaction may be too small to detect at current sensitivities.
+Detecting [dark matter](#dark-matter) directly remains one of the greatest challenges in physics. Experiments such as the Large Hadron Collider (LHC) and Xenon1T aim to detect [dark matter](#dark-matter) particles by measuring rare interactions between [dark matter](#dark-matter) and ordinary matter, but no definitive results have emerged yet. Underground detectors seek to capture [WIMP](../particle%20physics/WIMPs.html) interactions, but the cross-section (probability) of interaction may be too small to detect at current sensitivities.
+
+Other efforts include the mapping of [dark matter](#dark-matter) distribution in the Milky Way, where Gaia spacecraft observations have provided detailed data on the movement of stars, hinting at the gravitational influence of [dark matter](#dark-matter) in our galaxy.
 
-Other efforts include the mapping of dark matter distribution in the Milky Way, where Gaia spacecraft observations have provided detailed data on the movement of stars, hinting at the gravitational influence of dark matter in our galaxy.
-There are also alternative explanations, such as Modified Newtonian Dynamics (MOND), which propose adjustments to gravity on galactic scales, and self-interacting dark matter, which hypothesizes that dark matter particles can collide and interact with one another.
+There are also alternative explanations, such as Modified Newtonian Dynamics (MOND), which propose adjustments to gravity on galactic scales, and self-interacting [dark matter](#dark-matter), which hypothesizes that [dark matter](#dark-matter) particles can collide and interact with one another.
 
 ### Conclusion
 
-Dark matter remains a cornerstone of modern cosmology, explaining phenomena such as galaxy rotation curves, structure formation, and gravitational lensing that cannot be accounted for by visible matter alone. Although its exact nature remains a mystery, the search for [dark matter](dark%20matter.html) continues to push the boundaries of physics, and one day, it may lead to groundbreaking discoveries about the fundamental workings of the universe.
+[Dark matter](#dark-matter) remains a cornerstone of modern [cosmology](../cosmology), explaining phenomena such as galaxy rotation curves, structure formation, and gravitational lensing that cannot be accounted for by visible matter alone. Although its exact nature remains a mystery, the search for [dark matter](#dark-matter) continues to push the boundaries of physics, and one day, it may lead to groundbreaking discoveries about the fundamental workings of the universe.