positioning system satellites. Nature Commun 8(1):1195. https://doi.org/10.1038/s41467-017-01440-4. arXiv:1704.06844 [hep-ph]

Roberts BM et al (2020) Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks. New J Phys 22(9):093010. https://doi.org/10.1088/1367-2630/abaace. arXiv:1907.02661 [astro-ph.CO]

Rocha G, Trotta R, Martins C, Melchiorri A, Avelino PP, Bean R, Viana P (2004) Measuring $\alpha$ in the early universe: CMB polarisation, reionisation and the Fisher matrix analysis. Mon Not R Astron Soc 352:20–38. https://doi.org/10.1111/j.1365-2966.2004.07832.x. arxiv:astro-ph/0309211

Rohlf JW (1994) Modern physics from $\alpha$ to $Z^0$. Wiley, New York

Rosenband T, Hume DB, Schmidt PO, Chou CW, Brusch A, Lorini L, Oskay WH, Drullinger RE, Fortier TM, Stalnaker JE, Diddams SA, Swann WC, Newbury NR, Itano WM, Wineland DJ, Bergquist JC (2008) Frequency ratio of $Al^+$ and $Hg^+$ single-ion optical clocks; metrology at the 17th decimal place. Science 319:1808–1812. https://doi.org/10.1126/science.1154622

Ross AJ, Samushia L, Howlett C, Percival WJ, Burden A, Manera M (2015) The clustering of the SDSS DR7 main galaxy sample-I. A 4 per cent distance measure at $z = 0.15$. Mon Not R Astron Soc 449(1):835–847. https://doi.org/10.1093/mnras/stv154. arXiv:1409.3242 [astro-ph.CO]

Rothman T, Matzner R (1982) Scale-covariant gravitation and primordial nucleosynthesis. Astrophys J 257:450. https://doi.org/10.1086/160003

Rousselle O, Cladé P, Guellati-Khelifa S, Guérout R, Reynaud S (2022) Analysis of the timing of freely falling antihydrogen. New J Phys 24(3):033045. https://doi.org/10.1088/1367-2630/ac5b57

Rozental IL (1988) Big Bang, big bounce: how particles and fields drive cosmic evolution. Springer, Berlin

Rubakov VA, Shaposhnikov ME (1989) A comment on dynamical coupling constants and the anthropic principle. Mod Phys Lett A 4:107–109. https://doi.org/10.1142/S0217732389000149

Ruchika RH, Roy Choudhury S, Rentala V (2024) A gravitational constant transition within cepheids as supernovae calibrators can solve the Hubble tension. JCAP 06:056. https://doi.org/10.1088/1475-7516/2024/06/056. arXiv:2306.05450 [astro-ph.CO]

Safronova MS (2019) The search for variation of fundamental constants with clocks. Ann Phys 531(5):1800364. https://doi.org/10.1002/andp.201800364

Safronova MS, Budker D, DeMille D, Kimball D, Derevianko A, Clark CW (2018a) Search for new physics with atoms and molecules. Rev Mod Phys 90(2):025008. https://doi.org/10.1103/RevModPhys.90.025008. arXiv:1710.01833 [physics.atom-ph]

Safronova MS, Porsev SG, Kozlov MG, Thielking J, Okhapkin MV, Głowacki P, Meier DM, Peik E (2018b) Nuclear charge radii of $^{229}$Th from isotope and isomer shifts. Phys Rev Lett 121(21):213001. https://doi.org/10.1103/PhysRevLett.121.213001. arXiv:1806.03525 [physics.atom-ph]

Safronova MS, Porsev SG, Sanner C, Ye J (2018c) Two clock transitions in neutral Yb for the highest sensitivity to variations of the fine-structure constant. Phys Rev Lett 120(17):173001. https://doi.org/10.1103/PhysRevLett.120.173001. arXiv:1801.06239 [physics.atom-ph]

Sahni V, Shtanov Y (2014) Can a variable gravitational constant resolve the faint young Sun paradox? Int J Mod Phys D 23(12):1442018. https://doi.org/10.1142/S0218271814420188. arXiv:1405.4369 [astro-ph.SR]

Sakr Z, Sapone D (2022) Can varying the gravitational constant alleviate the tensions? JCAP 03(03):034. https://doi.org/10.1088/1475-7516/2022/03/034. arXiv:2112.14173 [astro-ph.CO]

Salomon C, Dimarcq N, Abgrall M, Clairon A, Laurent P, Lemonde P, Santarelli G, Uhrich P, Bernier LG, Busca G, Jornod A, Thomann P, Samain E, Wolf P, Gonzalez F, Guillemot P, Leon S, Nouel F, Sirmain C, Feltham S (2001) Cold atoms in space and atomic clocks: ACES. C R Acad Sci 2:1313–1330. https://doi.org/10.1016/S1296-2147(01)01274-4

Salumbides EJ, Niu ML, Bagdonaite J, de Oliveira N, Joyeux D, Nahon L, Ubachs W (2012) The CO A-X system for constraining cosmological drift of the proton–electron mass ratio. Phys Rev A 86:022510. https://doi.org/10.1103/PhysRevA.86.022510. arXiv:1208.4715 [physics.atom-ph]

Salumbides EJ, Bagdonaite J, Abgrall H, Roueff E, Ubachs W (2015) H2 Lyman and Werner band lines and their sensitivity for a variation of the proton–electron mass ratio in the gravitational potential of white dwarfs. Mon Not R Astron Soc 450(2):1237–1245. https://doi.org/10.1093/mnras/stv656

Sandage A (1962) The change of redshift and apparent luminosity of galaxies due to the deceleration of selected expanding universes. Astrophys J 136:319. https://doi.org/10.1086/147385
Sandora M, Airapetian V, Barnes L, Lewis GF, Pérez-Rodríguez I (2022) Multiverse predictions for habitability: element abundances. Universe 8(12):651. https://doi.org/10.3390/universe8120651

Sandvik HB, Barrow JD, Magueijo J (2002) A simple cosmology with a varying fine structure constant. Phys Rev Lett 88:031302. https://doi.org/10.1103/PhysRevLett.88.031302. arXiv:astro-ph/0107512

Santamaria L, Di Sarno V, Ricciardi I, Mosca S, De Rosa M, Santambrogio G, Maddaloni P, De Natale P (2014) Assessing the time constancy of the proton-to-electron mass ratio by precision ro-vibrational spectroscopy of a cold molecular beam. J Mol Spectrosc 300:116–123. https://doi.org/10.1016/j.jms.2014.03.013. (spectroscopic Tests of Fundamental Physics)

Santiago DI, Kalligas D, Wagoner RV (1997) Nucleosynthesis constraints on scalar-tensor theories of gravity. Phys Rev D 56:7627–7637. https://doi.org/10.1103/PhysRevD.56.7627

Sasaki S (1996) A new method to estimate cosmological parameters using the baryon fraction of clusters of galaxies. Publ Astron Soc Japan 48:L119–L122. https://doi.org/10.1093/pasj/48.6.L119. arXiv:astro-ph/9611033 [astro-ph]

Savalle E, Guerlin C, Delva P, Meynadier F, Le Poncin-Lafitte C, Wolf P (2019a) Gravitational redshift test with the future ACES mission. Class Quant Grav 36(24):245004. https://doi.org/10.1088/1361-6382/ab4f25. arXiv:1907.12320 [astro-ph.IM]

Savalle E, Roberts BM, Frank F, Pottie PE, McAllister BT, Dailey C, Derevianko A, Wolf P (2019b) Novel approaches to dark-matter detection using space-time separated clocks. arXiv e-prints arXiv:1902.07192 [gr-qc]

Savedoff M (1956) Physical constants in extra-galactic nebulae. Nature 178:688. https://doi.org/10.1038/1786888b0

Scherer H, Camarota B (2012) Quantum metrology triangle experiments: a status review. Measur Sci Tech 23:124010. https://doi.org/10.1088/0957-0233/23/12/124010. arXiv:1204.6500 [cond-mat.mes-hall]

