In the most basic terms, you have a mismatch of what you see on screen, and what your printer is capable of reproducing. There is a lot of good information in LarryHN's post, but Adobe RGB does not produce muddier colors. If anything, it will produce richer colors since it's a much wider color space than sRGB.
This is going to be lengthy, and I hope not too difficult to grasp. Color management is complicated. Until it clicks (and then it finally seems easy), it's like trying to grasp quantum mechanics when you're still in 1st grade.
Main point first. All inkjet printers use at minimum, CMYK inks. Yours uses those four colors. Other models use that and extra, richer colors to boost the color range beyond what CMYK alone can reproduce. Usually a rich red and a rich blue since CMYK alone cannot even come close to the saturated blues and reds of RGB. Those richer colors also help boost greens and reds past CMYK by combining that rich blue with yellow instead cyan, and the rich red with yellow instead of magenta.
Problem. Virtually all inkjet printers are RGB devices and work best with RGB images, despite the fact they use CMYK inks. There is no such thing of course as RGB inks. RGB is color described as additive light. CMYK is subtractive light and is the closest you can come to RGB using dyes or pigments.
What all inkjet printer manufacturers do is set up the hardware to do its own conversion of RGB data to CMYK. They do that simply because that's what the vast majority of home and office users print; RGB, not CMYK data. The conversion tables in the printer automatically divide out the RGB data to the richer inks (if your printer has them) to give you a closer match to the screen.
Second main point regarding a printer is the paper. This is true from professional printing companies on down. Paper type and the ink used changes color. It's an unavoidable fact of the media. Glossy papers will produce the richest, most colorful prints. Matte papers will have duller color with the same inks, from the same printer, from the same image. Uncoated stock is the worst. If you like dull, uncoated stock is for you.
The point here is that CMYK images throw RGB printers for a loop. The less expensive a unit is, the more likely it will fail to print anything you expect from a CMYK image. Essentially, the cyan channel is interpreted as red, magenta as green, and yellow as blue. The black data is ignored. Results stink. Also, the default, generic CMYK profile Apple has included with the Mac OS for years is the flattest, grayest, ugliest CMYK profile in the history of computers. Never use it.
LarryHN is right on the button with monitor calibration. Two points. One, all monitors drift. The provided profile for a brand new monitor is reasonably accurate for about a month, then it's useless. Two, the built in monitor calibration function in the System Preferences is equally useless. When you go to create a new profile, the software can only presume you are always starting with a monitor that is displaying a perfect 6500K white point at a perfect predefined brightness level. So when you move the sliders around, the software at least has some idea what the monitor is doing, even though it can't see anything. Since all monitors drift (usually to the pink side for LCD and LED), the brightness level decreases as the panel ages, and the colorants themselves weaken with age, it is literally impossible to create an accurate profile visually. Only you can tell what the monitor looks like, the OS has no idea what's actually happening.
If color is important to you, invest in a hardware/software profiling package for your monitor. It's the cheapest of the various profiling options available, and one of the most important. That's because no matter what profile you use as your working RGB or CMYK color space, it's the monitor profile that ColorSync tries to reproduce at the printer. I highly recommend the X-Rite i1 Display Pro. It can be found online for about $250. Don't go with the cheaper ColorMunki Display. It looks pretty much the same, but isn't as accurate, and reads the monitor at half the speed. Completely ignore the ColorMunki Smile. It's just a repackaged i1 Display 2, which is a much older, outdated design that doesn't even work right with newer wide gamut monitors.
If you purchase this, use the photographer's default settings of a 5500K white point and a 2.2 gamma. Do not use the 6500K white point that is the default on both the Mac and Windows. Almost nowhere in the world does anyone see a white point and gray ramp that blue. The worldwide average and most commonly measured white point color temperature is 5300K. Why anyone ever decided 6500K should be the default is beyond me, and anyone else who knows anything about color. Also the bluer you get (higher Kelvin numbers), the further away from paper white you get, making it only all the more difficult to match your output to the screen. Personally, I use 5000K and a 1.8 gamma for both CMYK and RGB work. But then, I do prepress CMYK all day, and those are the default settings in the printing industry. The settings also work very well for RGB since you're still working with paper white, whether it's off your own printer, or photo prints from a place such as Snapfish. Even photo paper white will not come anywhere near 6500K.
Okay, we've tackled the printer (not completely) and the monitor. So back to the printer. You have the basic limitation of CMYK as your inks, no matter what printer you're using. If the cyan of your RGB file is really bright and saturated on screen, don't ever expect to see it on paper. The cyan colorant of the printer is locked to whatever it can produce on the paper used. It cannot be forced to print brighter or richer. Same with the rest of the inks. Think of it like painting a room. If you bought a bright orange paint, and then decided you want it even brighter with even more color saturation, you have to go out and purchase another can of paint. The one you have can't simply have it's color saturation turned up by wishing. It is what it is and is stuck at that hue and saturation. So apply this across the board in regards to what you see on the screen as opposed to your printed output. There are a lot of hues and saturated colors you will never, ever reproduce on paper. It's just a fact.
So, what do you do:
1) Properly profile your monitor. And by proper, I mean a hardware/software solution. With a device like the i1 Display Pro, you aren't just creating a profile, you're creating one that is based on what the monitor is actually doing since the hardware is measuring that output directly from the display. The OS and ColorSync are no longer guessing what the monitor looks like. It knows what it looks like.
2) Use the correct paper profile for the paper being used. Download them from HP if they have them. Note that they will always only provide profiles for their own papers. So you have to use HP papers to get the correct results. Just changing the type of paper changes the color. Two soft gloss papers from two different companies that look the same will produce different color from the same printer using the same printer profile. Profiles are very specific to both the paper and printer used to create the profile. You can't mix and match them and expect it to work.
3) Always apply ColorSync only ONCE! That is, if the app has a way to apply your profiles for output to the printer, and then the print driver also gives you an option to set the same thing, only use one or the other, otherwise you are applying the ColorSync conversions twice and the results will be junk. You have to set one or the other to "No color management", or whatever term they use to bypass the function.
