How will the topic of my Master's thesis affect my PhD? Main question: 

Will the admission committee care about specific research topics or do they only care if I can/cannot do research irrespective of the topic? Will an off-topic thesis be looked as sign of inconsistent interests? 

It would be great if answers focus mainly on US schools, however answers for european schools are also welcome.

Related questions : Will an off-topic Masters hurt my chances of a PhD place? . My question is very very similar to this but with two main differences - 1) The author of that question had no option and was at liberty give this as a reason if it was brought up in the admission proces. But I cannot do this and thus, will it be looked at as sign of irregular intersts? 2) I want answers for US and not UK

Why I ask this question:

I am a Physics Master's student from India and will be starting my Master's thesis around 3-4 months from now.

Until this point (and even right now) my projects were in Cosmology-Dark Matter. I enjoyed them and I want to apply for PhD in Theoretical Cosmology/HEP/AstroPhysics groups. This decision is based on my chances to get a PhD position in a good place and how much I liked the topics.

I always wanted to study/work on "pure theoretical" topics such as Quantum Gravity. But after I started my Bachelor's I realized that it is impractical to pursue these topics, at least not for PhD (lack of positions and funding - from what I heard from seniors). However, I really want to research on these topics at least once, and I know for sure it will be next to impossible once I start my PhD. That's why I want to work on this for my Master's Thesis. I have read an interesting paper on semi-classical gravity and have even approached a professor in my department who is willing to guide me on a project related to the paper. However, I am not sure if this is a sensible choice. How will such a thesis affect my PhD application? I do not even know if I'll produce any new results but I really want to try this but at the same time I am worried if this would reduce my chances of getting PhD in a good place i.e will a thesis on Cosmology give a higher boost than this? My previous research projects on Cosmology were quite extensive, with one first author paper, so I can show that I have some experience in the topic. But I do not know if the admission committee compares specific research topics or do they only care if I can/cannot do research irrespective of the field. 

Thanks in advance!
In the US it should matter very little. Having a closely related area in mind might be an advantage, but changing might not be much of any disadvantage, within limits. In fact, having too narrow an interest might make it difficult to find an advisor in the US. Some flexibility is suggested.

Note that most beginning doctoral students in the US don't come with an MS or with much research experience. The first task is to pass qualifying examinations and some coursework is provided for that. Along the way you choose an advisor and a topic. But the topic has to be mutually agreed on. 

It isn't quite correct to say that all they care about is your ability to do research. But it is fairly correct provided that the fields you previously studied and the new one is fairly close. But expect to have to do some background work at least. 

And, even having a wildly different MS topic might not hurt your chances for admission. It would just add to the time to completion as it would for someone entering with a BS instead of an MS. But a lot of things will be looked at in any application: courses taken, grades, test results, letters of recommendation...