Schiller S, Korobov V (2005) Tests of time independence of the electron and nuclear masses with ultracold molecules. Phys Rev A 71:032505. https://doi.org/10.1103/PhysRevA.71.032505

Schiller S, Tino GM, Gill P, Salomon C et al (2009) Einstein gravity explorer—a medium-class fundamental physics mission. Exp Astron 23:573. https://doi.org/10.1007/s10686-008-9126-5

Schiller S, Bakalov D, Korobov V (2014) Simplest molecules as candidates for precise optical clocks. Phys Rev Lett 113:023004. https://doi.org/10.1103/PhysRevLett.113.023004

Schiller S et al (2006) Optical clocks in space. ESA Spec Publ 621:114 arXiv:gr-qc/0608081

Schimd C, Uzan JP, Riazuelo A (2005) Weak lensing in scalar-tensor theories of gravity. Phys Rev D 71:083512. https://doi.org/10.1103/PhysRevD.71.083512. arXiv:astro-ph/0412120

Schkolnik V et al (2023) Optical atomic clock aboard an Earth-orbiting space station (OACESS): enhancing searches for physics beyond the standard model in space. Quantum Sci Technol 8(1):014003. https://doi.org/10.1088/2058-9565/ac9f2b. arXiv:2204.09611 [physics.atom-ph]

Schlamminger S, Choi KY, Wagner TA, Gundlach JH, Adelberger EG (2008) Test of the equivalence principle using a rotating torsion balance. Phys Rev Lett 100:041101. https://doi.org/10.1103/PhysRevLett.100.041101. arXiv:0712.0607 [gr-qc]

Schlattl H, Heger A, Oberhummer H, Rauscher T, Csoto A (2003) Sensitivity of the C and O production on the 3* rate. Astrophys Space Sci 291:27 arXiv:astro-ph/0307528

Schlippert D, Hartwig J, Albers H, Richardson LL, Schubert C, Roura A, Schleich WP, Ertmer W, Rasel EM (2014) Quantum test of the universality of free fall. Phys Rev Lett 112:203002. https://doi.org/10.1103/PhysRevLett.112.203002

Schmidt TM, Bouchy F (2024) Characterization of the ESPRESSO line-spread function and improvement of the wavelength calibration accuracy. Mon Not R Astron Soc 530(1):1252–1273. https://doi.org/10.1093/mnras/stae920. arXiv:2404.05283 [astro-ph.IM]

Schmidt TM et al (2021) Fundamental physics with ESPRESSO: towards an accurate wavelength calibration for a precision test of the fine-structure constant. Astron Astrophys 646:A144. https://doi.org/10.1051/0004-6361/202039345. arXiv:2011.13963 [astro-ph.IM]

Schöneberg N, Vacher L (2025) The mass effect-variations of the electron mass and their impact on cosmology. JCAP 03:004. https://doi.org/10.1088/1475-7516/2025/03/004. arXiv:2407.16845 [astro-ph.CO]

Schöneberg N, Franco Abellán G, Pérez Sánchez A, Witte SJ, Poulin V, Lesgourgues J (2022) The H0 olympics: a fair ranking of proposed models. Phys Rept 984:1–55. https://doi.org/10.1016/j.physrep.2022.07.001. arXiv:2107.10291 [astro-ph.CO]
Schöneberg N, Vacher L, Dias J, Carvalho M, Martins C (2023) News from the swampland—constraining string theory with astrophysics and cosmology. JCAP 10:039. https://doi.org/10.1088/1475-7516/2023/10/039. arXiv:2307.15060 [astro-ph.CO]

Schwarz R, Dörscher S, Al-Masoudi A, Benkler E, Legero T, Sterr U, Weyers S, Rahm J, Lipphardt B, Lisdat C (2020) Long term measurement of the $^{87}$Sr clock frequency at the limit of primary Cs clocks. Phys Rev Res 2(3):033242. https://doi.org/10.1103/PhysRevResearch.2.033242. arXiv:2005.07408 [physics.atom-ph]

Scoccola CG, Landau SJ, Vucetich H (2008) WMAP-5yr constraints on time variation of $\alpha$ and $m_e$ in a detailed recombination scenario. Phys Lett B 669:212 arXiv:0809.5028 [astro-ph]

Scoccola CG, Landau SJ, Vucetich H (2009) WMAP 5-year constraints on time variation of $\alpha$ and $m_e$. Mem Soc Astron Ital 80:814 arXiv:0910.1083 [astro-ph.CO]

Scolnic D et al (2022) The pantheon+ analysis: the full data set and light-curve release. Astrophys J 938(2):113. https://doi.org/10.3847/1538-4357/ac8b7a. arXiv:2112.03863 [astro-ph.CO]

Scolnic DM et al (2018) The complete light-curve sample of spectroscopically confirmed SNe Ia from Pan-STARRS1 and cosmological constraints from the combined pantheon sample. Astrophys J 859(2):101. https://doi.org/10.3847/1538-4357/aab9bb. arXiv:1710.00845 [astro-ph.CO]

Seager S, Savelov DD, Scott D (1999) A new calculation of the recombination epoch. Astrophys J Lett 523:L1. https://doi.org/10.1086/312250. arXiv:astro-ph/9909275

Sekiguchi T, Takahashi T (2021) Early recombination as a solution to the $H_0$ tension. Phys Rev D 103(8):083507. https://doi.org/10.1103/PhysRevD.103.083507. arXiv:2007.03381 [astro-ph.CO]

Serna A, Alimi JM (1996) Scalar-tensor cosmological models. Phys Rev D 53:3074. https://doi.org/10.1103/PhysRevD.53.3074

Serot BD, Walecka JD (1997) Recent progress in quantum hadrodynamics. Int J Mod Phys E 6:515. https://doi.org/10.1142/S0218301397000299

Seto O, Toda Y (2024) DESI constraints on the varying electron mass model and axionlike early dark energy. Phys Rev D 110(8):083501. https://doi.org/10.1103/PhysRevD.110.083501. arXiv:2405.11869 [astro-ph.CO]

Seto O, Takahashi T, Toda Y (2023) Variation of the fine structure constant in light of recent helium abundance measurement. Phys Rev D 108(2):023525. https://doi.org/10.1103/PhysRevD.108.023525. arXiv:2305.16624 [astro-ph.CO]

Shapiro II (1990) Solar system tests of general relativity: recent results and present plans. In: Ashby N, Bartlett DF, Wyss W (eds) General relativity and gravitation. Cambridge University Press, Cambridge, pp 313–330

Shapiro II, Smith WB, Ash MB (1971) Gravitational constant: experimental bound on its time variation. Phys Rev Lett 26:27. https://doi.org/10.1103/PhysRevLett.26.27

Shapiro SS, Davis JL, Lebach DE, Gregory JS (2004) Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979–1999. Phys Rev Lett 92:121101. https://doi.org/10.1103/PhysRevLett.92.121101

Shaw DJ (2007) Detecting seasonal changes in the fundamental constants. arXiv e-prints arXiv:gr-qc/0702090

Shaw DJ, Barrow JD (2005) Varying couplings in electroweak theory. Phys Rev D 71:063525. https://doi.org/10.1103/PhysRevD.71.063525. arXiv:gr-qc/0412135

Shaw DJ, Barrow JD (2006) Local experiments see cosmologically varying constants. Phys Lett B 639:596–599 arXiv:gr-qc/0512117

Shaw DJ, Barrow JD (2009) Varying constants: constraints from seasonal variations. Mem Soc Astron Ital 80:791

Shelnikov A, Butcher RJ, Chardonnet C, Amy-Klein A (2008) Stability of the proton-to-electron mass ratio. Phys Rev Lett 100:150801. https://doi.org/10.1103/PhysRevLett.100.150801. arXiv:0803.1829 [physics.atom-ph]

Sherrill N et al (2023) Analysis of atomic-clock data to constrain variations of fundamental constants. New J Phys 25(9):093012. https://doi.org/10.1088/1367-2630/aceff6. arXiv:2302.04565 [physics.atom-ph]

