Authenticated encryption without padding I want to encrypt data and protect its integrity and confidentiality. However, I cannot increase the length of the data.

Are there any cipher modes of operation which provide confidentiality and integrity protection without increasing the length of the ciphertext?
If the data to protect has no built-in redundancy at all (for example, has each of its bit determined by fair coin toss), there is no way to protect integrity without expansion (Proof sketch: there are as many distinct possibilities for valid plaintext as there as possibilities for valid enciphered-and-protected data, hence every possible enciphered-and-protected data must be acceptable by the verify-and-decipher operation).

If the data to protect has some built-in redundant part (like, a fixed header of 16 octets), then we can remove it, use normal authenticated encryption, and restore the redundancy after the verify-and-decipher step. Variant: if we are certain that some lossless compression scheme will shrink the data enough (e.g. the plaintext is 2227 symbols restricted to 246 possible values, each coded as an octet, allowing to encode that plaintext as 2211 arbitrary octets by mere conversion from base 246 to base 256, making room for 16 octets), we can compress the data before applying the authenticated encryption, and expand after the verify-and-decipher step.

If the data to protect has some built-in redundancy that we have no way to turn into compressibility but can nevertheless characterize (like, plaintext is the result of applying Bzip2 compression to about one page of sensible English text), we have the option to use Format preserving encryption (that is, in the context, a block cipher with the block size equal to the data size, that implements a key-dependent, random-like, reversible transformation of the whole data). Any alteration of the ciphertext (other than replacing it with a known-valid ciphertext) will make the whole deciphered plaintext random, and we can reliably detect that (with a Bzip2 decompression algorithm hardened against rogue input, followed by even the most basic validation that the output contains a large-enough proportion of English words). Notice however that we loose something on confidentiality: contrary to the previous solution, the same plaintext will always be enciphered to the same ciphertext, which sometime is unacceptable, and does not match the modern goals of a cipher.