An online word counter puts your SOP at about 650 words, which I think is a good length. I aimed for 750 words (1.5 pages single spaced) when I wrote mine. I also disagree with adamyos's suggestion to not specifically name Profs X and Y. However, they do make a good point that your current paragraph does sound like you are restricting yourself to these two professors only. I would modify that paragraph to make it sound like those two professors are two potential people you could work with, not the only two people you want to work with.
Also keep in mind that some schools' writing centers will not help you correct your spelling and grammar, but instead, will only be able to help with things like brainstorming ideas, forming arguments and outlining a draft. But of course you would know your own writing center best. Just saying this because if you have not yet gone, be prepared for a different level of "service" than you expect.
I agree with adamyos's suggestion to remove unnecessary words. Usually this means you can remove adjectives such as "invaluable". And, there are some cases where, in my opinion, you are not using the appropriate word. The writing center may point these out, but they also may not. After all, what you are writing is technically and grammatically correct, however, it is not strong writing and not the "norm" in physics writing.
A few other examples of things to remove/modify:
i. "postulating dark energy" ---> maybe "invoking" or "requiring" is better than "postulating"; postulating has the correct meaning, but I just feel this is a use of a "fancy" word when a more simple word would suffice. But it could just be me.
ii. "conduct theoretical research in these models" ---> here, I feel like too many words are used to say a simple idea. Since this is just the introduction, you might just say something like "I am interested in determining whether these models can explain ...." ; then, later on you should give examples of how you would like to do this
iii. In paragraph 2, you write about how you want to become a professor but then you focus all on teaching. Most schools will not consider teaching a primary function of a professor. I think you should shorten this section and move it to a later section (focus on research first, and address this near the end where most people write about their future career plans / why they want to go to grad school).
iv. "My research experience consists of ... " ---> You can say it more simply: "I worked with Professor David Mugglin ...."
v. "From consider this, ...." ---> Just remove this, get to the point: "I learned to manipulate ...."
vi. "Prior to my research, I downplayed the importance of numerical methods in theory." ---> Remove this. I don't see how this content can help your case. Modify the sentence that follows to use say that this experience taught you to use more computational methods!
vii. I don't think you ever defined DGP. In addition, I would recommend you just do not use abbreviations at all, except for maybe CCPP if that's what the CCPP refers to itself. In most cases, you use the long form once and define the abbreviation but then you only use the abbreviated form one other time. It's not worth defining an abbreviation if you aren't going to use it repeatedly---just spell it out the long way both times. Abbreviations like DGP, or PDP or KAM might mean a lot to you and others who study what you study, but remember that the admissions committee will consists of all sorts of physics professors, and these abbreviations will not come naturally. (Also, you define GR at the very end but do not even use it again!)
viii. "Professor Scoccimarro's research is ... of great interests ...." ---> remove "great"
I think the first thing you should do to strengthen your SOP is to remove unnecessary words and make your writing a little tighter. Maybe one reason why adamyos felt your SOP is short (even though the word count isn't that short) was that despite being wordy, it didn't have a lot of content. I hope that was not too harsh---I am trying to be honest and helpful. Once you edit out extra words, you would then know how much space you have left to add more content. Here are some ideas on additional content to include (i.e. what questions I had for you when I read your SOP draft):
1. Why do you want a PhD? That is, what are your specific academic and career goals that you will achieve with a PhD?
2. How will a PhD in Cosmology and Particle Physics help you achieve the above goals?
3. How does CCPP specifically help you achieve these goals? You said a few things and gave example faculty, which is good. But I think you can make a stronger case.
4. What are the outcomes of your undergraduate research projects? You say what you did and who you worked with. But what happened in the end? Did you present the work? Did you publish? Did you write a report? How were your results used? Did others in the group follow up on your research? Did you create a new method or tool to help the group? Tell us about your impact!