Slyakhter AI (1976) Direct test of the constancy of the fundamental constants using Oklo nuclear reactor. Nature 264:340. https://doi.org/10.1038/264340a0

Sievers JL et al (2013) The Atacama cosmology telescope: cosmological parameters from three seasons of data. JCAP 10:060. https://doi.org/10.1088/1475-7516/2013/10/060. arXiv:1301.0824 [astro-ph.CO]
Sigurdson K, Kurylov A, Kamionkowski M (2003) Spatial variation of the fine-structure parameter and the cosmic microwave background. Phys Rev D 68:103509. https://doi.org/10.1103/PhysRevD.68.103509. arxiv:astro-ph/0306372

Silva MF, Winther HA, Mota DF, Martins C (2014) Spatial variations of the fine-structure constant in symmetron models. Phys Rev D 89(2):024025. https://doi.org/10.1103/PhysRevD.89.024025. arXiv:1310.2152 [astro-ph.CO]

Sisterna P, Vucetich H (1990) Time variation of fundamental constants: bounds from geophysical and astronomical data. Phys Rev D 41:1034. https://doi.org/10.1103/PhysRevD.41.1034

Sloan D, Alves Batista R, Townsend Hicks M, Davies R (eds) (2020) Fine tuning in the physical universe. Cambridge University Press, Cambridge. https://doi.org/10.1017/9781108614023

Smith GL, Hoyle CD, Gundlach JH, Adelberger EG, Heckel BR, Swanson HE (2000) Short range tests of the equivalence principle. Phys Rev D 61:022001. https://doi.org/10.1103/PhysRevD.61.022001

Smith TL, Grin D, Robinson D, Qi D (2019) Probing spatial variation of the fine-structure constant using the CMB. Phys Rev D 99(4):043531. https://doi.org/10.1103/PhysRevD.99.043531. arXiv:1808.07486 [astro-ph.CO]

Smoliar M, Walker R, Morgan J (1996) Re-Os ages from group IIA, IIIA, IVA and IVB iron meteorites. Science 271:1099. https://doi.org/10.1126/science.271.5252.1099

Songaila A, Cowie LL (2014) Constraining the variation of the fine structure constant with observations of narrow quasar absorption lines. Astrophys J 793:103. https://doi.org/10.1088/0004-637X/793/2/103. arXiv:1406.3628 [astro-ph.CO]

Spite M, Spite F (2009) Li isotopes in metal-poor halo dwarfs, a more and more complicated story. In: Charbonnel C, Tosi M, Primas F, Chiappini C (eds) Light elements in the universe. IAU symposia, vol 268. Cambridge University Press, Cambridge, pp 201–210. https://doi.org/10.1017/S1743921310004138arXiv:1002.1004 [astro-ph.GA]

Srianand R, Chand H, Petitjean P, Aracil B (2004) Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars. Phys Rev Lett 92:121302. https://doi.org/10.1103/PhysRevLett.92.121302. arXiv:astro-ph/0402177

Srianand R, Chand H, Petitjean P, Aracil B (2007) Reply to the Comment by M.T. Murphy, J.K. Webb, and V.V. Flambaum. Phys Rev Lett 99:239002. https://doi.org/10.1103/PhysRevLett.99.239002. arXiv:0711.1742 [astro-ph]

Srianand R, Noterdaeme P, Ledoux C, Petitjean P (2008) First detection of CO in a high-redshift damped Lyman-α system. Astron Astrophys 482:L39–L42. https://doi.org/10.1051/0004-6361:200809727

Srianand R, Petitjean P, Chand H, Noterdaeme P, Gupta N (2009) Probing the variation of fundamental constants using QSO absorption lines. Mem Soc Astron Ital 80:842

Srianand R, Gupta N, Petitjean P, Noterdaeme P, Ledoux C (2010) Detection of 21-cm, $H_2$ and deuterium absorption at $z > 3$ along the line of sight to J1337+3152. Mon Not R Astron Soc 405:1888–1900. https://doi.org/10.1111/j.1365-2966.2010.16574.x. arXiv:1002.4620 [astro-ph.CO]

Stadnik YV (2020) New bounds on macroscopic scalar-field topological defects from non-transient signatures due to environmental dependence and spatial variations of the fundamental constants. Phys Rev D 102:115016. https://doi.org/10.1103/PhysRevD.102.115016. arXiv:2006.00185 [hep-ph]

Stadnik YV (2021) Robust laboratory limits on a cosmological spatial gradient in the electromagnetic fine-structure constant from accelerometer experiments. Phys Rev A 103(6):062807. https://doi.org/10.1103/PhysRevA.103.062807. arXiv:2010.01798 [physics.atom-ph]

Stadnik YV, Flambaum VV (2015a) Can dark matter induce cosmological evolution of the fundamental constants of Nature? Phys Rev Lett 115(20):201301. https://doi.org/10.1103/PhysRevLett.115.201301. arXiv:1503.08540 [astro-ph.CO]

Stadnik YV, Flambaum VV (2015b) Manifestations of dark matter and variations of fundamental constants in atoms and astrophysical phenomena. arXiv e-prints arXiv:1509.00966 [physics.atom-ph]

Stadnik YV, Flambaum VV (2015c) Searching for dark matter and variation of fundamental constants with laser and maser interferometry. Phys Rev Lett 114:161301. https://doi.org/10.1103/PhysRevLett.114.161301. arXiv:1412.7801 [hep-ph]

Stadnik YV, Flambaum VV (2016a) Enhanced effects of variation of the fundamental constants in laser interferometers and application to dark matter detection. Phys Rev A 93(6):063630. https://doi.org/10.1103/PhysRevA.93.063630. arXiv:1511.00447 [physics.atom-ph]
Stadnik YV, Flambaum VV (2016b) Improved limits on interactions of low-mass spin-0 dark matter from atomic clock spectroscopy. Phys Rev A 94(2):022111. https://doi.org/10.1103/PhysRevA.94.022111. arXiv:1605.04028 [physics.atom-ph]

Starkman GD, Trotta R (2006) Why anthropic reasoning cannot predict A. Phys Rev Lett 97:201301. https://doi.org/10.1103/PhysRevLett.97.201301. arxiv:astro-ph/0607227

Stefanescu P (2007) Constraints on time variation of the fine structure constant from WMAP-3yr data. New Astron 12:635 arXiv:0707.0190 [astro-ph]

Steinhardt PJ, Wesley D (2010) Exploring extra dimensions through observational tests of dark energy and varying Newton's constant. arXiv e-prints arXiv:1003.2815 [astro-ph.CO]

Steinmetz T, Wilken T, Araujo-Hauck C, Holzwarth R, Hänsch TW, Pasquini L, Manescau A, D'Odorico S, Murphy MT, Kentischer T, Schmidt W, Udem T (2008) Laser frequency combs for astronomical observations. Science 321:1335-1337. https://doi.org/10.1126/science.1161030. arXiv:0809.1663 [astro-ph]

Stoeger WR (2006) Retroduction, multiverse hypotheses and their testability. arXiv e-prints arXiv:astro-ph/0602356

Stoeger WR, Ellis GFR, Kirchner U (2004) Multiverses and cosmology: philosophical issues. arXiv e-prints arXiv:astro-ph/0407329

Stollenwerk PR, Kokish MG, de Oliveira-Filho A, Ornellas FR, Odom BC (2018) Optical pumping of TeH⁺: implications for the search for varying $m_p/m_e$. Atoms 6(3):53. https://doi.org/10.3390/atoms6030053. arXiv:1807.04248 [physics.atom-ph]

Su Y, Heckel BR, Adelberger EG, Gundlach JH, Harris M, Smith GL, Swanson HE (1994) New tests of the universality of free fall. Phys Rev D 50:3614-3636. https://doi.org/10.1103/PhysRevD.50.3614

