Any theory proposed to explain dark matter, dark energy, the evolution of the early Universe, and other unsolved problems must correctly reproduce existing observational and experimental data, including the properties of gravitational waves. Therefore, we discuss the main properties of gravitational waves such as the propagation velocity, characteristic amplitudes, polarizations, and other features predicted by extended theories of gravity: scalar-tensor gravity, including the Brans—Dicke models; Horndeski theories; $f(R)$-gravity; theories with a massive graviton; modified Newtonian dynamics; quantum theories of gravity, including loop quantum gravity and string theory IIB; Horava—Lifshitz theory; higher-dimensional theories, including the general case of $D$-dimensional spacetime and Kaluza—Klein theory; and non-Riemannian geometry, including both the general case of metric affine gravity and various versions of teleparallel gravity $f(T)$ and $f(Q)$, as well as the extended cases $f(T, B)$ and $f(T, T_{\rm G})$. With increasing experimental accuracy, the discussed characteristics of gravitational waves will be discovered, helping in the selection of gravity theories.

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Keywords: gravitational waves, general relativity, Brans—Dicke theory, scalar-tensor gravity, Horndeski theory, teleparallel gravity, metric affine gravity, gravitational-wave astronomy PACS: 04.30.−w, 04.50.−h, 04.60.−m (all) DOI: 10.3367/UFNe.2026.05.040140 URL: https://ufn.ru/en/articles/2026/7/a/ Citation: Alexeyev S O, Kuzmin S K, Pluzshnikov E A, Stamov R A, Chekh I I "Gravitational waves in extended gravity theories" Phys. Usp. 69 (7) (2026) Received: 14th, October 2025, revised: 28th, April 2026, accepted: 13th, May 2026 Оригинал: Алексеев С О, Кузьмин С К, Плужников Е А, Стамов Р А, Чех И И «Гравитационные волны в расширенных теориях гравитации» УФН 196 677–706 (2026); DOI: 10.3367/UFNr.2026.05.040140