Alternatives to Dark Matter hypothesis
Our Milky Way is a spiralling Galaxy containing 100-400 billion stars, with a stellar disk diameter of approximately 150,000-200,000 light-years and depth of 2000 light-years. There are primary 4 spirals coming out from the centre, with other minor arms. Our sun is around 25,000-28,000 light-years away from the Galactic centre in the inner edge of Orion-Cygnus arm. The Galactic centre is known as Sagittarius A*, a supermassive black-hole.
Our sun revolves about the Galactic centre taking around 240 million years to complete one revolution (a galactic year). Like our sun, all the stars and gases in our galaxy revolve around the galactic centre. Interestingly, however, contradicting to the intuition and Kepler’s laws, most objects revolve at approximately the same speed of 220 km/s irrespective of the distance from the galactic centre. Thus, it seems to follow a rigid-body rotation and not the differential rotation as is observed with-in our own solar system. On top, the rate at which it revolves, the galaxies should be torn apart due to the mere force, while accounting for gravitation, but as we know they don’t, requiring extra force to keep galaxies together.
Red line – expected velocities depending on the mass-structure etc. of Milky Way. Blueline is the observed velocity. source: https://commons.wikimedia.org/wiki/File:Rotation_curve_(Milky_Way).JPG
As discussed in the article about Dark Matter, one of the solutions of this anomaly is explained by dark matter. This framework is the dominantly accepted one but there are some physicists who have proposed another solution which doesn't require the hypothetical dark matter.
MOND
General relativity gives describes with great accuracy at the scales of the solar system. However, at galactic and intergalactic scale, it shows deviations and so different theories are required, like MOND.
MOND stands for Modified Newtonian Dynamics, developed by Mordehai Milgrom, the hypothesis that the discrepancy in the velocities could be rectified by modifying Newtonian force field. The basic premise of MOND is that while Newton’s laws have been tested in high acceleration environment, like the scale of the solar system, they haven’t been tested in a low acceleration environment. The latter is similar to places where such anomalies in galaxies are observed, that is, where acceleration is in order of 10-10 m/s2. But the problem which MOND proponents face is describing how gravity switches from one field to another.
MOND introduces an interpolating function and a new constant having dimensions of acceleration which determines the switch in the gravitation. The force law, therefore, becomes, Fn = mμ(a/a0)a
When, a >> a0, → 1 and when, a << a0 (deep MOND regime), → a/a0
So, in the deep MOND, we would get, (independent of r)
Interestingly, this relation conforms the Tully Fisher type relation in which the mean rotational velocity v in a disc galaxy is correlated with the luminosity of the galaxy L, with .
Along with this, since MOND modifies Newtonian dynamics, it provides a relationship between acceleration at any radius and the unseen mass present within that radius based on the Newtonian analysis. This is known as mass-discrepancy acceleration relation. This tells us that the amount of unseen mass goes to zero where a > a0. The unseen matter is only required for a < a0 regime. This remains a problem for dark matter proponents to explain this behaviour of dark matter.
Instead of having an ad-hoc interpolating function, rich underlying theories are required to give such relation. So in this way MOND is still an incomplete theory with work in progress.
The gravity and thermodynamics approach? Verlinde's ideas
Some researchers working on it are trying to get a deeper and fundamental understanding, where gravity comes from. These researchers have been trying to combine gravity and quantum mechanics and have found that they are more related to thermodynamics and entropy.
In 1998, there was the discovery that the universe is expanding at an accelerated pace. However, interestingly the acceleration seems to be increasing with time and not reducing as was expected by gravity. The explanation which came was that there’s some energy which is dark and doesn’t interact and is repulsive and pushing everything away. So, dark energy pushing things away, accelerating it, would create a horizon beyond which we won't be able to observe because at this horizon the push would create so much acceleration that things would be going apart by the speed of light. In this way, the universe with the dark energy acts like a black hole (the universe’s horizon acts as an event horizon). This is where a connection could be made between the universe and the black holes.
In the blackholes, there was the problem with respect to entropy as John Wheeler had asked (he also coined the term black hole). Suppose an object of temperature T falls into a black hole. 2nd law says that the entropy of the black hole should increase. However, having passed the event horizon we may not be able to see it and the information seems to be lost. What has now been understood is that the entropy of black hole in the area of its mouth, thanks to Birkenstein and Hawking. When blackhole takes in such an object, its area increases, thereby increasing its entropy. Thus, black holes have temperature, entropy and emit radiation as well. The thermodynamic law is similar to black law physics.
So, the way black holes have entropy and temperature, the universe will also have those properties related to the horizon of the universe. Since the horizon arose due to dark energy, the entropy and temperature of the universe would be the result of dark energy, which therefore needs to better understanding.
The researchers having this view propose that using the better understanding of gravity, what generates additional gravitational pull, one may reproduce same models and predictions using the simulations as is done by dark matter proponents (and discussed above). This is essentially so because the dark matter theorists also put matter which essentially produces gravity only.
Upon looking back on the graph where there’s a departure between the expected and observed rotational velocities of objects in the galaxy, it is found that the departure happens at a critical value, the value which depends on Hubble constant (the rate of expansion of the universe). This opens up a possible connection between the anomaly and the rate of expansion of the universe caused by the dark energy.
The mathematics used by researchers show that in the neighbourhood of galaxies, the expelled dark energy tries to push back again and the interaction between dark energy and the matter would create the additional force required to hold the galaxies together and not fly off. However, to be able to explain the structures in the universe and other things as the dark particles do, there is a requirement to develop this theory further. However, the essential thing is that there’s no need to discover new particles to get the extra pull but an only better understanding of gravity.
References (short):
[1] - Wiki
[2] - Earthsky
[5] - Caltech
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