Sun B, An J, Cao Z (2024) Constrain the time variation of the gravitational constant via the propagation of gravitational waves. Phys Lett B 848:138350. https://doi.org/10.1016/j.physletb.2023.138350. arXiv:2308.00233 [gr-qc]

Susskind L (2003) The anthropic landscape of string theory. arXiv e-prints arXiv:hep-th/0302219

Suzuki N et al (2012) The Hubble Space Telescope cluster supernova survey: V. Improving the dark energy constraints above $z > 1$ and building an early-type-hosted supernova sample. Astrophys J 746:85. https://doi.org/10.1088/0004-637X/746/1/85. arXiv:1105.3470 [astro-ph.CO]

Syme AM, McKemmish LK (2020) Computational insight into diatomic molecules as probes to measure the variation of the proton-to-electron mass ratio. Res Notes AAS 4(8):139. https://doi.org/10.3847/2515-5172/abae03. arXiv:2008.10799 [physics.atom-ph]

Syme AM, Mousley A, Cunningham M, McKemmish LK (2019) Diatomic rovibronic transitions as potential probes for proton-to-electron mass ratio across cosmological time. Austral J Chem 73(8):743-756. https://doi.org/10.1071/CH19448. arXiv:2001.06121 [physics.chem-ph]

Tahara H, Kobayashi T, Yokoyama J (2020) A new mechanism for freezing extra dimensions with higher-order curvature terms. Phys Lett B 811:135857. https://doi.org/10.1016/j.physletb.2020.135857. arXiv:2005.14481 [gr-qc]

Talmadge C, Berthias JP, Hellings RW, Standish EM (1988) Model independent constraints on possible modifications of Newtonian gravity. Phys Rev Lett 61:1159-1162. https://doi.org/10.1103/PhysRevLett.61.1159

Tamm C, Huntemann N, Lipphardt B, Gerginov V, Nemitz N, Kazda M, Weyers S, Peik E (2014) Cs-based optical frequency measurement using cross-linked optical and microwave oscillators. Phys Rev A 89(2):023820. https://doi.org/10.1103/PhysRevA.89.023820. arXiv:1310.8190 [physics.atom-ph]

Tarallo MG, Mazzoni T, Poli N, Sutyrin DV, Zhang X, Tino GM (2014) Test of Einstein equivalence principle for 0-spin and half-integer-spin atoms: search for spin-gravity coupling effects. Phys Rev Lett 113:023005. https://doi.org/10.1103/PhysRevLett.113.023005

Taveras V, Yunes N (2008) The Barbero-Immirzi parameter as a scalar field: $K$-inflation from loop quantum gravity? Phys Rev D 78:064070. https://doi.org/10.1103/PhysRevD.78.064070. arXiv:0807.2652 [gr-qc]

Taylor TR, Veneziano G (1988) Dilaton couplings at large distance. Phys Lett B 213:450-454. https://doi.org/10.1016/0370-2693(88)91290-7

Tegmark M, Rees MJ (1998) Why is the level fluctuation level $10^{-5}$? Astrophys J 499:526 arxiv:astro-ph/9709058
Tegmark M, Aguirre A, Rees MJ, Wilczek F (2006) Dimensionless constants, cosmology and other dark matters. Phys Rev D 73:023505. https://doi.org/10.1103/PhysRevD.73.023505. arxiv:astro-ph/0511774

Teller E (1948) On the change of physical constants. Phys Rev 73:801. https://doi.org/10.1103/PhysRev.73.801

Terno DR, Vedovato F, Schiavon M, Smith A, Magnani P, Vallone G, Villoresi P (2023) Proposal for an optical interferometric measurement of the gravitational redshift with satellite systems. Phys Rev D 108(8):084063. https://doi.org/10.1103/PhysRevD.108.084063. arXiv:1811.04835 [gr-qc]

Thielking J, Okhapkin MV, Głowacki P, Meier DM, von der Wense L, Seiferle B, Düllmann CE, Thirolf PG, Peik E (2018) Laser spectroscopic characterization of the nuclear-clock isomer$^{229}$Th. Nature 556(7701):321–325. https://doi.org/10.1038/s41586-018-0011-8. arXiv:1709.05325 [nucl-ex]

Thirolf PG, Seiferle B, von der Wense L (2019a) Improving our knowledge on the 229m thorium isomer: toward a test bench for time variations of fundamental constants. Ann Phys 531(5):1800381. https://doi.org/10.1002/andp.201800381

Thirolf PG, Seiferle B, von der Wense L (2019b) The 229-thorium isomer: doorway to the road from the atomic clock to the nuclear clock. J Phys B 52(20):203001. https://doi.org/10.1088/1361-6455/ab29b8

Thompson RI (1975) The determination of the electron-to-proton inertial mass via molecular transitions. Astrophys Lett 16:3

Thompson RI (2009) Observational determinations of the proton to electron mass ratio in the early universe. Mem Soc Astron Ital 80:870

Thompson RI (2017a) Fundamental constant observational bounds on the variability of the QCD scale. Mon Not R Astron Soc 467(4):4558–4564. https://doi.org/10.1093/mnras/stx433. arXiv:1702.06132 [astro-ph.CO]

Thompson RI (2017b) Fundamental constants as monitors of the universe. In: 14th Marcel Grossmann meeting on recent developments in theoretical and experimental general relativity, astrophysics, and relativistic field theories, vol 4, pp 3657–3663. https://doi.org/10.1142/9789813226609_0476. arXiv:1602.03192 [astro-ph.CO]

Thompson RI, Bechtold J, Black JH, Eisenstein D, Fan X, Kennicutt RC, Martins C, Prochaska JX, Shirley YL (2009) An observational determination of the proton to electron mass ratio in the early universe. Astrophys J 703:1648. https://doi.org/10.1088/0004-637X/703/2/1648. arXiv:0907.4392 [astro-ph.CO]

Thomson DR, LeMere M, Tang YC (1977) Systematic investigation of scattering problems with the resonating-group method. Nucl Phys A 286:53–66. https://doi.org/10.1016/0375-9474(77)90007-0

Thorsett SE (1996) The gravitational constant, the Chandrasekhar limit, and neutron star masses. Phys Rev Lett 77:1432–1435. https://doi.org/10.1103/PhysRevLett.77.1432

Tiedau J, Okhapkin MV, Zhang K, Thielking J, Zitzer G, Peik E, Schaden F, Pronebner T, Morawetz I, De Col LT, Schneider F, Leitner A, Pressler M, Kazakov GA, Beeks K, Sikorsky T, Schumm T (2024) Laser excitation of the Th-229 nucleus. Phys Rev Lett 132:182501. https://doi.org/10.1103/PhysRevLett.132.182501

Tiesinga E, Mohr PJ, Newell DB, Taylor BN (2021) CODATA recommended values of the fundamental physical constants: 2018. Rev Mod Phys 93(2):025010. https://doi.org/10.1103/RevModPhys.93.025010

Tilanus RPJ et al (2014) Future mmVLBI research with ALMA: a European vision. arXiv e-prints arXiv:1406.4650 [astro-ph.IM]

Tobar ME, Wolf P, Bize S, Santarelli G, Flambaum V (2010) Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser. Phys Rev D 81:022003. https://doi.org/10.1103/PhysRevD.81.022003. arXiv:0912.2803 [gr-qc]

Tobar ME et al (2013) Testing local position and fundamental constant invariance due to periodic gravitational and boost using long-term comparison of the SYRTE atomic fountains and H-masers. Phys Rev D 87(12):122004. https://doi.org/10.1103/PhysRevD.87.122004. arXiv:1306.1571 [gr-qc]

Toda Y, Giarè W, Özülker E, Di Valentino E, Vagnozzi S (2024) Combining pre- and post-recombination new physics to address cosmological tensions: case study with varying electron mass and sign-switching cosmological constant. Phys Dark Univ 46:101676. https://doi.org/10.1016/j.dark.2024.101676. arXiv:2407.01173 [astro-ph.CO]
Tohfa HM, Crump J, Baker E, Hart L, Grin D, Brosius M, Chluba J (2024) Cosmic microwave background search for fine-structure constant evolution. Phys Rev D 109(10):103529. https://doi.org/10.1103/PhysRevD.109.103529. arXiv:2307.06768 [astro-ph.CO]

