Eleven days your grass should be a bit more lush than what I see. 11 days it should be needing its virgin mow. This lawn needs another week. What has the weather been like, where is it you live?
Yes, those 'bare' spots will fill in. If not, you'll be able to tell in a month and be able to over seed. Use the same seed. Did you just water this lawn before this picture? How much have you been watering to keep the germinating seed alive? This is the only time in a cool season grass lawn's life where shallow, frequent watering is critical. After the virgin mow one can start training their grass for deep roots by deep watering and allowing to dry just to the point of seeing one's footprints on the grass stay down before watering deeply again. No sooner no later.
I'd like to know how you prepared your seed bed. What type of soil have you used? Did you add anything such as fertilizer or mulch or peat moss? Is this lawn primarily in the sun with maybe a little partial sun but not shade? You will need to add fertilizer soon, but tell me what you've added first! I never use Scott's or Ortho anything with one exception but that is not pertinent here.
Is your mower capable of being raised to cut no lower than 3"? Are the blades super super sharp? Your lawn is not ready to mow for at least another week. I can see you were using a drop spreader! Cute! I like the cheapo Scott's hand spreader myself. Or a rotary spreader that is far more controllable and being able to make many passes is essential. Don't use a drop spreader for fertilizer either. Or you'll get a pattern apparent.
The amount of growth you've got is normal for about a week's growth. But that is attributable to many different elements. Weather for one. Sun is another. Soil bed preparation is a big one; did you use a roller to compact the soil for good soil/seed contact? That should have been used at least 2 if not 3 times over the entire bed in preparation. When I seed I scratch up the surface with a soft rake and then seed. The more passes the better always in a different direction, pattern. Just like mowing. After seeding I use the roller one more time. If you haven't done this, this would account for the sparse germination.
Not to worry. This can be fixed. But not now. Give more information, get your mower blades sharpened (you should have an extra set handy anyway as well as air and gas filters), find non-ethanol gasoline, check your oil, do not over fill. Tip your mower the opposite direction of the oil tank to get at the blades. Don't touch the blades unless that spark plug is detached...!
Send a picture in one week or before that. We'll get what you've got growing thick and able to withstand a lawn mower. And please bag your clippings! Explain later or there are other answers on how to deal with this beast called a lawn!
Peat moss shouldn't be used for 2 reasons. Makes the soil more acidic (lower pH) and lawns love pH verging on alkaline or at least neutral. The other reason is peat moss is a finite resource that is critical for the ecosystems it inhabits. We have to stop using this stuff. Please get a soil test or at the very least a pH test.
I am glad you tilled in compost and that you actually rolled your lawn. Kudos! Reel mowers are wonderful but does yours have a bag to collect clippings? I always bagged clippings. Always. There is not a mower alive that can chop clippings up small enough to decompose on the lawn. Great stuff for compost and smothering weeds, feeding plant beds. But not lawns.
My biggest problem out of the information you just gave was killing grubs. I know this stuff quite well. Grubs are controlled normally by soil organisms, birds, moles, voles...they are never a big deal unless one applies pesticide for grubs which also kills all the controlling soil life that normally keeps grubs in control, poisons the moles, voles and birds and the next year you are certainly set up to have a massive grub population that will kill your grass. You do not want to kill your soil organisms just because of grubs. Stop using any pesticides. You might just have to repeat all this work next year but if you don't have a 'live' soil full of micro and macro soil organisms you will always have to kill your soil just for grubs? Sigh. This is akin to building a healthy immune system in animals. I hate to say this but you will almost certainly have a major grub problem next year. If this doesn't happen it will be a major miracle! But let's just say your lawn is decimated next year by larvae who eat the roots and crowns of your grass crop. I would not do seed again. I would purchase sod after removing the crop you now have. A sod cutter. Use this sod for building up plant beds, making new plant beds or smothering a section of your property full of weeds. Just turn the sod upside down and top with 2" of topsoil.
Installing sod will negate any weeds, you will have instant lawn (after a week) and hopefully your soil will be full of life again with which to control grubs. Are these Cranefly grubs? Whoever told you to apply pesticide for grubs needs to be thwacked upside the head! Let me know. Was it Lowes or Home Depot? They might have to purchase your new sod. I am serious. Definitely get that 'organic' fertilizer I cited and purchase Mycorrhizae fungus if not added in the fertilizer. This will help build your soil life back up. Decomposed organic matter will also facilitate life coming back. We can talk about that as well, later.
Do not worry about stones. Soil, after all is an accumulation of tinier stones. I only remove stones that are fist sized. No problem. Applying grub killer (please let me know what that product and formulation was) was a huge mistake. I am fairly sure that pesticide you used for grubs was not specific and it killed all of the life in your soil. I've seen this happen too many times. Grubs will kill a lawn within a month right down to bare soil. Healthy soil will always be able to take care of grubs. I am not a fan of Ortho or Scotts!