what are the formats supported in AVAudioRecorder for recording sound?

As per apple docs Apple Core Audio Format Specification 1.0 it should now support mp3 although I haven't tested it, this is the current enumeration they support:

enum {
    kAudioFormatLinearPCM      = 'lpcm',
    kAudioFormatAppleIMA4      = 'ima4',
    kAudioFormatMPEG4AAC       = 'aac ',
    kAudioFormatMACE3          = 'MAC3',
    kAudioFormatMACE6          = 'MAC6',
    kAudioFormatULaw           = 'ulaw',
    kAudioFormatALaw           = 'alaw',
    kAudioFormatMPEGLayer1     = '.mp1',
    kAudioFormatMPEGLayer2     = '.mp2',
    kAudioFormatMPEGLayer3     = '.mp3',
    kAudioFormatAppleLossless  = 'alac'
};

List above just

currently defined values for the mFormatID field

not supported for recording.

There are tested with AVAudioRecorder formats (with sample rates):

"MPEG4AAC (8000, 11025, 22050, 32000, 44100, 48000)",
"AppleLossless (8000, 11025, 22050, 32000, 44100, 48000)",
"MPEG4AAC_HE (32000, 44100, 48000)",
"MPEG4AAC_LD (22050, 32000, 44100, 48000)",
"MPEG4AAC_ELD (22050, 32000, 44100, 48000)",
"MPEG4AAC_ELD_SBR (22050, 32000, 44100, 48000)",
"MPEG4AAC_ELD_V2 (22050, 32000, 44100, 48000)"

Example:

[[AVAudioRecorder alloc] initWithURL:outputFileURL
                            settings:@{
                                       AVFormatIDKey : @(kAudioFormatMPEG4AAC),
                                       AVSampleRateKey : @(44100.0),
                                       AVNumberOfChannelsKey : @(2)
                                       }
                               error:&error];

also Supported Audio file formats