Touboul P et al (2017) MICROSCOPE mission: first results of a space test of the equivalence principle. Phys Rev Lett 119(23):231101. https://doi.org/10.1103/PhysRevLett.119.231101. arXiv:1712.01176 [astro-ph.IM]

Touboul P et al (2019) Space test of the equivalence principle: first results of the MICROSCOPE mission. Class Quant Grav 36(22):225006. https://doi.org/10.1088/1361-6382/ab4707. arXiv:1909.10598 [gr-qc]

Touboul P et al (2022) MICROSCOPE mission: final results of the test of the equivalence principle. Phys Rev Lett 129(12):121102. https://doi.org/10.1103/PhysRevLett.129.121102. arXiv:2209.15487 [gr-qc]

Trachenko K (2023) Viscosity and diffusion in life processes and tuning of fundamental constants. Rept Prog Phys 86(11):112601. https://doi.org/10.1088/1361-6633/acfd3e. arXiv:2307.05273 [physics.bio-ph]

Truppe S, Hendricks RJ, Tokunaga SK, Lewandowski HJ, Kozlov MG, Henkel C, Hinds EA, Tarbutt MR (2013) A search for varying fundamental constants using Hz-level frequency measurements of cold CH molecules. Nature Commun 4:2600. https://doi.org/10.1038/ncomms3600. arXiv:1308.1496 [physics.atom-ph]

Tsai YD, Eby J, Safronova MS (2023) Direct detection of ultralight dark matter bound to the Sun with space quantum sensors. Nature Astron 7(1):113–121. https://doi.org/10.1038/s41550-022-01833-6. arXiv:2112.07674 [hep-ph]

Tsanavaris P, Murphy MT, Webb JK, Flambaum VV, Curran SJ (2007) Probing variations in fundamental constants with radio and optical quasar absorption-line observations. Mon Not R Astron Soc 374:634–646. https://doi.org/10.1111/j.1365-2966.2006.11178.x. arXiv:astro-ph/0610326

Turyshev SG (2008) Experimental tests of general relativity. Annu Rev Nucl Part Sci 58:207–248. https://doi.org/10.1146/annurev.nucl.58.020807.111839. arXiv:0806.1731 [gr-qc]

Tutusaus I, Lamine B, Blanchard A, Dupays A, Roussel Y, Zolnierowski Y (2016) Dark sectors of the universe: a Euclid survey approach. Phys Rev D 94(12):123515. https://doi.org/10.1103/PhysRevD.94.123515. arXiv:1607.08016 [astro-ph.CO]

Tzalenchuk A, Spethmann N, Prior T, Hendricks JH, Pan Y, Bubanja V, Temporão GP, Yu DH, Ilić D, Goldstein BL (2022) The expanding role of national metrology institutes in the quantum era. Nature Phys 18(7):724–727. https://doi.org/10.1038/s41567-022-01659-z

Tzanavaris P, Webb JK, Murphy MT, Flambaum VV, Curran SJ (2005) Limits on variations in fundamental constants from 21-cm and ultraviolet quasar absorption lines. Phys Rev Lett 95:041301. https://doi.org/10.1103/PhysRevLett.95.041301. arXiv:astro-ph/0412649

Ubachs W (2018) Search for varying constants of nature from astronomical observation of molecules. Space Sci Rev 214(1):3. https://doi.org/10.1007/s11214-017-0432-y. arXiv:1709.07704 [astro-ph.CO]

Ubachs W, Bagdonaitė J, Salumbides EJ, Murphy MT, Kaper L (2016a) Search for a drifting proton-electron mass ratio from H₂. Rev Mod Phys 88:021003. https://doi.org/10.1103/RevModPhys.88.021003. arXiv:1511.04476 [astro-ph.GA]

Ubachs W, Koelemeij J, Eikema K, Salumbides EJ (2016b) Physics beyond the Standard Model from hydrogen spectroscopy. J Mol Spectrosc 320:1–12. https://doi.org/10.1016/j.jms.2015.12.003. arXiv:1511.00985 [physics.atom-ph]

Ubachs W, Salumbides EJ, Murphy MT, Abgrall H, Roueff E (2019) H₂/HD molecular data for analysis of quasar spectra in search of varying constants. Astron Astrophys 622:A127. https://doi.org/10.1051/0004-6361/201834782. arXiv:1812.03628 [astro-ph.CO]

Ubaldi L (2010) Effects of theta on the deuteron binding energy and the triple-alpha process. Phys Rev D 81:025011. https://doi.org/10.1103/PhysRevD.81.025011. arXiv:0811.1599 [hep-ph]

Unzicker A (2009) A look at the abandoned contributions to cosmology of Dirac, Sciama and Dicke. Ann Phys (Berlin) 18(1):57. https://doi.org/10.1002/andp.200810335. arXiv:0708.3518 [physics.gen-ph]

Upadhye A (2012) Dark energy fifth forces in torsion pendulum experiments. Phys Rev D 86(10):102003. https://doi.org/10.1103/PhysRevD.86.102003

Uzan JP (1999) Cosmological scaling solutions of nonminimally coupled scalar fields. Phys Rev D 59:123510. https://doi.org/10.1103/PhysRevD.59.123510. arXiv:gr-qc/9903004

Uzan JP (2003a) Tests of gravity on astrophysical scales and variation of the constants. Ann Henri Poincaré 4:S347–S369. https://doi.org/10.1007/s00023-003-0927-9
Uzan JP (2003b) The fundamental constants and their variation: observational and theoretical status. Rev Mod Phys 75:403-455. https://doi.org/10.1103/RevModPhys.75.403. arxiv:hep-ph/0205340

Uzan JP (2004) Variation of the constants of nature in the early and late universe. In: Martins C, Avelino PP, Costa MS, Mack K, Mota MF, Parry M (eds) Phi in the sky: the quest for cosmological scalar fields. AIP conference proceedings, vol 736. American Institute of Physics, Melville, pp 3-20. https://doi.org/10.1063/1.1835171arxiv:astro-ph/0409424

Uzan JP (2007) The acceleration of the universe and the physics behind it. Gen Relativ Gravit 39:307. https://doi.org/10.1007/s10714-006-0385-z. arxiv:astro-ph/0605313

Uzan JP (2009) Fundamental constants, general relativity and cosmology. Mem Soc Astron Ital 80:762

Uzan JP (2010a) Dark energy, gravitation and the Copernican principle. In: Ruiz-Lapuente P (ed) Dark energy: observational and theoretical approaches. Cambridge University Press, Cambridge, pp 3-47 arXiv:0912.5452 [gr-qc]

Uzan JP (2010b) Fundamental constants and tests of general relativity—theoretical and cosmological considerations. Space Sci Rev 148:249 arXiv:0907.3081 [gr-qc]

Uzan JP (2010c) Tests of general relativity on astrophysical scales. Gen Relativ Gravit 42:2219. https://doi.org/10.1007/s10714-010-1047-8. arXiv:0908.2243 [astro-ph.CO]

Uzan JP (2011) Varying constants, gravitation and cosmology. Living Rev Relativ 14:2. https://doi.org/10.12942/lrr-2011-2. arXiv:1009.5514 [astro-ph.CO]

Uzan JP (2015) The stability of fundamental constants. C R Phys 16:576-585. https://doi.org/10.1016/j.cphy.2015.03.007

Uzan JP (2021) The big-bang theory: construction, evolution and status. Prog Math Phys 76:1-72. https://doi.org/10.1007/978-3-030-67392-5_1. arXiv:1606.06112 [astro-ph.CO]

Uzan JP, Bernardeau F (2001) Lensing at cosmological scales: a test of higher dimensional gravity. Phys Rev D 64:083004. https://doi.org/10.1103/PhysRevD.64.083004. arXiv:hep-ph/0012011

Uzan JP, Leclercq B (2008) The natural laws of the universe: understanding fundamental constants. Springer-Praxis Books in popular astronomy. Springer, New York

Uzan JP, Leclercq B (2020) L'importance des constantes. Dunod, Paris

Uzan JP, Lehoucq R (2005) Les constantes fondamentales. Belin, Paris

Uzan JP, Pitrou C (2024) Hubble tension as a window on the gravitation of the dark matter sector: exploration of a family of models. Phys Rev D 109(10):103505. https://doi.org/10.1103/PhysRevD.109.103505. arXiv:2312.12408 [astro-ph.CO]

Uzan JP, Aghanim N, Mellier Y (2004) The distance duality relation from x-ray and SZ observations of clusters. Phys Rev D 70:083533. https://doi.org/10.1103/PhysRevD.70.083533. arXiv:astro-ph/0405620

Uzan JP, Bernardeau F, Mellier Y (2008a) Time drift of cosmological redshifts and its variance. Phys Rev D 77:021301(R). https://doi.org/10.1103/PhysRevD.77.021301. arXiv:0711.1950 [astro-ph]

Uzan JP, Clarkson C, Ellis G (2008b) Time drift of cosmological redshifts as a test of the Copernican principle. Phys Rev Lett 100:191303. https://doi.org/10.1103/PhysRevLett.100.191303. arXiv:0801.0068 [astro-ph]

Vaas R (2010) Multiverse scenarios in cosmology: classification, cause, challenge, controversy, and criticism. J Cosmol 4:664-673

Vacher L, Schöneberg N (2024) Incompatibility of fine-structure constant variations at recombination with local observations. Phys Rev D 109(10):103520. https://doi.org/10.1103/PhysRevD.109.103520. arXiv:2403.02256 [astro-ph.CO]

Vacher L, JaF D, Schöneberg N, Martins C, Vinzl S, Nesseris S, Cañas Herrera G, Martinelli M (2022) Constraints on extended Bekenstein models from cosmological, astrophysical, and local data. Phys Rev D 106(8):083522. https://doi.org/10.1103/PhysRevD.106.083522. arXiv:2207.03258 [astro-ph.CO]

Vacher L, Schöneberg N, Dias J, Martins C, Pimenta F (2023) Runaway dilaton models: improved constraints from the full cosmological evolution. Phys Rev D 107(10):104002. https://doi.org/10.1103/PhysRevD.107.104002. arXiv:2301.13500 [astro-ph.CO]

Van Tilburg K, Leefer N, Bougas L, Budker D (2015) Search for ultralight scalar dark matter with atomic spectroscopy. Phys Rev Lett 115(1):011802. https://doi.org/10.1103/PhysRevLett.115.011802. arXiv:1503.06886 [physics.atom-ph]

Varshalovich DA, Levshakov SA (1993) On a time dependence of physical constants. J Exp Theor Phys Lett 58:231

Varshalovich DA, Potekhin AY (1996) Have the masses of molecules changed during the lifetime of the Universe? Astron Lett 22:1
Vayonakis CE (1988) Variation of low-energy parameters, primordial nucleosynthesis and a new weak force. Phys Lett B 213:419-421. https://doi.org/10.1016/0370-2693(88)91284-1

van Veldhoven J, Kupper J, Bethlem H, Sartakov B, van Roij A, Meijer G (2004) Decelerated molecular beams for high-resolution spectroscopy: the hyperfine structure of $^{15}$ND$_3$. Eur Phys J D 31:337-349. https://doi.org/10.1140/epjd/e2004-00160-9

Veneziano G (1986) A stringy nature needs just two constants. Europhys Lett 2:199. https://doi.org/10.1209/0295-5075/2/3/006

Veneziano G (2002) Large-$N$ bounds on, and compositeness limit of, gauge and gravitational interactions. J High Energy Phys 2002(06):051. https://doi.org/10.1088/1126-6708/2002/06/051. arxiv:hep-th/0110129

Verbiest J, Bailes M, van Straten W, Hobbs GB, Edwards RT, Manchester RN, Bhat N, Sarkissian JM, Jacoby BA, Kulkarni SR (2008) Precision timing of PSR J0437-4715: an accurate pulsar distance, a high pulsar mass and a limit on the variation of Newton's gravitational constant. Astrophys J 679:675-680. https://doi.org/10.1086/529576. arXiv:0801.2589 [astro-ph]

Vernet J et al (2011) X-shooter, the new wide band intermediate resolution spectrograph at the ESO very large telescope. Astron Astrophys 536:A105. https://doi.org/10.1051/0004-6361/201117752. arXiv:1110.1944 [astro-ph.IM]

Vessot R, Levine MW (1979) A test of the equivalence principle using a space-borne clock. Gen Relativ Gravit 10:181-204. https://doi.org/10.1007/BF00759854

Viatkina AV, Kozlov MG (2014) Sensitivity of tunneling-rotational transitions in ethylene glycol to variation of electron-to-proton mass ratio. J Molec Spectrosc 300:94. https://doi.org/10.1016/j.jms.2014.03.002. arXiv:1401.6561 [physics.atom-ph]

Vielzeuf PE, Martins C (2014) Varying constants and dark energy with the E-ELT. Mem Soc Ast It 85(1):155-160 arXiv:1309.7771 [astro-ph.CO]

Vijaykumar A, Kapadia SJ, Ajith P (2021) Constraints on the time variation of the gravitational constant using gravitational-wave observations of binary neutron stars. Phys Rev Lett 126(14):141104. https://doi.org/10.1103/PhysRevLett.126.141104. arXiv:2003.12832 [gr-qc]

Vikram V, Sakstein J, Davis C, Neil A (2018) Astrophysical tests of modified gravity: stellar and gaseous rotation curves in dwarf galaxies. Phys Rev D 97:104055. https://doi.org/10.1103/PhysRevD.97.104055

Vila SC (1976) Changing gravitational constant and white dwarfs. Astrophys J 206:213. https://doi.org/10.1086/154373

Vilenkin A (1995) Predictions from quantum cosmology. Phys Rev Lett 74:846-849. https://doi.org/10.1103/PhysRevLett.74.846. arXiv:gr-qc/9406010

Vilenkin A, Shellard P (1994) Cosmic strings and other topological defects. Cambridge University Press

Volovik GE (2002) Fundamental constants in effective theory. J Exp Theor Phys Lett 76:77. https://doi.org/10.1134/1.1510061. arXiv:physics/0203075

Volovik GE (2009) *ħ* as parameter of Minkowski metric in effective theory. J Exp Theor Phys Lett 90:697-704. https://doi.org/10.1134/S0021364009230027. arXiv:0904.1965 [gr-qc]

van de Bruck C, Mifsud J, Nunes NJ (2015) The variation of the fine-structure constant from disformal couplings. JCAP 12:018. https://doi.org/10.1088/1475-7516/2015/12/018. arXiv:1510.00200 [astro-ph.CO]

van Weerdenburg F, Murphy MT, Malec AL, Kaper L, Ubachs W (2011) First constraint on cosmological variation of the proton-to-electron mass ratio from two independent telescopes. Phys Rev Lett 106:180802. https://doi.org/10.1103/PhysRevLett.106.180802. arXiv:1104.2969 [astro-ph.CO]

von der Wense L et al (2016) Direct detection of the 229Th nuclear clock transition. Nature 533:47-51. https://doi.org/10.1038/nature17669. arXiv:1710.11398 [nucl-ex]

Wagner TA, Schlamminger S, Gundlach JH, Adelberger EG (2012a) Torsion-balance tests of the weak equivalence principle. Class Quant Grav 29:184002. https://doi.org/10.1088/0264-9381/29/18/184002. arXiv:1207.2442 [gr-qc]

Wagner TA, Schlamminger S, Gundlach JH, Adelberger EG (2012b) Torsion-balance tests of the weak equivalence principle. Class Quant Grav 29:184002. https://doi.org/10.1088/0264-9381/29/18/184002. arXiv:1207.2442 [gr-qc]

Wang K, Chen L (2022) Consistency test of the fine-structure constant from the whole ionization history. JCAP 10:070. https://doi.org/10.1088/1475-7516/2022/10/070. arXiv:2207.06719 [astro-ph.CO]
Wcisło P et al (2018) New bounds on dark matter coupling from a global network of optical atomic clocks. Sci Adv 4(12):eaaau4869. https://doi.org/10.1126/sciadv.eaau4869. arXiv:1806.04762 [physics.atom-ph]

Webb JK, Flambaum VV, Churchill CW, Drinkwater MJ, Barrow JD (1999) Search for time variation of the fine structure constant. Phys Rev Lett 82:884–887. https://doi.org/10.1103/PhysRevLett.82.884. arXiv:astro-ph/9803165

Webb JK, Murphy MT, Flambaum VV, Dzuba VA, Barrow JD, Churchill CW, Prochaska JX, Wolfe AM (2001) Further evidence for cosmological evolution of the fine structure constant. Phys Rev Lett 87:091301. https://doi.org/10.1103/PhysRevLett.87.091301. arXiv:astro-ph/0012539

Webb JK, King JA, Murphy MT, Flambaum VV, Carswell RF, Bainbridge MB (2011) Indications of a spatial variation of the fine structure constant. Phys Rev Lett 107:191101. https://doi.org/10.1103/PhysRevLett.107.191101. arXiv:1008.3907 [astro-ph.CO]

Webb JK, Lee CC, Milaković D, Flambaum VV, Dzuba VA, Magueijo J (2025) The mystery of alpha and the isotopes. Mon Not R Astron Soc 539(1):L1–L6. https://doi.org/10.1093/mnrasl/slaf012. arXiv:2401.00888 [astro-ph.CO]

Wei JN, Chen RJ, Wei JJ, López-Corredoira M, Wu XF (2024) Measuring the time variation of the fine-structure constant with quasars detected by LAMOST. Res Astron Astrophys 24(12):125021. https://doi.org/10.1088/1674-4527/ad9654. arXiv:2409.01554 [astro-ph.CO]

Weinberg S (1983a) Charges from extra dimensions. Phys Lett B 125:265–269. https://doi.org/10.1016/0370-2693(83)91281-9

Weinberg S (1983b) Overview of theoretical prospects for understanding the values of fundamental constants. Philos Trans R Soc London Ser A 310:249. https://doi.org/10.1098/rsta.1983.0086

Weinberg S (1987) Anthropic bound on the cosmological constant. Phys Rev Lett 59:2607–2610. https://doi.org/10.1103/PhysRevLett.59.2607

Weinberg S (1989) The cosmological constant problem. Rev Mod Phys 61:1–23. https://doi.org/10.1103/RevModPhys.61.1

Weiss A, Walter F, Downes D, Carrili CL, Henkel C, Menten KM, Cox P (2012) On the variations of fundamental constants and AGN feedback in the QSO host galaxy RXJ0911.4+0551 at z = 2.79. Astrophys J 753:102. https://doi.org/10.1088/0004-637X/753/2/102. arXiv:1204.5614 [astro-ph.CO]

Welsh L, Cooke R, Fumagalli M, Pettini M (2020) A bound on the 12C/13C ratio in near-pristine gas with ESPRESSO. Mon Not R Astron Soc 494(1):1411–1423. https://doi.org/10.1093/mnras/staa807

Weltman A et al (2020) Fundamental physics with the square kilometre array. Publ Astron Soc Austral 37:e002. https://doi.org/10.1017/pasa.2019.42. arXiv:1810.02680 [astro-ph.CO]

Wendt M, Molaro P (2011) Robust limit on a varying proton-to-electron mass ratio from a single H2 system. Astron Astrophys 526:A96. https://doi.org/10.1051/0004-6361/201014835. arXiv:1009.3133 [astro-ph.CO]

Wendt M, Molaro P (2012) QSO 0347-383 and the invariance of m_p/m_e in the course of cosmic time. Astron Astrophys 541:A69. https://doi.org/10.1051/0004-6361/201218862. arXiv:1203.3193 [astro-ph.CO]

Wendt M, Reimers D (2008) Variability of the proton-to-electron mass ratio on cosmological scales. Eur Phys J Special Topics 163:197–206. https://doi.org/10.1140/epjst/e2008-00820-x. arXiv:0802.1160 [astro-ph]

Wetterich C (2003a) Crossover quintessence and cosmological history of fundamental ‘constants’. Phys Lett B 561:10 arXiv:hep-ph/0301261

Wetterich C (2003b) Probing quintessence with time variation of couplings. JCAP 2003(10):002. https://doi.org/10.1088/1475-7516/2003/10/002. arXiv:hep-ph/0203266

Wetterich C (2007) Growing neutrinos and cosmological selection. Phys Lett B 655:201–208. https://doi.org/10.1016/j.physletb.2007.08.060. arXiv:0706.4427 [hep-ph]

Whitmore JB, Murphy MT (2015) Impact of instrumental systematic errors on fine-structure constant measurements with quasar spectra. Mon Not R Astron Soc 447(1):446–462. https://doi.org/10.1093/mnras/stu2420. arXiv:1409.4467 [astro-ph.IM]

Whitmore JB, Murphy MT, Griest K (2010) Wavelength calibration of the VLT-UVES spectrograph. Astrophys J 732:89–99. https://doi.org/10.1088/0004-637X/723/1/89. arXiv:1004.3325 [astro-ph.IM]

Wicht A, Hensley JM, Sarajlic E, Chu S (2002) A Preliminary measurement of the fine structure constant based on atom interferometry. Phys Scr 2002(T102):82. https://doi.org/10.1238/Physica.Topical.102a00082
Wignall J (2000) How many fundamental constants does quantum physics need? Int J Mod Phys A 15:875

Wiklind T, Combes F (1997) Molecular absorption lines at high redshift: PKS 1413+135 ($z = 0.247$). Astron Astrophys 328:48 arXiv:astro-ph/9708051

Wilcox H, Nichol RC, Zhao GB, Bacon D, Koyama K, Romer AK (2016) Simulation tests of galaxy cluster constraints on chameleon gravity. Mon Not R Astron Soc 462(1):715–725. https://doi.org/10.1093/mnras/stw1617

Wilczek F (2005) Enlightenment, knowledge, ignorance, temptation. arXiv e-prints arXiv:hep-ph/0512187

Wilczek F (2007) Fundamental constants. arXiv e-prints arXiv:0708.4361 [hep-ph]

Wilczynska MR et al (2020) Four direct measurements of the fine-structure constant 13 billion years ago. Sci Adv 6(17):eaay9672. https://doi.org/10.1126/sciadv.aay9672. arXiv:2003.07627 [astro-ph.CO]

Wilkinson DH (1958) Do the 'constants of nature' change with time? Philos Mag 3:582. https://doi.org/10.1080/14786435808565799

Will CM (1993) Theory and experiment in gravitational physics, 2nd edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511564246

Will CM (2014) The confrontation between general relativity and experiment. Living Rev Relativ 17:4. https://doi.org/10.12942/lrr-2014-4. arXiv:1403.7377 [gr-qc]

Williams JG, Dicke RH, Bender PL, Alley CO, Carter WE, Currie DG, Eckhardt DH, Faller JE, Kaula WM, Mulholland JD, Plotkin HH, Poultney SK, Shelus PJ, Silverberg EC, Sinclair WS, Slade MA, Wilkinson DT (1976) New test of the equivalence principle from lunar laser ranging. Phys Rev Lett 36:551–554. https://doi.org/10.1103/PhysRevLett.36.551

Williams JG, Newhall XX, Dickey JO (1996) Relativity parameters determined from lunar laser ranging. Phys Rev D 53:6730–6739. https://doi.org/10.1103/PhysRevD.53.6730

Williams JG, Turyshev SG, Boggs DH (2004) Progress in lunar laser ranging tests of relativistic gravity. Phys Rev Lett 93:261101. https://doi.org/10.1103/PhysRevLett.93.261101. arXiv:gr-qc/0411113

Williams JG, Turyshev SG, Boggs D (2012) Lunar laser ranging tests of the equivalence principle. Class Quant Grav 29:184004. https://doi.org/10.1088/0264-9381/29/18/184004. arXiv:1203.2150 [gr-qc]

Witten E (1981) Search for a realistic Kaluza–Klein theory. Nucl Phys B 186:412. https://doi.org/10.1016/0550-3213(81)90021-3

Witten E (1984) Some properties of O(32) superstrings. Phys Lett B 149:351–356. https://doi.org/10.1016/0370-2693(84)90422-2

Wolf P, Bordé CJ, Clairon A, Duchayne L, Landragin A et al (2009) Quantum physics exploring gravity in the outer solar system: the SAGAS project. Exp Astron 23:651–687. https://doi.org/10.1007/s10686-008-9118-5. arXiv:0911.0304 [gr-qc]

Wolfe AM, Broderick JJ, Condon JJ, Johnston KJ (1976) 3C 286: a cosmological QSO? Astrophys J Lett 208:L47. https://doi.org/10.1086/182230

Wu F, Chen X (2010) Cosmic microwave background with Brans-Dicke gravity II: constraints with the WMAP and SDSS data. Phys Rev D 82:083003. https://doi.org/10.1103/PhysRevD.82.083003. arXiv:0903.0385 [astro-ph.CO]

Wu J, Li Q, Liu J, Xue C, Yang S, Shao C, Tu L, Hu Z, Luo J (2019) Progress in precise measurements of the gravitational constant. Ann Phys 531(5):1900013. https://doi.org/10.1002/andp.201900013

Wu YS, Wang Z (1986) Time variation of Newton's gravitational constant in superstring theories. Phys Rev Lett 57:1978. https://doi.org/10.1103/PhysRevLett.57.1978

Xu YY, Deng XB, Duan XC, Cao LS, Zhou MK, Shao CG, Hu ZK (2022) de-Broglie wavelength enhanced weak equivalence principle test for atoms in different hyperfine states. arXiv e-prints arXiv:2210.08533 [physics.atom-ph]

Yang J, Schramm DN, Steigmann G, Rood RT (1979) Time variation of Newton's gravitational constant in superstring theories. Astrophys J 227:697

Yeh TH, Olive KA, Fields BD (2021) The impact of new $d(p, \gamma)/3$ rates on Big Bang nucleosynthesis. JCAP 03:046. https://doi.org/10.1088/1475-7516/2021/03/046. arXiv:2011.13874 [astro-ph.CO]

Yeh TH, Shelton J, Olive KA, Fields BD (2022) Probing physics beyond the standard model: limits from BBN and the CMB independently and combined. JCAP 10:046. https://doi.org/10.1088/1475-7516/2022/10/046. arXiv:2207.13133 [astro-ph.CO]

Yong D, Grundahl F, Lambert DL, Nissen PE, Shetrone MD (2003) Mg isotopic ratios in giant stars of the globular cluster NGC 6752. Astron Astrophys 402:985–1001. https://doi.org/10.1051/0004-6361:20030296. arXiv:astro-ph/0303057
Yoo JJ, Scherrer RJ (2003) Big Bang nucleosynthesis and cosmic background constraints on the time variation of the Higgs vacuum expectation value. Phys Rev D 67:043517. https://doi.org/10.1103/PhysRevD.67.043517. arxiv:astro-ph/0211545

Yuan L, Wu J, Yang SJ (2023) Current status and prospects on high-precision quantum tests of the weak equivalence principle with cold atom interferometry. Symmetry 15(9):1769. https://doi.org/10.3390/sym15091769

Yunes N, Pretorius F, Spergel D (2010) Constraining the evolutionary history of Newton's constant with gravitational wave observations. Phys Rev D 81:064018. https://doi.org/10.1103/PhysRevD.81.064018. arXiv:0912.2724 [gr-qc]

Yunes N, Siemens X, Yagi K (2025) Gravitational-wave tests of general relativity with ground-based detectors and pulsar-timing arrays. Living Rev Relativ 28:3. https://doi.org/10.1007/s41114-024-00054-9. arXiv:2408.05240 [gr-qc]

Yurchenko SN, Tennyson J, Barber RJ, Thiel W (2013) Vibrational transition moments of CH₄ from first principles. J Molec Spectrosc 291:69. https://doi.org/10.1016/j.jms.2013.05.014. arXiv:1302.1720 [astro-ph.SR]

Zaheer MH, Matjelo NJ, Hume DB, Safronova MS, Leibrandt DR (2025) Quantum metrology algorithms for dark matter searches with clocks. Phys Rev A 111(1):012601. https://doi.org/10.1103/PhysRevA.111.012601. arXiv:2302.12956 [quant-ph]

Zelevinsky T, Kotochigova S, Ye J (2008) Precision test of mass ratio variations with lattice-confined ultracold molecules. Phys Rev Lett 100:043201. https://doi.org/10.1103/PhysRevLett.100.043201. arXiv:0708.1806 [physics.atom-ph]

Zhai ZX, Liu XM, Zhang ZS, Zhang TJ (2013) Estimations of cosmological parameters from the observational variation of the fine structure constant. Res Astron Astrophys 13(12):1423-1437. https://doi.org/10.1088/1674-4527/13/12/003. arXiv:1207.2926 [astro-ph.CO]

Zhang C et al (2024) Frequency ratio of the $^{229}$Th nuclear isomeric transition and the $^{87}$Sr atomic clock. Nature 633(8028):63-70. https://doi.org/10.1038/s41586-024-07839-6. arXiv:2406.18719 [physics.atom-ph]

Zhang J, Frieman JA (2023) Mirror dark sector solution of the Hubble tension with time-varying fine-structure constant. Phys Rev D 107(4):043529. https://doi.org/10.1103/PhysRevD.107.043529. arXiv:2211.03236 [astro-ph.CO]

Zhang X, Banerjee A, Leyser M, Perez G, Schiller S, Budker D, Antypas D (2023) Search for ultralight dark matter with spectroscopy of radio-frequency atomic transitions. Phys Rev Lett 130:251002. https://doi.org/10.1103/PhysRevLett.130.251002

Zhao W, Wright BS, Li B (2018) Constraining the time variation of Newton's constant G with gravitational-wave standard sirens and supernovae. JCAP 10:052. https://doi.org/10.1088/1475-7516/2018/10/052. arXiv:1804.03066 [astro-ph.CO]

Zhou L, He C, Yan ST, Chen X, Gao DF, Duan WT, Ji YH, Xu RD, Tang B, Zhou C, Barthwal S, Wang Q, Hou Z, Xiong ZY, Zhang YZ, Liu M, Ni WT, Wang J, Zhan MS (2021) Joint mass-and-energy test of the equivalence principle at the $10^{-10}$ level using atoms with specified mass and internal energy. Phys Rev A 104:022822. https://doi.org/10.1103/PhysRevA.104.022822

Zhu WW et al (2015) Testing theories of gravitation using 21-year timing of pulsar binary J1713+0747. Astrophys J 809(1):41. https://doi.org/10.1088/0004-637X/809/1/41. arXiv:1504.00662 [astro-ph.SR]

Zyla PA et al (2020) Review of particle physics. PTEP 2020(8):083C01. https://doi.org/10.1093/ptep/ptaa104

**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
# Authors and Affiliations

Jean-Philippe Uzan<fnref n="1" />,<fnref n="2" /> ID

<figure><img src="image_38.png" /></figure>

Jean-Philippe Uzan
uzan@iap.fr

<figure><img src="image_39.png" /></figure>

<footnote n="1">¹ Institut d'Astrophysique de Paris, UMR-7095 du CNRS, Université Pierre et Marie Curie, 98 bis bd Arago, 75014 Paris, France</footnote>

<footnote n="2">² Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan</footnote>